Software - MORE

Except for slot machines, blackjack is probably the casino game that. to 7; 88 ALWAYS split; 99 split 2-9 except STAND AGAINST DEALER 7.

Enjoy!

We noticed that in European BJ, the dealer does not pull a hole card.

If the dealer has an ace, he asks for insurance, but continues to deal to the players.

Is this an advantage or disadvantage over U.

On blackjack split 88 hand, not turning over a BJ and letting the players play, can give the players a better chance of tying the dealer if they do pull 21.

On the flip side, in the US, if you have 11, and the dealer has ace, but after checking does not have 21, doesn't blackjack split 88 give the player an advantage?

A natural blackjack beats any total of 21 that is composed of 3 or more cards.

So, where does the house get its extra 0.

For this reason, the basic strategy differs if a casino uses the no-peek rule.

Whereas basic strategy tells us to always split AA and 88 in an American game, we blackjack split 88 not split AA vs a dealer ace up, and we should not blackjack split 88 88 vs a dealer Ace or ten-valued card.

Also, in the European no-peek game, we should not double down on a total of 11 vs a dealer ace or ten-valued card.

Software - MORE

splitting. By using dealer probability caching methods and revising the method for recursively generating. 2.1 Blackjack and Splitting Rules. This section.... for 4-deck blackjack. The American Statistician, 29(2):84�88, 1975.

Enjoy!

I'd suggest that you might be better off betting less and playing a max-EV game.

If you're already at the table minimum.

If you're considering this it might be a sign that you're over-betting your bankroll.

I agree with Axiom, the EV difference is too much to give up.

And one BJ decision shouldn't be making you or breaking you in this spot.

I think it's a little bit more complicated than that.

IIRC there was something in Interblock blackjack strategy attack about this.

I don't remember, though, I will have to check when I get home.

I think that the idea was that if you lowered the variance on certain plays, you could increase your bet size and have the same ROR, and thus increase the SCORE.

In other words, the increased bet size would more than make up for the slight decrease blackjack split 88 EV.

Or something like that.

I'll have to check.

For the non-counter, I don't think that this applies.

ROR doesn't really make much sense any more.

You are going to lose all your money, since you are 3 blackjack 21 3 top a -EV game.

So, what's the goal?

Probably to make the money last as long as possible.

I'm pretty sure that the expected amount of time that your blackjack split 88 lasts is inversely proportional to the house edge, so the only source to increase this is to lower the house edge -- ie, play perfect basic strategy.

I think that you can get an improvement over the worst case by making risk-averse plays, but it still decreases the expected amount of time that your money will last.

For the non-counting BS player, the best bet is to surrender 88 vs 10 if S17.

Split 88 vs A, however.

My primary source blackjack split 88 Joshua Hornick Mensa Guide to Blackjack.

Hornick was a member of the famous infamous?

Fred Renzy--another authoritative source--recommends that in a H17 game, the best move is to surrender 88 vs both 10 and A.

I play in PA, where late surrender is allowed.

Whenever I get an 88 against a blackjack split 88 and surrender, I'll sometimes get odd looks or comments.

I've noticed that more and more people who play in PA are employing it now, but many of them tend to misuse it, surrendering on 14 vs 10 and the like.

Reinforces that old adage about a little bit of knowledge being a dangerous thing.

I think that you are misreading the info in that link.

Yeah, that's not right.

You should split 8,8 against 10.

I just went and double checked, to make sure I wasn't wrong.

The index for surrendering is 1, I think, Quote: AxiomOfChoice I think that you are misreading the info in that link.

Yep, you're absolutely right.

I stand corrected on Renzey's strategy.

Two card 16 and 88 are not the same.

I've never played in a H17 game where late surrender was allowed, so I'm unfamiliar with Renzey's subtle change in how to handle 16 and 88 vs 10 and A.

Sorry 'bout the confusion on my part.

When I'm not counting cards in a S17 game, then I prefer Hornick's strategy to surrender 88 vs 10, but to split 88 vs A.

Renzey would split 88 vs 10 in such a situation.

I blackjack split 88 surrender 15 vs 10 and 16 vs 9, 10 and A.

I'll sometimes employ Red 7 count and adjust my surrender startegy, depending on the count.

Quote: Pabo When I'm not counting cards in a S17 game, then I prefer Hornick's strategy to surrender 88 vs 10, but to split 88 vs A.

Are blackjack 24/7 sure that that's his strategy?

That just sounds wrong.

I am pretty sure that splitting 88 vs 10 is higher EV.

I would have to look it up to be 100% sure.

I almost never play in a game that offers surrender, so I don't remember most of the finer points.

Quote: AxiomOfChoice Are you sure that that's his strategy?

That just sounds wrong.

I am pretty sure that splitting 88 vs 10 is higher EV.

I would have to look it up to blackjack split 88 100% sure.

I almost never play in a game that offers surrender, so I don't remember most of the finer points.

Here's a quote from Hornick's book, page 52: "There is one more case where it makes sense to surrender.

That is when you hold a pair of 8s for the dreaded 16 and the dealer shows a 10.

If you can, you should surrender rather than splitting and hoping to get two big hands and then still having to get lucky to win.

I am fairly new to casino blackjack, but I have been reading the posts here for a while and have been.. 88 vs 10 is almost a coin toss on surrender, split or hit.

Enjoy!

For the poker hand, see.

For other uses, see.

Two aces and two eights in a standard deck of.

Rules vary across gambling establishments regarding resplitting, doubling, multiple card draws, and the payout for blackjack, and there are conditional strategic responses that depend upon the number of decks used, the blackjack split 88 of shuffling and dealer's cards.

However, regardless of the various situations, the common strategic wisdom in the blackjack community is to "Always split and eights" when dealt either pair as initial cards.

This is generally the first rule of any splitting strategy.

The object of blackjack is for a player to defeat the by obtaining a total as close to 21 as possible without accumulating a total that exceeds this number.

In blackjack, the standard rule is that if the player is dealt a pair of identically ranked initial cards, known as a pair, the player is allowed to them into separate hands and ask for a new second card for each while placing a full initial bet continue reading to the original wager with each.

After placing the wager for the split hands the dealer gives the player an additional agree, blackjack mulligan finisher remarkable for each split card.

The two hands created by blackjack split 88 are considered independently in competition against the dealer.

Splitting allows the gambler to turn a bad hand into one or two hands with a good possibility of winning.

It also allows the player to double the bet when the dealer.

Some rules even allow for resplitting until the player has as many as four hands or allow doubling the bet after a split so that each blackjack split 88 has a bet double the original.

The standard rules are that when a bet is doubled on a hand, the player is only allowed to draw one more card for that hand.

Aces A pair of aces gives the blackjack player a starting hand value of either here 2 or a 12 which is a problematic starting hand in either case.

Splitting aces gives a player two chances to hit 21.

Splitting aces is so favorable to the player that most gambling establishments have rules limiting the player's rights to do so.

In most casinos the player is only allowed to draw one card on each split ace.

As a general rule, a ten on a split ace or vice versa is not considered a and does not get any bonus.

Prohibiting resplitting and redoubling is also common.

Regardless of the payout for blackjack, the rules for resplitting, the rules for doubling, the rules for multiple card draws and the dealer's cards, one should always split aces.

Eights If a player is dealt a pair of eights, the total of 16 is considered a troublesome hand.

In fact, the value 16 is said to be the worst hand one can have in blackjack.

Since sixteen of the other fifty cards have a value of 10 and four have a value of 11, there is a strong chance of getting at least an 18 with either or both split cards.

A hand totaling 18 or 19 is much stronger than having a 16.

Splitting eights limits one's losses and improves one's hand.

Probabilistic research of expected value scenarios shows that by splitting eights one can convert a hand that presents an expected loss to two hands that may present an expected profit or a reduced loss, depending on what the https://pink-stuf.com/blackjack/blackjack-strategy-martingale.html is showing.

A split blackjack split 88 of eights is expected to win against dealer of 2 through 7 and to lose less against dealer upcards of 8 through ace.

Blackjack's "Four Horsemen", andusingdetermined that splitting eights was less costly than playing the pair of eights as a 16.

They were part of a 1950s group that discovered that strategy could reduce the to almost zero in blackjack.

Now a typical strategy involves the following sequence of playing decisions: one decides whether to surrender, whether to split, whether to double down, and whether to hit or stand.

One of the earliest proponents of the strategy of splitting eights iswho developed the strategy on an as part of an overall blackjack strategic theory published in Beat blackjack split 88 Dealer: A Winning Strategy for the Game of Twenty-One in blackjack split 88 />Thorp was the originator of the system for blackjack.

Retrieved 24 July 2009.

Retrieved 24 July 2009.

Retrieved 30 May 2009.

The Everything Blackjack Strategy Book: Surefire ways to beat the blackjack split 88 every time.

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Enjoy!

You have far and away the best gambling site on the 'net.

Being an myself ACASI love to see someone putting their math skills to good use.

My question � When late surrender is allowed, do you still want to split eights with a ten showing?

I'm guessing yes, but one of the hardest plays in BJ is splitting eights vs a ten.

As a side note, I just spent three days in Vegas, if you haven't done so already, you must try the Las Vegas Club and the World's Most Liberal blackjack Rules.

At six decks, I figured the house advantage to be 0.

Thanks for all of your hard work!!

Thanks for the kind words, Jim.

Yes, you still want to split eights, even if late surrender is offered.

Even if you can't double after a split you should still decline to surrender.

Based on a two-deck game, where you can not double after splitting, the expected value of splitting 8,s against a 10 is -0.

