BS & Table Composition

As we all know BS is the results from calculations of billions of hands played at BJ, however BS has been calculated using 2 starting cards against the dealers up card. I'm wondering if much research has been done on BS for hands comprising of 3,4 or 5 cards and/or based on table composition for 6 deck games? I'm not talking about counting all cards played as I'm not rainman or worried about how the count is (I18 etc.) , I'm just purely interested in what we can see in the hands currently being played out.

I'm sure most people know of the "rule of 45" (described in Blackjack Bluebook II by Fred Renzey) where if you have a 16 made up of 4's and or 5's (ie. 4,5,7 or 5,5,6 etc.) against a dealers 10 you are better off standing than hitting. This is due to the fact that two of your key cards are out of play and that hitting or standing with 16 against a 10 is such a close call in the first place. This is of course is also true if other players have 4's & 5's in their hands.

A hand that also comes to mind, is soft 18 against a dealers 10. So here BS tells us to hit but what happens if your soft 18 is made up of 3,2,2,A. or 2,2,2,A,A or 3,3,A,A ? Would it still the right play to hit with 2 or 3 key cards out of play? What if other players are also holding more 3's and 2's?

I'm sure there must serveral other instances where table composition would affect the most profitable play, does anybody have any knowledge on this subject or able point me in the right direction for further references?

jay28 said:

As we all know BS is the results from calculations of billions of hands played at BJ, however BS has been calculated using 2 starting cards against the dealers up card.

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We may "all know it," but it isn't true. First, BS is calculated via combinatorial analysis, not from hands played. Also, it is from all possible hands according to frequency, not just the first two cards.

jay28 said:

I'm wondering if much research has been done on BS for hands comprising of 3,4 or 5 cards and/or based on table composition for 6 deck games? I'm not talking about counting all cards played as I'm not rainman or worried about how the count is (I18 etc.) , I'm just purely interested in what we can see in the hands currently being played out.

I'm sure most people know of the "rule of 45" (described in Blackjack Bluebook II by Fred Renzey) where if you have a 16 made up of 4's and or 5's (ie. 4,5,7 or 5,5,6 etc.) against a dealers 10 you are better off standing than hitting. This is due to the fact that two of your key cards are out of play and that hitting or standing with 16 against a 10 is such a close call in the first place. This is of course is also true if other players have 4's & 5's in their hands.

A hand that also comes to mind, is soft 18 against a dealers 10. So here BS tells us to hit but what happens if your soft 18 is made up of 3,2,2,A. or 2,2,2,A,A or 3,3,A,A ? Would it still the right play to hit with 2 or 3 key cards out of play? What if other players are also holding more 3's and 2's?

I'm sure there must serveral other instances where table composition would affect the most profitable play, does anybody have any knowledge on this subject or able point me in the right direction for further references?

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Waste of time. Much easier to learn to count which obsoletes composition-dependent play.

QFIT said:

Waste of time. Much easier to learn to count which obsoletes composition-dependent play.

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The more deviations I can make from BS or card counting techniques, the less I feel that I look like a card counter. For example, I love raising my bets when the count is negative, dropping, or at the start of a shoe after shuffle tracking a clump of high cards. I guess I'm looking for more options when TC is between -1 to +1, also I've found a venue, where I've been getting away with spreading 20 units, so I want further option with cover play, that isn't going to cost me anything or even puts me at an advantage at times. I thought that occasional table composition play might be an option, especially during even counts?

Problem is, if it is a close play in a reasonably frequent hand at a near neutral count, it already has an index and making a composition-dependent play won't make you look less like a counter.

The only thing I can think of is T,2 vs 4 is a hit, while a 12 made up of any other combination vs 4 is a stand.

QFIT said:

Problem is, if it is a close play in a reasonably frequent hand at a near neutral count, it already has an index and making a composition-dependent play won't make you look less like a counter.

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Your wisdom is much appreciated and more than likely right, although I'm not that bothered if they're infrequent plays, well that's if I can find a few to put together.

cardcounter0 said:

The only thing I can think of is T,2 vs 4 is a hit, while a 12 made up of any other combination vs 4 is a stand.

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Thanks Cardcounter, I do already use this play at the correct counts and think it's a good one, especially when it gets questioned at the tables by the ploppies, who then think i'm an idiot.

QFIT said:

We may "all know it," but it isn't true. BS is calculated from all possible hands according to frequency, not just the first two cards.

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Norm -- Back in 1977, I received Julian Braun's paper titled, "The Development and Analysis of Winning Strategies for the Casino game of Blackjack". In it, was a description of his fortran program to analyze, and refine Thorp's earlier version of the correct basic strategy. If I understood his description correctly, Braun's program used a "3 card code" in analyzing each of the player's 55 possible two-card holdings vs. all 10 possible dealer up-cards.

Are things being done differently now? That is, does the square in a modern basic strategy chart that refers to soft 18 vs. 10 take into account the times you'll have A/2/A/3/A? Or did I misinterpret Braun's program description? This really has me wondering.

For what little it's worth, I've never read anything to suggest BS is anything but your two cards and the dealers up card. I've read quite extensively on the subject and this is the first I'm reading of it.

Renzey said:

Norm -- Back in 1977, I received Julian Braun's paper titled, "The Development and Analysis of Winning Strategies for the Casino game of Blackjack". In it, was a description of his fortran program to analyze, and refine Thorp's earlier version of the correct basic strategy. If I understood his description correctly, Braun's program used a "3 card code" in analyzing each of the player's 55 possible two-card holdings vs. all 10 possible dealer up-cards.

Are things being done differently now? That is, does the square in a modern basic strategy chart that refers to soft 18 vs. 10 take into account the times you'll have A/2/A/3/A? Or did I misinterpret Braun's program description? This really has me wondering.

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Yes, the square in a BS chart gives the Total-Dependent strategy. At least when I do it.

QFIT said:

Yes, the square in a BS chart gives the Total-Dependent strategy. At least when I do it.

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Have BS calculations changed, always been this way or coincidently work out the same either way you calculate?

Could it be the case that you will much more often hold any particular total with two cards, therefore averages are distorted ?

Renzey said:

That is, does the square in a modern basic strategy chart that refers to soft 18 vs. 10 take into account the times you'll have A/2/A/3/A? Or did I misinterpret Braun's program description? This really has me wondering.

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QFIT answered this already, but I wanted to make sure the answer is clear... Yes, modern basic strategy charts use full combinatorial analysis and consider every possible composition of a particular total, weighted by the appropriate probability of that composition's appearance.

KenSmith said:

QFIT answered this already, but I wanted to make sure the answer is clear... Yes, modern basic strategy charts use full combinatorial analysis and consider every possible composition of a particular total, weighted by the appropriate probability of that composition's appearance.

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One thing that can be confusing when comparing BS charts to strategy