Contrary to their claim of having the "World's Most Liberal Blackjack Rules" there are better single-deck games right across the street at the Horseshoe or the Golden Gate.

It is the six decks at the Las Vegas Club which work against the player.

Don't feel badly about falling for their marquee, I fell for it myself in my younger days before I knew the effects of rule variations.

Update: After this question, the Las Vegas Club changed their rules to pay 6 to 5 on a blackjack in their so-called "World's Most Liberal Blackjack Rules.

You are much better blackjack split 88 at any ordinary 3-2 game, which are easy to find elsewhere.

With single-deck blackjack, are the cards dealt face-down?

And what are the general rules for single-deck?

I know you mentioned double downs only on 9-11 or 10-11, but do you know what the general rules are for double-after-split, dealer-hitting-soft-17, etc.

I'm a basic strategy player, and wanted to find out just what the rules tend to be for single-deck I've only ever done 6 or 8 deck so I can prepare the perfect spreadsheet from blackjackinfo.

Thanks so much for your help!

Single deck blackjack rules are usually tight.

Cards are dealt face down.

Doubling is usually restricted to 9 to 11, or 10 to 11.

The dealer will hit a soft 17 and double after a split will probably not be allowed.

Be sure to NOT play if blackjack pays less then 3 to 2, which is usually the case with single-deck games.

You can always see the relatively current blackjack rules in Vegas at my site.

In your blackjack strategy you surrender 16 against A,10,9.

You say to split a pair of 8's against those cards.

I have been told that a pair of 8's is a 16 and should be surrendered.

What do you think?

Whoever told you to surrender two 8's gave you incorrect advice, assuming American late.

To illustrate why you should split 8's against a 10, check my.

This shows expected return for any initial situation for any given click at this page />The table shows that splitting 8's against a 10 in double deck has an expected return of -0.

In other words, you can expect to lose 47.

This is less than the 50% you would 2 americanpoker by surrendering.

If not allowed to double after a split, then the rate of return is -0.

Splitting 8's against a 9 or ace has an even greater return.

If the dealer checks his hole card, and does not have blackjack, then why hit a soft 18 against an ace.

Also, why not double on an 11?

In blackjack there are seldom simple answers.

You have to consider everything that could happen and weigh every outcome by their probability.

The best play is the one with the greatest expected return.

According to mythe expected return in a double deck game of hitting a soft 18 against an ace is -0.

So hitting is just a hair better.

It is actually composition dependent in both single and double decks, in other words depending on which two cards that total 11 determines how to play the hand.

However if you don't wish to memorize thethen you should double on 11 against an ace in single and double deck and hit with four or more decks.

Hi there -- love your site!

If I have blackjack, and the dealer is showing an ace, I am given the option of taking even money or continuing the hand.

Should I take the even money or play on?

This is another way of looking at the decision to take insurance.

The expected return of taking even money is obviously 1.

Lets assume an infinite deck of cards for the sake of simplicity.

If the dealer gets a blackjack, then you push.

If not, then you win 1.

Thus declining insurance, or even money, and playing the hand is the better bet.

In an actual game with a finite number of decks the odds are even better since one 10 is already out of the deck in your hand which lowers the dealer's probability of having a blackjack.

How does this strategy play out?

This would be a bad play.

For example, my shows the return both ways by playing 10 and 6 cards against a dealer 7.

Hitting has an expected loss of 39.

However, standing has an expected loss of 47.

There is no easy explanation I can give why hitting is better.

You have to consider everything that can happen, weight it by its probability, and take the sum.

Overall hitting is better of two bad plays.

Regarding your exceptions to surrender inhow should I best adapt it to the Unified Gaming single-deck game with early surrender against the ace?

Thanks for any help and great site.

Thanks for the compliment.

You should use appendix six only if the dealer is showing a ten in a Unified Gaming blackjack game.

There are no exceptions to the when the dealer has an ace showing.

I just came back from Costa Rica.

They pay even money on a blackjack.

What is this worth to the house and should I double down on 21 versus say a dealer 3-6, since I am only going to get paid 1to1?

Hi, I just looked at your Microgaming blackjack basic strategy card.

I notice that on 7,7 you advise that the player not hit against a 10.

Why is this, and does this override the advice to hit on 14 against a 10?

This is the correct play in all my single-deck blackjack strategies.

With the low hope of beating a blackjack split 88 20, it is better to hit, or surrender if you can.

Yes, this does override my advice to hit 14 against a 10.

I have been a dealer now for 10 years, and trying to get out of it.

I can not count how many times I have heard people say, "Always assume there is a 10 in the hole".

You and I know this cannot be correct all the time.

I understand why they say it, but, what are the odds that it really is a ten, and when the dealer has an Ace up, and checks in the card reader for a blackjack, does not have one, you know definitely it is not a ten.

What should you assume it is then?

I don't like that expression either.

At best it is a memory device to help people remember to hit a stiff hand if the dealer has a 7 to 10 showing.

There is no simple rule of thumb that works in all situations.

I was studying your on the blackjack site, and came across something odd.

Basic strategy in a six-deck game blackjack game hosting double after split, dealer stays on soft 17 etc.

Yet, on the appendix, the player's expected return is HIGHER if you hit, rather than double compare.

The same is true for an A,4 v.

All of the other splits and doubles work out.

What's up with these two examples?

Appendix 1 is based on an infinite deck.

Both hands you mention are borderline plays and the number of decks affects which play is better.

For example, A-4 against a 4 favors doubling with 26 decks and hitting with 27 decks.

A-2 against a 5 also crosses over somewhere between 8 and an infinite number of decks.

As a BJ player I regularly split 10s vs.

This move has a positive expectation, but isn't as profitable as standing pat.

Could you please show this friend of mine how much worse splitting 10s is than standing pat, in a neutral deck?

Also, lots of BJ players get upset at someone who splits 10s vs.

Can you set the record straight on this?

I took great pains to create my blackjack appendices 9A-9H to answer these kinds of questions.

For example, in a six-deck game where the dealer stands on soft 17, you would use blackjack appendix 9G.

There you can see the expected return by standing on two 10's against a dealer 6 is 0.

The expected return by splitting in this situation is 0.

So, the player can expect to win an extra 8.

Don't pay much stock in what other players say or do at the blackjack table.

Wiz, this is a spliting 8's against a dealer's 10 question.

Splitting is the is the correct play on single hand basis.

However, I believe for the typical blackjack player it is better to stand when considering you are doubling the amount of the bet.

Why double your bet against such poor, way below average, odds?

After all, the goal is to maximize your overall return i.

Your site's great and advertising like banner ads and sidebars is understandable but invasive advertising like pop up windows and question prompts that try to force you to another site gets to be a bit much IMO.

Although this is a close play, standing is article source third worst option.

The expected returns for doubling and splitting are based on the total return for that hand relative to the initial bet.

Luckily I was only playing for fun on an Internet gaming site at the time.

Yes, you should keep splitting as long as you keep getting tens.

Playing one hand and losing does not disprove anything.

Millions of hands must be played both ways and the results tabulated to truly know the best play.

On a 4-deck blackjack game if you split aces against 5 or 6, and you get another ace.

You should double or hit?

Another question in 4 deck BJ for 10,2 against 4, one site listed a hit.

I would like a confirmation from you.

However if you can you should double on the 6 only.

This is true whether or not the dealer hits a soft 17.

If the dealer stands on a soft 17 the expected returns against a 5 are.

Against a 6 the expected returns are.

So doubling is the better play.

You can see these numbers for yourself in my.

About your other question, yes in a 4-deck game the player should hit a 10,2 against a 4, but only if the dealer stands on a soft 17.

Following this exception will help you win more unit every 113396 hands, or lower the house edge by 0.

Not worth the bother of memorizing the exception in my opinion.

This is an interesting situation.

Following is the expected return by hitting each way to compose a 15.

In other words the odds just barely favor surrendering a 10,5 and 9,6 but the odds click here hitting 8,7 by a much wider margin.

My question is about table maximum bets in BJ.

Can I double down, or have I already reached the limit?

Can Source split them, turning one hand into two hands?

Yes, you could double or split in those situations.

The maximum applies to the initial bet.

I checked your web site and I could only find appendixes for multiple card hands in 1 and 2 deck games.

Is this article correct?

The fewer the decks and the greater the number of cards the more this is true.

To test the most likely case to favor hitting, 8 decks and only 3 cards, I ran every possible situation through my combinatorial program.

The following table displays the results.

So standing is the marginally better play.

Following this rule clearly blackjack party ideas think result in an extra unit once every 1117910 hands.

It would take about 5 years playing blackjack 40 hours a week before this piece of advice saved the player one unit.

I like to use your to fine tune my play in online single deck blackjack.

I see you have updated this page in December, and it seems like there are a few new moves in the 2-card section.

Is the key that the dealer can have an A in the hole with the 6?

Are these new strategies, and if so, what brought them about?

Yes, I made a couple changes to the two-card list.

I removed 9+3 Vs 3 and added 10+2 Vs 6.

In a single deck game where the dealer stands on soft 17 and the player has 10+2 against a dealer 6 the expected value of hitting is -0.

So you lose less on average by hitting.

I hate to give sound bite answers to the basic strategy because there are numerous ways the cards can play out.

However as you said the dealer is also more likely to get a 17 with a 6 showing than a 5.

A 17 is not a good hand and motivates the player to hit and try to beat it.

If you have 15 and the dealer shows an eight.

In this case, whether you hit or stay your chance of losing is over 70%.

The expected value of hitting would be 0.

This is greater than the expected value of -0.

I just wanted to make sure that the correct play in the Microgaming single deck game of A,A vs A is to split as shown on your card.

Any chance you have the EV of hitting vs splitting on this hand?

Based on one deck the expected value of each hand considering the possibility of a dealer blackjack is -0.

So splitting is better by about 31% of a unit.

Splitting casino table layouts also better for the 4-deck game, which no Microgaming player should be playing since a 1-deck game with the same rules is available.

After performing my own infinite deck analysis for Blackjack with the same rules as yours dealer stands all 17s, re-splitting allowed to 4 hands except Aces, which can only be split once, doubling after splitting, draw only one card to split AcesI came across your site.

In comparing expected values, I obtained the same numbers as you in all cases, except for pair splitting, which were slightly different.

It took me years to get the splitting pairs correct myself.

Cindy of was very helpful.

Resplitting up to four hands is allowed.

Here is how I did it.

For each rank determine the probability of that rank, given that the probability of another 8 is zero.

Take the dot product of the probability and expected value over each rank.

The hardest part of all this is step 3.

I have a very ugly subroutine full of long formulas I determine using probability trees.

It gets especially ugly when the dealer has a 10 or ace up.

I have a question about the two blackjack strategies your.

First off, the underlying assumption before this question is that hitting on a soft 17 is an advantage to the dealer.

Why does the strategy have the player double down more often in situations where the dealer might hit a soft 17,i.

If hitting a soft 17 gives the house more of an advantage, why would one want to put more money on the table at those times?

Is it possible that the two charts are switched?

However this is a generality and not true of every situation.

When you have a strong hand of 18 to 21 you want the dealer to stand on a soft 17.

However if you have a weak hand under 17 you want the dealer to hit a soft 17.

An example of a strategy difference is you should double soft 19 against a 6 when the dealer hits a soft 17, and stand if the dealer stands on soft 17.

The reason is that there is a good chance of having drawing a bad card on the double, resulting in 16 or less points.

When the dealer hits a soft 17 he busts more often, making doubling a little safer in this example.

Now your site is teaching me Blackjack.

Thank you for the compliment.

To answer your question the dealer will just ask you what you want to do.

Normally all decisions in blackjack must be visible, however click the following article is the only exception I can think of.

However if you want to avoid being asked when it is your turn simply hold up you index finger to denote that you want one card.

Most dealers know what this means.

Coincidentally I just learned yesterday that in Bulgaria if you wish to double you put your extra bet behind the original bet, and if you want to split you put it next to the original bet.

Another reader wrote in to state that in North Dakota it is the state to follow the Bulgarian rule for doubling and splitting.

My question is, why stand?

You were willing to take another card anyway.

Thanks for your time!

If the player had the option to double his bet and stand that would be better than a conventional double.

The basic strategy chart for blackjack states to hit on a 16 if the dealer has an ace showing.

I was wondering if the chart takes into account the fact that once it is known insurance is not paying then the dealer does not have a 10 value card down?

Yes, the basic strategy assumes the dealer does not have a ten in the hole.

When the dealer has an ace, assuming no blackjack, the probability of making 17 or more is 83.

So standing is not even a very borderline play, the odds definitely favor hitting.

If the dealer does not check for blackjack with a ten showing, instead taking only the original wager at the end of the hand, does that necessitate any strategy changes?

As long as you stand to lose only the original wager you should play assuming the dealer does not have a blackjack.

If the dealer does have blackjack there is nothing you can do about it anyway.

You make a good mathematical argument that the player should refuse insurance.

Most people would feel like a fool giving up a bird in the hand to lose a shot at 1.

Gambling is about taking risks.

The successful gambler does not try to maximize his probability of a net win each hand but takes risks to maximize his overall return.

Both in gambling and in life one must sometimes take short term risks for long term gain.

So think less about the present and more about the future.

The player should be more aggressive hitting in Blackjack Switch because a dealer 22 results in a push.

Much of the value in standing in regular blackjack is realized when the dealer busts.

In Blackjack Switch many of those wins are turned into a push, making hitting a better play in comparison.

What are the hands that are closest to 50-50 so that my wife can limit her hunch plays to those?

Here are some borderline plays, as evidenced by having a card counting index equal to zero.

This list is for multiple decks where the dealer stands on soft 17 and double after a split is allowed.

The best play is listed first and an alternative second.

No, you never touch your chips once the bet has been made until the hand is over.

The signal to surrender is click to see more use your index finger and pretend to draw a line along the blackjack table, just behind your bet from left to right.

It is just as good to simply say "surrender.

This works strongly to the dealers favor and should be a disincentive to put more money on the table by doubling or splitting.

What would the expected loss be for that play?

This would be a terrible play.

For example if you doubled on a blackjack against a 5 six decks dealer stands on soft 17 your expected gain would be 0.

So even in an even money game this would still be an error costing about 38% of the bet.

Wong states in on page 23 the following, "If you get to twelve by 10-2 or 2-10 where 10 means any 10-count cardand two or fewer decks are being used or seven or fewer if the dealer stands on soft seventeenyou should hit.

Wong is referring to a player 12 against a dealer 4 and is quotingpage 176, by Peter Griffin.

Yes, he is right.

In a seven deck game the expected value by hitting is -0.

However with eight decks hitting is -0.

This is such a borderline play that the number of decks does make a difference between seven and eight.

Here is an even better example.

With A-4 against a 4 you should double all the way through 26 decks but hit with 27 or more.

Are there any basic strategy exceptions for doubling and splitting on the Internet when cash back applies to the total amount bet thus giving the player an extra incentive to double or split.

Please assume article source cash back rate of 0.

I could not find any hand where an extra 0.

The closest case I could find, based on six decks and the dealer standing on soft 17, is Blackjack split 88 against a dealer 4.

In that hand doubling costs the player just under 0.

So if you can get 0.

Other borderline hands I examined cost the player at least 1% to double or split, and I have never seen cash back that high in blackjack.

In blackjack the strategy for 16 vs.

It is true that in general you should stand on 16 vs.

So if my chart was based on the casino offering the surrender option then you would be right.

However that assumption is not made.

If I changed the key to Rs surrender if allowed, otherwise stand then that would imply that the player should stand on a 2-card 16 against a 10 if surrender was not allowed.

In your blackjack appendix 9 you indicate that the player has a positive expectation hitting 10 against a 10?

This should give the dealer an advantage because the dealer will win if both bust.

I stated in the explanation to that appendix that I already assume the dealer does not have a blackjack.

That is why the player has a slight edge in that situation, after the dealer peeks and confirms he blackjack split 88 not have a blackjack.

The index number of 16 against a 10 in most blackjack counting systems is zero.

So if the deck were completely neutral you should stand, because you stand if the count is equal or exceeds the index number.

Yet the basic strategy tables tell us to hit.

This seems to be a contradiction.

In all honesty this is an old question but I got a better answer from Chris F.

A good example of this is that in single deck the correct play is to stand on 7,7 click at this page a 10, because half of the sevens in the deck are already gone, and that is what you need to beat a dealer 20 with 3 cards.

Either way two cards that would bust the player by hitting have been removed.

So the deck is slightly rich in small cards that will not bust the player, giving the player an incentive to hit.

While this is true I was skeptical because in an infinite deck game the odds still favor hitting.

However except in a few Internet casinos an infinite deck is just an abstraction.

Then I gave the dealer a 10 link myself a 10 and 6.

So the player was playing this hand against a neutral deck with 31 of each card A-9 and 124 tens.

Here is the blackjack directions values: Play Expected Value Stand -0.

It is the same if I remove the following: A,2,3,4,5,6,8,10,10,10 to simulate 9,7 vs 10, because the player is going against the exact same neutral shoe.

It just goes to show how powerful the effect of removal is, even when just three cards in an eight-deck game.

So as I just showed going into a neutral deck the odds favor standing.

The reason hitting is correct in an infinite deck is because there is no effect of removal.

If you accidentally hit a 16 vs 10 in a neutral shoe, and got a low card, then the just click for source would have a better chance of getting a 10 in the hole.

This fact is reflected in the higher expected value for standing in an 8-deck game, but would not matter in an infinite deck.

For the record, here are the expected values in an infinite deck game: Sometimes the dealer exposes his hole card in blackjack.

What is the correct basic strategy when that happens?

Stanford Wong gives such a basic strategy in his booksee table 46.

He also said that in 1995 the Bourbon Street casino in Vegas had a promotion in which every 50 minutes the dealer would expose both his cards for five hands.

The player advantage during those was about 10%, according to Wong.

That is a good question.

Personally I eyeball the borderline plays based on what has already been played, especially on the second hand to be played.

If forced I would say using the exceptions is better than the basic strategy only.

However the way the basic strategy exceptions were created was on the initial hand only, so they are not entirely accurate for splitting, because the deck composition will be a little different.

Your strategy cards for Blackjack I presume here basic strategy for the initial cards player's first two cards and dealer's up card.

However, after hitting or splitting the deck composition has changed and the basic strategy may have changed.

What I think would be more appropriate is a basic strategy based on the overall game of blackjack, including after splitting and hitting.

Is there any situation where your initial hand basic strategy and one for the overall game are different?

Yes, my basic strategy charts are designed to be the best play based on the first two cards.

This is the usual approach to developing the basic strategy.

One benefit to this approach is the expected values of each play can be calculated exactly and compared to other sources.

However, you bring up a valid point.

So I asked Don Schlesinger, author ofif there were any known play where the best play on the initial hand is different from the best play to maximize the expected value of the overall game of blackjack.

He replied that a soft 18 against a dealer ace, in a double-deck game, where the dealer stands on soft 17, was such a play.

As my shows the expected value for standing is -0.

So, based on the first two cards, the odds favor hitting by 0.

However, there are many more ways to see soft 18 than one ace and one seven.

The following table shows all the ways this hand can turn up.

Player cards Conditional Probability Hit EV Stand EV Hit Return Stand Return A7 0.

Hit EV:Expected value by hitting Stand EV:Expected value by standing Hit Return:Product of probability and hit expected value Stand Return:Product of probability and stand expected value The right two cells of the bottom row show that overall the expected value of hitting is -0.

So, the table shows the odds favor standing by 0.

To confirm these results I ran two simulations under the rules in question, one simulation hitting and one standing on this play.

I counted only hands where soft 18 against a dealer ace happened at any time during play.

Here are my results.

Soft 17 Hands Played Total Win Expected Value Stand 3857490 -396224 -0.

Thus, for practical purposes of playing all hands, the best play is to stand, contrary to what my basic strategy chart says.

I just stumbled onto your site, and I think it's a fabulous site for blackjack info.

I have a question, though.

Can you explain how is there a positive expectation when you follow basic strategy and have a total of ten against a dealer 10 or ace showing no dealer blackjack.

Your table shows a positive expectation for both these scenarios, but I can't understand how.

I would think under this scenario the player and dealer follow the same strategy, that is to hit until 17 or better or bust.

The soft 17 is eliminated for the player under this scenario so I can't understand where the positive expectation comes from.

Thanks for the kind words.

Let's assume six decks it doesn't matter whether the dealer hits or stands on soft 17.

My shows the expected value of 6+4 against an ace to be +0.

The blackjack split 88 the expected values are positive is my expected value tables assume the dealer already has peeked for a blackjack and has confirmed that he doesn't have one.

Meanwhile, the player can still draw an ace for a 21.

In other words the player can make 21 on his next card and the dealer can not by assumption.

If I had such a table under the European no-peek rule, then the expected values would indeed be negative.

On my recent visit in Vegas I saw two dealers independent from each others one at The Orleans, one at Circus-Circus suggest to double on 4-4 vs.

I was the BJ guy of our group and so my friends started to ask me about that.

All I could say was: no, splitting is the right decision.

Of course provided that double after split is allowed.

Can I find out the probabilities of these alternatives or can you tell me?

Splitting fours against a five or six is a frequent play where both players and dealers incorrectly rebuke splitting.

Sometimes you hear people say falsely that you should never split "anything that starts with F", in other words fours, fives, and faces.

That is true about fives and faces but the player should indeed split fours against a five or six if double after split is allowed.

Otherwise the player should hit, except in single deck he should double if allowed.

My shows in a six-deck game where the dealer hits a soft 17 the following expected values of 4,4 against a 6.

I was intrigued by the analysis from your about when to stand with 16 vs.

Being a math person myself I want to maximize the odds, but also understand the slim gain.

Thanks for all you do!

Thanks for the kind words.

If it is a face-up game, with other players, I scan the table and just use my best judgment.

However if the dealer accidentally flipped over both his cards, showing a total of 10 or 11, the player should hit against a 10 and stand against an 11.

So you can play your hand more aggressively.

In you have the effect of removing a 6 less than a 5 or 4.

Up Card Expected Value 2 9.

While sixes are bad for the dealer they are bad for the player as well.

All things considered, if you could remove one card from the shoe you should choose a five.

Is it available any where?

There are not many situations to surrender, but those situations happen often, so I think they are worth memorizing.

In a six-deck game surrender is worth 0.

My friend I were playing in LV.

We had a go here argument on what has statistically better odds, double down with player totaling 10 versus dealer showing 7, or double down with player totaling 11 versus dealer showing 10, in a two deck game.

I thought it was the prior.

My was created for just these kinds of questions.

Assuming 6 decks, my table shows the expected value of doubling 8+2 vs.

The expected value of doubling 8+3 vs.

So you are right, 10 vs.

According to standard BJ rules and perfect basic strategy, how many percent of my DOUBLED DOWN hands should I expect to win, push and lose?

Assuming liberal Vegas Strip rules six decks, dealer stands on blackjack split 88 17, double after split allowed, late surrender allowed, resplitting aces allowed the following are the probabilities of each possible outcome when doubling on the initial two cards.

This does not include doubling after splitting.

I think he should wait because he could get a two, three, four, five, etc.

What do you think?

Or is my friend just a whiner?

Thank you for your time.

Maybe you can take advantage of his complaining by offering to buy his hand for less than the fair 79 cents on the dollar.

I had a situation playing blackjack last weekend, where the dealer had a 6 on top but when he was tucking in the down card he accidentally showed that he had a 3 in the hole.

The player on my right had a 15, I had an 11, and the player on my left had a 12.

Knowing that the dealer had a total hand of 9, the player on my right hit his hand and busted with a 10.

I wound up doubling down and got a 2.

The player on the left hit his hand getting a 5, for a total of 17.

The dealer opened his hand of 9 and hit a ten for a total of 19.

The dealer told us even though you saw the 3 under that you should play your hand as if you did not know the down card.

I wanted to ask you what you would have done in the situation for all three players.

This is the first time that has ever happened since I have been playing blackjack.

My shows what to do in any situation where the dealer accidentally exposes his hole card.

Using that rule of thumb, all three players played correctly.

Contrary to what the dealer said, the player has every right to use any information gleaned from dealer errors like this.

Thanks for creating a great site, with such detailed information.

Are there any basic strategy exceptions that are worth making to maximize profit in a large 6+ decks shoe?

I assume you would hit more if you were one card away from a Charlie against an ace, since it is so unlikely for the dealer to bust, but I would love to see specific instructions.

For those readers who may not understand the question, a "Charlie" is a rule in which the player automatically wins if he hits to some number of cards, usually five to seven, without busting.

The following table, for three or more cards, shows the basic strategy if the player is one blackjack split 88 two cards away from such an automtic winner.

Can you please tell us the proper pair-splitting strategy when the "behind" wager far exceeds the regular wager, assuming the two bettors are working together?

I have studied and used your dealer exposes hole-card strategy for some time read article, and there is still one play that I can not find a go here explanation for: A2 vs.

What am I not seeing?

The reason is my blackjack basic strategy is based on 8 or see more decks, and the flashing dealer strategy is based on an infinite number of decks.

In an infinite-deck blackjack game you should hit A2 vs.

An infinite-deck assumption is the lazy way to analyze blackjack.

The reason I went that way is I believe that is not a frequently used page, and the cost in errors is very small, only one unit for every 202,000 units bet.

I think I noticed an error in your for blackjack.

It states that you should only play one hand if the person you are back-betting splits 10s vs.

But a hard 10 no double vs.

The reason is that my table assumes the front-player will keep resplitting, if he can.

That depresses the value of a single 10, because I assume the front-player will keep making the same mistake, if he can.

I just added that condition to that page.

Thank you for your detailed site.

In you state the expected value for the game and the expected value for each play.

When I try this calculation I get a different result.

For example, six decks, dealer hits on soft 17, and player may not double after split I get 0.

Those tables assume the dealer does not have a blackjack.

Making correct double and split decisions should be based on the conditional expected value, given the dealer does not have a blackjack.

Otherwise, the player would be overly timid about doubling or splitting against a ten or ace.

Adding up the dot product of probabilities and expected values will give an click here result, because there is no here represented for a dealer blackjack.

To get the house edge of the overall game you should subtract the expected loss when the dealer has a blackjack.

However, the player will only lose when he does not have a blackjack.

So, the probability of the player losing to a dealer blackjack is 0.

You should subtract this number from your dot product above: 0.

Thus, the house edge under the rules stated in the appendix is 0.

I follow your 4+ deck Blackjack basic strategy 100% of the time and I always get dirty looks whenever I hit my 12 against a dealer 2 and especially a 3.

I feel your pain.

You can imagine how bad it gets in Spanish 21, which calls for such plays as hitting 14 against a 3.

As long as it is just looks, I would let it slide.

If it gets to blackjack stringing instructions, I would say something like, "There are lots of other tables in here.

The more ridiculous a belief is, the more tenaciously it tends to be held.

There is usually no sound-bite explanation anyway to why one play is better than another.

To know why the correct play is what it is, one must either consider every possible way the remaining cards could fall, for both player and dealer, or play out the hand thousands of times, even millions for very borderline hands.

The decision with the highest expected value is the one you should take.

Only refusing insurance yields itself to being easily explained.

My question is what is this doing to the house edge?

The effect of each basic strategy change is the probability of the hand occurring and the cost of not making the correct play when it does.

My shows both the probability of each hand and the expected value of each play.

So hitting 8,8 against a dealer 9, 10 or ace increases the house edge by 0.

If the player surrenders instead of hitting, the effect drops to 0.

So, it is not a significant mistake.

To put it in comparison, taking "even money" with a blackjack against a dealer ace increases the house edge by 0.

If the player insures every blackjack and 20 a common mistakethen the error cost jumps to 0.

This question was raised and discussed in the forum of my companion site.

I was playing 6-5 blackjack at a Strip casino a while back and had consumed just enough free booze that I doubled every time I got a blackjack against a dealer 2-6.

Fortunately, I won every time.

But, I wonder how bad my decision was.

Would it make sense if blackjack paid even money?

My is useful to answer questions like this.

For example, assuming six decks and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.

Both are much less than 1.

Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack.

The only game where you should not stand on a blackjack is inwhere the player should triple on a blackjack against a dealer 6.

This question was raised and discussed in the forum of my companion site.

Your blackjack basic strategy tables are based on maximizing the expected value per hand.

However, are there situations where doubling or splitting is such a marginally bad play compared to hitting or standing that the cost of the error is less than the house edge of playing an additional hand?

If the player were to double, the expected value of that error would be -0.

According to mythe house edge under those rules � assuming surrender, double after a split and re-splitting aces � is 0.

So, as long as the dealer hits a soft 17 in a 6-deck game, the cost of doubling soft 17 against a 2 is less than the cost of betting the same amount on an additional hand.

You could make your same point in any game that involves raising.

For example in Three Card Poker, if you want to minimize the expected loss per hand, then the optimal strategy is to raise on Q64 or better, as I state on my.

However, if your goal is to blackjack live the expected loss per total amount bet, then the optimal strategy is to raise on Q62 or better.

This begs the question of why do gambling writers like me base strategy on minimizing the expected loss per original bet, rather than the total amount bet?

My answer is that it is mainly out of tradition.

That is how the blackjack basic strategy was created, and everybody has kept that methodology out of habit and simplicity.

I tend to think most players have a time-based goal, favoring the conventional strategies.

This question was raised and discussed in the forum of my companion site.

I know a lot of blackjack players don't like to split eights against a 9, 10 or ace.

Do you think that play is the one gambling blackjack no frequently played incorrectly?

If not, what do you think is?

The play that I think has the highest probability of being played incorrectly by blackjack players is splitting 4,4 against a 5 or 6 when double after split is allowed.

The probability of getting one or the other situation in a six-deck game is 1 in 1135.

According to myassuming the player hits instead of splitting, the cost in expected value is 2.

Overall, the house edge of the game goes up by 0.

So, it isn't a very costly error, because it happens so infrequently.

When I do, the dealers and other players usually roll their eyes.

That guess would be that the 1 error is not soft doubling when you are supposed to.

Seldom do I see recreational players double a hand like soft 17 against a 6.

The following table shows the increase in the house edge as a result of four commonly made mistakes.

This table assumes the player always makes the error when the situation occurs, instead taking the second best option.

For standing on 12 against a 2 or 3 I did not include a player 6,6.

Cost per Incident Cost per Hand Never soft double 0.

Why is it that the basic strategy says to https://pink-stuf.com/blackjack/blackjack-strain-grow-info.html on 16 vs.

Isn't the basic continue reading based on a full shoe, thus with a count of zero?

It would seem both can't be right.

First, it bears repeating that 16 vs.

If you're allowed to surrender, that is much better than either hitting or standing for the basic strategy player.

Otherwise, hitting is a tiny bit better, on average.

It would take the removal of just one small card from an eight-deck shoe to sway the odds in favor of standing, because with one fewer small card there are more large cards left, making hitting more dangerous.

That is why I say that if your 16 is composed of three or more cards you should stand, because a 3-card 16 has usually removed at least two small cards from the shoe.

Second, on the first hand after a shuffle, if the basic strategy and a card counting strategy differ on how to play the hand, then the basic strategy prevails.

The basic strategy was carefully created to consider the exact deck composition based on the specific cards observed.

A table of index values is a blunter instrument that is applicable throughout the shoe.

In this particular case a card counter could either hit or stand, depending on how he rounds the true count.

If he rounds down, the true count will be -1, causing him to hit.

If he rounds up, or to the nearest integer, the true count will be 0, causing him to stand.

As long as I bring this up, according to Blackjack Blackjack how count cards by Don Schlesinger, the methodology of please click for source for rounding is "flooring," or rounding down, in this case to -1, causing the player to correctly hit.

Another similar situation is 15 vs.

Rounding down would cause the player to incorrectly hit, when surrendering is better.

The bottom line is that for the first decision after a shuffle, with no other cards known from other players, the card counter should use basic strategy.

After that, resume using index numbers.

This question was raised and discussed in the forum of my companion site.

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In order to win, players need to play blackjack perfectly.. 3, 4, 5 or 6, otherwise hit; 77 � split when dealer shows 2, 3, 4, 5, 6 or 7, otherwise hit; 88 � always split.

Enjoy!

Software - MORE

Except for slot machines, blackjack is probably the casino game that. to 7; 88 ALWAYS split; 99 split 2-9 except STAND AGAINST DEALER 7.

Enjoy!

This is a long read regarding the 10 most difficult hands in blackjack.. one that will save you more money during your blackjack playing career, is to split the.. ten dollars and all of a sudden you have 50 or more on it and get 88 against 10?

Enjoy!

r/blackjack: A subreddit dedicated to the card game Blackjack for counters and casual players. All the strategy charts I've seen online say to always split 8's.

Enjoy!

You have far and away the best gambling site on the 'net.

Being an myself ACASI love to see someone putting their math skills to good use.

My question � When late surrender is allowed, do you still want to split eights with a ten showing?

I'm guessing yes, but one of the hardest plays in BJ is splitting eights vs a ten.

As a side note, I just spent three days in Vegas, if you haven't done so already, you must try the Las Vegas Club and the World's Most Liberal blackjack Rules.

At six decks, I figured the house advantage to be 0.

Thanks for all of your hard work!!

Thanks for the kind words, Jim.

Yes, you still want to split blackjack split 88, blackjack split tens if late surrender is offered.

Even if you can't double after a split you should still decline to surrender.

Based on a two-deck game, where you can not double after splitting, the expected value of splitting 8,s against a 10 is -0.

Contrary to their claim of having the "World's Most Liberal Blackjack Rules" there are better single-deck games right across the street at the Horseshoe or the Golden Gate.

It is the six decks at the Las Vegas Club which work against the player.

Don't feel badly about falling for their marquee, I fell for it myself in my younger days before I knew the effects of rule variations.

Update: After this question, the Las Vegas Club changed their rules to pay 6 to 5 on a blackjack in their so-called "World's Most Liberal Blackjack Rules.

You are much better off at any ordinary 3-2 game, which are easy to find elsewhere.

With single-deck blackjack, are the cards dealt face-down?

And what are the general rules for single-deck?

I know you mentioned double downs only on 9-11 or 10-11, but do you know what the general rules are for double-after-split, dealer-hitting-soft-17, etc.

I'm a basic strategy player, and wanted to find out just what the rules tend to be for single-deck I've only ever done 6 or 8 deck so I can prepare the perfect spreadsheet from blackjackinfo.

Thanks so much for your help!

Single deck blackjack rules are usually tight.

Cards are dealt face down.

Doubling is usually restricted to 9 to 11, or 10 to 11.

The dealer will hit a soft 17 and double after a split will probably not be allowed.

Be sure to NOT play if blackjack pays less then 3 to 2, which is usually the case with single-deck games.

You can always see the relatively current blackjack rules in Vegas at my site.

In your blackjack strategy you surrender betting on pairs in against A,10,9.

You say to split a pair of blackjack split 88 against those cards.

I have been told that a pair of 8's is a 16 and should be surrendered.

What do you think?

Whoever told you to surrender two 8's gave you incorrect advice, assuming American late.

To illustrate why you should split 8's against a 10, check my.

This shows expected return for any initial situation for any given play.

The table shows that splitting 8's against a 10 in double deck has an expected return of -0.

In other words, you can expect to lose 47.

This is less than the 50% you would lose by surrendering.

If not allowed to double after a split, then the rate of return is -0.

Splitting 8's against a 9 or ace has an even greater return.

If the dealer checks his hole card, and does not have blackjack, then why hit a soft 18 against an ace.

Also, why not source on an 11?

In blackjack there are seldom simple answers.

You have to consider everything that could happen and weigh every outcome by their probability.

The best play is the one with the greatest expected return.

According to mythe expected return in a double deck game of hitting a soft 18 against an ace is -0.

So hitting is just a hair better.

It is actually composition dependent in both single and double decks, in other words depending on which two cards that total 11 determines how to play the hand.

However if you don't wish to memorize thethen you should double on 11 against an ace in single and double deck and hit with four or more decks.

Hi there -- love your site!

If I have blackjack, and the dealer is showing an ace, I am given the option of taking even money or continuing the hand.

Should I take the even money or play on?

This is another way of looking at the decision to take insurance.

The expected return of taking even money is obviously 1.

Lets assume an infinite deck of cards for the sake of simplicity.

If the dealer gets a blackjack, then you push.

If not, then you win 1.

Thus declining ever hand biggest blackjack, or even money, and playing the hand is the better bet.

In an actual game with a finite number of decks the odds are even better since one 10 is already out of the deck in your hand which lowers the dealer's probability of having a blackjack.

How does this strategy play out?

This would be a bad play.

For example, my shows the return both ways by playing 10 and 6 cards against a dealer 7.

Hitting has an expected loss of 39.

However, standing has an expected loss of 47.

There is no easy explanation I can give why hitting is better.

You have to consider everything that can happen, weight it by its probability, and take the sum.

Overall hitting is better of two bad plays.

Regarding your exceptions to surrender inhow should I best adapt it to the Unified Gaming single-deck game with early surrender against the ace?

Thanks for any help and great site.

Thanks for the compliment.

You should use appendix six only if the dealer is showing a ten in a Unified Gaming blackjack game.

There are no exceptions apologise, pokemon sun pokerus consider the when the dealer has an ace showing.

I just came back from Costa Rica.

They pay even money on a blackjack.

What is this worth to the house and should I double down on 21 versus say a dealer 3-6, since I am only going to get paid 1to1?

Hi, I just looked at your Microgaming blackjack basic strategy card.

I notice that on 7,7 you advise that the player not hit against a 10.

Why is this, and does this override the advice to hit on 14 against a 10?

This is the correct play in all my single-deck blackjack strategies.

With the low hope of beating a dealer 20, it is better to hit, or surrender if you can.

Yes, this does override my advice to hit 14 against a 10.

I have been a dealer now for 10 years, and trying to get out of it.

I can not count how many times I have heard people say, "Always assume there is a 10 in the hole".

You and I know this cannot be correct all the time.

I understand why they say it, but, what are the odds that it really is a ten, and when the dealer has an Ace up, and checks in the card reader for a blackjack, does not have one, you know definitely it is not a ten.

What should you assume it is then?

I don't like that expression either.

At best it is a memory device to help people remember to hit a stiff hand if the dealer has a 7 to 10 showing.

There is no simple rule of thumb that works in all situations.

I was studying your on the blackjack site, and came across something odd.

Basic strategy in a six-deck game with double after split, dealer stays on soft 17 etc.

Yet, on the appendix, the player's expected return is HIGHER if you hit, rather than double compare.

The same is true for an A,4 v.

All of the other splits and doubles work out.

What's up with these two examples?

Appendix 1 is based on an infinite deck.

Both hands you mention are borderline plays and the number of decks affects which play is better.

For example, A-4 against a 4 favors doubling with 26 decks and hitting with 27 decks.

A-2 against a 5 also crosses over somewhere between 8 and an infinite number of decks.

As a BJ player I regularly split 10s vs.

This move has a positive expectation, but isn't as profitable as standing pat.

Could you please show this friend of mine how much worse splitting 10s is than standing click the following article, in a neutral deck?

Also, lots of BJ players get upset at someone who splits 10s vs.

Can you set the record straight on this?

I took great pains to create my blackjack appendices 9A-9H to answer these kinds of questions.

For example, in a six-deck game where the dealer stands on soft 17, you would use blackjack appendix 9G.

There you can see the expected return by standing on two 10's against a dealer 6 is 0.

The expected return link splitting in this situation is 0.

So, the player can expect to win an extra 8.

Don't pay much stock in what other players say or do at the blackjack table.

Wiz, this is a spliting 8's against a dealer's 10 question.

Splitting is the is the correct play on single hand basis.

However, I believe for the typical blackjack player it is better to stand when considering you are doubling the amount of the bet.

Why double your bet against such poor, way below average, odds?

After all, the goal is to maximize your overall return i.

Your site's great and advertising like banner ads and sidebars is understandable but invasive advertising like pop up windows and question prompts that try to force you to another site gets to be a bit much IMO.

Although this is a close play, standing is the third worst option.

The expected returns for doubling and splitting are based on the total return for that hand relative to the initial bet.

Luckily I was only playing for fun on an Internet gaming site at the time.

Yes, you should keep splitting as long as you keep getting tens.

Playing one hand and losing does not disprove anything.

Millions of hands must be played both ways and the results tabulated to truly know the best play.

On a 4-deck blackjack game if you split aces against 5 or 6, and you get another ace.

You should double or hit?

Another question in 4 deck BJ for 10,2 against 4, one site listed a hit.

I would like a confirmation from you.

However if you can you should double on the 6 only.

This is true whether or not the dealer hits a soft 17.

If the dealer stands on a soft 17 the expected returns against a 5 are.

Against a 6 the expected returns are.

So doubling is the better play.

You can see these numbers for yourself in my.

About your other question, yes in a 4-deck game the player should hit a 10,2 against a 4, but only if the dealer stands on a soft 17.

Following this exception will help you win more unit every 113396 hands, or lower the house edge by 0.

Not worth the bother of memorizing the exception in my opinion.

This is an interesting situation.

Following is the expected return by hitting each way to compose a 15.

In other words the odds just barely favor surrendering a 10,5 and 9,6 but the odds favoring hitting 8,7 by a much wider margin.

My question is about table maximum bets in BJ.

Can I double down, or have I already reached the limit?

Can I split them, turning one hand into two hands?

Yes, you could double or split in those situations.

The maximum applies to the initial bet.

I checked your web site and I could only find appendixes for multiple card hands this web page 1 and 2 deck games.

Is this article correct?

check this out fewer the decks and the greater the number of cards the more this is true.

To test the most likely case to favor hitting, 8 decks and only 3 cards, I ran every possible situation through my combinatorial program.

The following table displays the results.

So standing is the marginally better play.

Following this rule will result in an extra unit once every 1117910 hands.

It would take about 5 years playing blackjack 40 hours a week before this piece of advice saved the player one unit.

I like to use your to fine tune my play in online single deck blackjack.

I see you have updated this page in December, and it seems like there are a few new moves in the 2-card section.

Is the key that the dealer can have an A in the hole with the 6?

Are these new strategies, and if so, what brought them about?

Yes, I made a couple changes to the two-card list.

I removed 9+3 Vs 3 and added 10+2 Vs 6.

In a single deck game where the dealer stands on soft 17 and the player has 10+2 against a dealer 6 the expected value of hitting is -0.

So you lose less on average by hitting.

I hate to give sound bite answers to the basic strategy because there are numerous ways the cards can play out.

However as you said the dealer is also more likely to get a 17 with a 6 showing than a 5.

A 17 is not a good hand and motivates the player to hit and try to beat it.

If you have 15 and see more dealer shows an eight.

In this case, whether you hit or stay your chance of losing is over 70%.

The expected value of hitting would be 0.

This is greater than the expected value of -0.

I just wanted to make sure that the correct play blackjack split 88 the Microgaming single deck game of A,A vs A is to split as shown on your card.

Any chance you have the EV of hitting vs splitting on this hand?

Based on one deck the expected value of each hand considering the possibility of a dealer blackjack is -0.

So splitting is better by about 31% of a unit.

Splitting is also better for the 4-deck game, which no Microgaming player should be playing since a 1-deck game with the same rules is available.

After performing my own infinite deck analysis for Blackjack with the same rules as yours dealer stands all 17s, re-splitting allowed to 4 hands except Aces, which can only be split once, doubling after splitting, draw only one card to split AcesI came across your site.

In comparing expected values, I obtained the same numbers as you in all cases, except for pair splitting, which were slightly different.

It took me years to get the splitting pairs correct myself.

Cindy of was very helpful.

Resplitting up to four hands is allowed.

Here is how I did it.

For each rank determine the probability of that rank, given that the probability of another 8 is zero.

Take the dot product of the probability and expected value over each rank.

The hardest part of all this is step 3.

I have a very ugly subroutine full of long formulas I determine using probability trees.

It gets especially ugly when the dealer has a 10 or ace up.

I have a question about the two blackjack strategies your.

First off, the underlying assumption before this question is that hitting on a soft 17 is an advantage to the dealer.

Why does the strategy have the player double down more often in situations where the dealer might hit a soft 17,i.

If hitting a soft 17 gives the house more of an advantage, why would one want to put more money on the table at those times?

Is it possible that the two charts are switched?

However this is a generality and not true of every situation.

When you have a strong hand of 18 to 21 you want the dealer to stand on a soft 17.

However if you have a weak hand under 17 you want the dealer to hit a soft 17.

An example of a strategy difference is you should double soft 19 against a 6 when the dealer hits a soft 17, and stand if the dealer stands on soft 17.

The reason is that there is a good chance of having drawing a bad card on the double, resulting in 16 or less points.

When the dealer hits a soft 17 he busts more often, making doubling a little safer in this example.

Now your site is teaching me Blackjack.

Thank you for the compliment.

To answer your question the dealer will just ask you what you want to do.

Normally all decisions in blackjack must be visible, however this is the only exception I can think of.

However if you want to avoid being asked when it is your turn simply hold up you index finger to denote that you want one card.

Most dealers know what this means.

Coincidentally I just learned yesterday that in Bulgaria if you wish to double you put your extra bet behind the original bet, and if you want to split you put it next to the original bet.

Another reader wrote in to state that in North Dakota it is the state to follow the Bulgarian rule for doubling and splitting.

My question is, why stand?

You were willing to take another card anyway.

Thanks for your time!

If the player had the option to double his bet and stand that would be better than a conventional double.

The basic strategy chart for blackjack states to hit on a 16 if the dealer has an ace showing.

I was wondering if the chart takes into account the fact that once it is known insurance is not paying then the dealer does not have a 10 value card down?

Yes, the basic strategy assumes the dealer does not have a ten in the hole.

When the dealer has an ace, macau blackjack no blackjack, the probability of making 17 or more is 83.

So standing is not even a very borderline play, the odds definitely favor hitting.

If the dealer does not check for blackjack with a ten showing, instead taking only the original wager at the end of the hand, does that necessitate any strategy changes?

As long as you stand to lose only the original wager you should play assuming the dealer does not have a blackjack.

If the dealer does have blackjack there is nothing you can do about it anyway.

You make a good mathematical argument that the player should refuse insurance.

Most people would feel like a fool giving up a bird in the hand to lose a shot at 1.

Gambling is about taking risks.

The successful gambler does not try to maximize his probability of a net win each hand but takes risks to maximize his overall return.

Both in gambling and in life one must sometimes take short term risks for long term gain.

So think less about the present and more about the future.

The player should be more aggressive hitting in Blackjack Switch because a dealer 22 results in a push.

Much of the value in standing in regular blackjack is realized when the dealer busts.

In Blackjack Switch many of those wins are turned into a push, making hitting a better play in comparison.

What are the hands that are closest to 50-50 so that my wife can limit her hunch plays to those?

Here are some borderline plays, as evidenced by having a card counting index equal to zero.

This list is for multiple decks where the dealer stands on soft 17 and double after a split is allowed.

The best play is listed first and an alternative second.

No, you never touch your chips once the bet has been made until the hand is over.

The signal to surrender is to use your index finger and pretend to draw a line along the blackjack table, just behind your bet from left to right.

It is just as good to simply say "surrender.

This works strongly to the dealers favor source should be a disincentive to put more money on the table by doubling or splitting.

What would the expected loss be for that play?

This would be a terrible play.

For example if you doubled on a blackjack against a 5 six decks dealer stands on soft 17 your expected gain would be 0.

So even in an even money game this would still be an error costing about 38% of the bet.

Wong states in on page 23 the following, "If you get to twelve by 10-2 or 2-10 where 10 means any 10-count cardand two or fewer decks are being used or seven or fewer if the dealer stands on soft seventeenyou should hit.

Wong is referring to a player 12 against a dealer 4 and is quotingpage 176, by Peter Griffin.

Yes, he is right.

In a seven deck game the expected value by hitting is -0.

However with eight decks hitting is -0.

This is such a borderline play that the number of decks does make a difference between seven and eight.

Here is an even better example.

With A-4 against a 4 you should double all the way through 26 decks but hit with 27 or more.

Are there any basic strategy exceptions for doubling and splitting on the Internet when cash back applies to the total amount bet thus giving the player an extra incentive to double or split.

Please assume a cash back rate of 0.

I could not find any hand where an extra 0.

The closest case I could find, based on six decks and the dealer standing on soft 17, is A,4 against a dealer 4.

In that hand doubling costs the player just under 0.

So if you can get 0.

Other borderline hands I examined cost the player at least 1% to double or split, and I have never seen cash back that high in blackjack.

In blackjack the strategy for 16 vs.

It is true that in general you should stand on 16 vs.

So if my chart was based on the casino offering the surrender option then you would be right.

However that assumption is not made.

If I changed the key to Rs surrender if allowed, otherwise stand then that would imply that the player should stand on a 2-card 16 against a 10 if surrender was not allowed.

In your blackjack appendix 9 you indicate that the player has a positive expectation hitting 10 against a 10?

This should give the dealer an advantage because the dealer will win if both bust.

I stated in the explanation to that appendix that I already assume the dealer does not have a blackjack.

That is why the player has a slight edge in that situation, after the dealer peeks and confirms he does not have a blackjack.

The index number of 16 against a 10 in most blackjack counting systems is zero.

So if the deck were completely neutral you should stand, because you stand if the count is equal or exceeds the index number.

Yet the basic strategy tables tell us to hit.

This seems to be a contradiction.

In all honesty this is an old question but I got a better answer from Chris F.

A good example of this is that in single deck the correct play is to stand on 7,7 against a 10, because half of the sevens in the deck are already gone, and that is what you need to beat a dealer 20 with 3 cards.

Either way two cards that would bust the player by hitting have been removed.

So the deck is slightly rich in small cards that will not bust the player, giving the player an incentive to hit.

While this is true I was skeptical because in an infinite deck game the odds still favor hitting.

However except in a few Blackjack split 88 casinos an infinite deck is just an abstraction.

Then I gave the dealer a 10 and myself a 10 and 6.

So the player was playing this hand against a neutral deck with 31 of each card A-9 and 124 tens.

Here is the expected values: Play Expected Value Stand -0.

It is the same if I remove the following: A,2,3,4,5,6,8,10,10,10 to simulate 9,7 vs 10, because the player is going against the exact same neutral shoe.

It just goes to show how powerful the effect of removal is, even when just three cards in an eight-deck game.

So as I just showed going into a neutral deck the odds favor standing.

The reason hitting is correct in an infinite deck is because there is no effect of removal.

If you accidentally hit a 16 vs 10 in a neutral shoe, and got a low card, then the dealer would have a better chance of getting a 10 in the hole.

This fact is reflected in the higher expected value for standing in an 8-deck game, but would not matter in an infinite deck.

For the record, here are the expected values in an infinite deck game: Sometimes the dealer exposes his hole card in blackjack.

What is the correct basic strategy when that happens?

Stanford Wong gives such a basic strategy in his booksee table 46.

He also said that in 1995 the Bourbon Street casino in Vegas had a promotion in which every 50 minutes the dealer would expose both his cards for five hands.

The player advantage during those was about 10%, according to Wong.

That is a good question.

Personally I eyeball the borderline plays based on what has already been played, especially on the second hand to be played.

If forced I would say using the exceptions is better than the basic strategy only.

However the way the basic strategy exceptions were created was on the initial hand only, so they are not entirely accurate for splitting, because the deck composition will be a little different.

Your strategy cards for Blackjack I presume is basic strategy for the initial cards player's first two cards and dealer's up card.

However, after hitting or splitting the deck composition has changed and the basic strategy may have changed.

What I think would be more appropriate is a basic strategy based on the overall game of blackjack, including after splitting and hitting.

Is there any situation where your initial hand basic strategy and one for the overall game are different?

Yes, my basic strategy charts are designed to be the best play based on the first two cards.

This is the usual approach to developing the basic strategy.

One benefit to this approach is the expected values of each play can be calculated exactly and compared to other sources.

However, you bring up a valid point.

So I asked Don Schlesinger, author ofif there were any known play where the best play on the this web page hand is different from the best play to maximize the expected value of the overall game of blackjack.

He replied that a soft 18 against a dealer ace, in a double-deck game, where the dealer stands on soft 17, was such a play.

As my shows the expected value for standing is -0.

So, based on the first two cards, the odds favor hitting by 0.

However, there are many more ways to see soft 18 than one ace and one seven.

The following table shows all the ways this hand can turn up.

Player cards Conditional Probability Hit EV Stand EV Hit Return Stand Return A7 0.

Hit EV:Expected value by hitting Stand EV:Expected value by standing Hit Return:Product of probability and hit expected value Stand Return:Product of probability and stand expected value The right two cells of the bottom row show that overall the expected value of hitting is -0.

So, the table shows the odds favor standing by 0.

To confirm these results I ran two simulations under the rules in question, one simulation hitting and one standing on this play.

I counted only hands where soft 18 against a dealer ace happened at any time during play.

Here are my results.

Soft 17 Hands Played Total Win Expected Value Stand 3857490 -396224 -0.

Thus, for practical purposes of playing all hands, the best play is to stand, contrary to what my basic strategy chart says.

I just stumbled onto your site, and I think it's a fabulous site for blackjack info.

I have a question, though.

Can you explain how is there a positive expectation when you follow basic strategy and have a total of ten against a dealer 10 or ace showing no dealer blackjack.

Your table shows a positive perfect pairs 213 blackjack crown for both these scenarios, but I can't understand how.

I would think under this scenario the player and dealer follow the same strategy, that is to hit until 17 or better or bust.

The soft 17 is eliminated for the player under this scenario so I can't understand where the positive expectation comes from.

Thanks for the kind words.

Let's assume six decks it doesn't matter whether the dealer hits or stands on soft 17.

My shows the expected value of 6+4 against an ace to be +0.

The reason the expected values are positive is my expected value tables assume the dealer already has peeked for a blackjack and has confirmed that he doesn't have one.

Meanwhile, the player can still draw an ace for a 21.

In other words the player can make 21 on his next card and the dealer can not by assumption.

If I had such a table under the European no-peek rule, then the expected values source indeed be negative.

On my recent visit in Vegas I saw two dealers independent from each others one at The Orleans, one at Circus-Circus suggest to double on 4-4 vs.

I was the BJ guy of our group and so my friends started to ask me about that.

All I could say was: no, splitting is the right decision.

Of course provided that double after split is allowed.

Can I find out the probabilities of these alternatives or can you tell me?

Splitting fours against a five or six is a frequent play where both players and dealers incorrectly rebuke splitting.

Sometimes you hear people say falsely that you should never split "anything that starts with F", in other words fours, fives, and faces.

That is true about fives and faces but the player should indeed split fours against a five or six if double after split is allowed.

Otherwise the player should hit, except in single deck he should double if allowed.

My shows in a six-deck game where the dealer hits a soft 17 the following expected values of 4,4 against a 6.

I was intrigued by the analysis from your about when to stand with 16 vs.

Being a math person myself I want to maximize the odds, but also understand the slim gain.

Thanks for all you do!

Thanks for the kind words.

If it is a face-up game, with other players, I scan the table and just use my best judgment.

However if the dealer accidentally flipped over both his cards, showing a total of 10 or 11, the player should hit against a 10 and stand against an 11.

So you can play your hand more aggressively.

In you have the effect of removing a 6 less than a 5 or 4.

Up Card Expected Value 2 9.

While sixes are bad for the dealer they are bad for the player as well.

All things considered, if you could remove one card from the shoe you should choose a five.

Is it available any where?

There are not many situations to surrender, but those situations happen often, so I think they are worth memorizing.

In a six-deck game surrender is worth 0.

My friend I were playing in LV.

We had a big argument on what has statistically better odds, double down with player totaling 10 versus but how to deal pitch blackjack consider showing 7, or double down with player totaling 11 versus dealer showing 10, in a two deck game.

I thought it was the prior.

My was created for just these kinds of questions.

Assuming 6 decks, my table shows the expected value of doubling 8+2 vs.

The expected value of doubling 8+3 vs.

So you are right, 10 vs.

According to standard BJ rules and perfect basic strategy, how many percent of my DOUBLED DOWN hands should I expect to win, push and lose?

Assuming liberal Vegas Strip rules six decks, dealer stands on soft 17, double after split allowed, late surrender allowed, resplitting aces allowed the following are the probabilities of each possible outcome when doubling on the initial two cards.

This does not include doubling after splitting.

I think he should wait because he could get a two, three, four, five, etc.

What do you think?

Or is my friend just a whiner?

Thank you for your time.

Maybe you can take advantage of his complaining by offering to buy his hand for less than the fair 79 cents on the dollar.

I had a situation playing blackjack last weekend, where the dealer had a 6 on top but when he was tucking in the down card he accidentally showed that he had a 3 in the hole.

The player on my right had a 15, I had an 11, and the player on my left had a 12.

Knowing that the dealer had a total hand of 9, the player on my right hit his hand and busted with a 10.

I wound up doubling down and got a 2.

The player on the left hit his hand getting a 5, for a total of 17.

The dealer opened his hand of 9 and hit a ten for a total of 19.

The dealer told us even though you saw the 3 under that you should play your hand as if you did not know the down card.

I wanted to ask you what you would have done in the situation for all three players.

This is the first time that has ever happened since I have been playing blackjack.

My shows what to do in any situation where the dealer accidentally exposes his hole card.

Using that rule of thumb, all three players played correctly.

Contrary to what the dealer said, the player has every right to use any information gleaned from dealer errors like this.

Thanks for creating a great site, with such detailed information.

Are there any basic strategy exceptions that are worth making to maximize profit in a large 6+ decks shoe?

I assume you would hit more if you were one card away from a Charlie against an ace, since it is so unlikely for the dealer to bust, but I would love to see specific instructions.

For those readers who may not understand the question, a "Charlie" is a rule in which the player automatically wins if he hits to some number of cards, usually five to seven, without busting.

The following table, for three or more cards, shows the basic strategy if the player is one or two cards away from such an automtic winner.

Can you please tell us the proper pair-splitting strategy when the "behind" wager far exceeds the regular wager, assuming the two bettors are working together?

I have studied and used your dealer exposes hole-card strategy for some time now, and there is still one play that I can not find a mathematical explanation for: A2 vs.

What am I not seeing?

The reason is my blackjack basic strategy is based on 8 or fewer decks, and the flashing dealer strategy is based on an infinite number of decks.

In an infinite-deck blackjack game you should hit A2 vs.

An infinite-deck assumption is the lazy way to analyze blackjack.

The reason I went that way is I believe that is not a frequently used page, and the cost in errors is very small, only one unit for every 202,000 units bet.

I think I noticed an error in your for blackjack.

It states that you should only play one hand if the person you are back-betting splits 10s vs.

But a hard 10 no double vs.

The reason is that my table assumes the front-player will keep resplitting, if he can.

That depresses the value of a single 10, because I assume the front-player will keep making the same mistake, if he can.

I just added that condition to that page.

Thank you for your detailed site.

In you state the expected value for the game and the expected value for each play.

When I try this calculation I get a different result.

For example, six decks, dealer hits on soft 17, and player may not double after split I get 0.

Those tables assume the dealer does not have a blackjack.

Making correct double and split decisions should be based on the conditional expected value, given the dealer does not have a blackjack.

Otherwise, the player would be overly timid about doubling or splitting against a ten or ace.

Adding up the dot product of probabilities and expected values will give an incorrect result, because there is no loss represented for a dealer blackjack.

To get the house edge of the overall game you should subtract the expected loss when the dealer has a blackjack.

However, the player will only lose when he does not have a blackjack.

So, the probability of the player losing to a dealer blackjack is 0.

You should subtract this number from your dot product above: 0.

Thus, the house edge under the rules stated in the appendix is 0.

I follow your 4+ deck Blackjack basic strategy 100% of the time and I always get dirty looks whenever I hit my 12 against a dealer 2 and especially a 3.

I feel your pain.

You can imagine how bad it gets in Spanish 21, which calls for such plays as hitting 14 against a 3.

As long as it is just looks, I would let it slide.

If it gets to words, I would say something like, "There are lots of other tables in here.

The more ridiculous a belief is, the more tenaciously it tends to be held.

There is usually no sound-bite explanation anyway to why one play is better than another.

To know why the correct play is what it is, one must either consider every possible way the remaining cards could fall, for both player and dealer, or play out the hand thousands of times, even millions for very borderline hands.

The decision with the highest expected value is the one you should take.

Only refusing insurance yields itself to being easily explained.

My question is what is this doing to the house edge?

The effect of each basic strategy change is the probability of the hand occurring and the cost of not making the correct play when it does.

My shows both the probability of each hand and the expected value of each play.

So hitting 8,8 against a dealer 9, 10 or ace increases the house edge by 0.

If the player surrenders instead of hitting, the effect drops to 0.

So, it is not a significant mistake.

To put it in comparison, taking "even money" with a blackjack against a dealer ace increases the house edge by 0.

If the player insures every blackjack and 20 a common mistakethen the error cost jumps to 0.

This question was raised and discussed in the forum of my companion site.

I was playing 6-5 blackjack at a Strip casino a while back and had consumed just enough free booze that I doubled every time I got a blackjack against a dealer 2-6.

Fortunately, I won every time.

But, I wonder how bad my decision was.

Would it make sense if blackjack paid even money?

My is useful to answer questions like this.

For example, assuming six decks and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.

Both are much less than 1.

Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack.

The blackjack split 88 game where you should not stand on a blackjack is inwhere the player should triple on https://pink-stuf.com/blackjack/blackjack-system-strategy-betting.html blackjack against a dealer 6.

This question was raised and discussed in the forum of my companion site.

Your blackjack basic strategy tables are based on maximizing the expected value per hand.

However, are there situations where doubling or splitting is such a marginally bad play compared to hitting or standing that the cost of the error is less than the house edge of playing an additional hand?

If the player were to double, the expected value of that error would be -0.

According to mythe house edge under those rules � assuming surrender, double after a split and re-splitting aces � is 0.

So, as long as the dealer hits a soft 17 in a 6-deck game, the cost of doubling soft 17 against a 2 is less than the cost of betting the same amount on an additional hand.

You could make your same point in any game that involves raising.

For example in Three Card Poker, if you want to minimize the expected loss per hand, then the optimal strategy is to raise on Q64 or better, as I state on my.

However, if your goal is to minimize the expected loss per total amount bet, then the optimal strategy is to raise on Q62 or better.

This begs the question of why do gambling writers like me base strategy on minimizing the expected loss per original bet, rather than the total amount bet?

learn more here answer is that it is mainly out of tradition.

That is how the blackjack basic strategy was created, and everybody has kept that methodology out of habit and simplicity.

I tend to think most players have a time-based goal, favoring the conventional strategies.

This question was raised and discussed in the forum of my companion site.

I know a lot of blackjack players don't like to split eights against a 9, 10 or ace.

Do you think that play is the one most frequently played incorrectly?

If not, what do you think is?

The play that I think has the highest probability of being played incorrectly by blackjack players is splitting 4,4 against a 5 or 6 when double after split is allowed.

The probability of getting one or the other situation in a six-deck game is 1 in 1135.

According to myassuming the player hits instead of splitting, the cost in expected value is 2.

Overall, the house edge of the game goes up by 0.

So, it isn't a very costly error, because it happens so infrequently.

When I do, the dealers and other players usually roll their eyes.

That guess would be that the 1 error is not soft doubling when you are supposed to.

Seldom do I see recreational players double a hand like soft 17 against a 6.

The following table shows the increase in the house edge as a result of four commonly made mistakes.

This table assumes the player always makes the error when the situation occurs, instead taking the second best option.

For standing on 12 against a 2 or 3 I did not include a player 6,6.

Cost per Incident Cost per Hand Never soft double 0.

Why is it that the basic strategy says to hit on 16 vs.

Isn't the basic strategy based on a full shoe, thus with a count of zero?

It would seem both can't be right.

First, it bears repeating that 16 vs.

If you're allowed to surrender, that is much better than either hitting or standing for the basic strategy player.

Otherwise, hitting is a tiny bit better, on average.

It would take the removal of just one small card from an eight-deck shoe to sway the odds in favor of standing, because with one fewer small card there are more large cards left, making hitting more dangerous.

That is why I say that if your 16 is composed of three or more cards you should stand, because a blackjack split 88 16 has usually removed at least two small cards from the shoe.

Second, on the first hand after a shuffle, if the basic strategy and a card counting strategy differ on how to play the hand, then the basic strategy prevails.

The basic strategy was carefully created to consider the exact deck composition based on the specific cards observed.

A table of index values is a blunter instrument that is applicable throughout the shoe.

In this particular case a card counter could either hit or stand, depending on how he rounds the true count.

If he rounds down, the true count will be -1, causing him to hit.

If he rounds up, or to the nearest integer, the true count will be 0, causing him slotland eu stand.

As long as I bring this up, according to Blackjack Attack by Don Schlesinger, the methodology of choice for rounding is "flooring," or rounding down, in this case to -1, causing the player to correctly hit.

Another similar situation is 15 vs.

Rounding down would cause the player to incorrectly hit, when surrendering is better.

The bottom line is that for the first decision after a shuffle, with no other cards known from other players, the card counter should use basic strategy.

After that, resume using index numbers.

This question was raised and discussed in the forum of my companion site.

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r/blackjack: A subreddit dedicated to the card game Blackjack for counters and casual players. All the strategy charts I've seen online say to always split 8's.

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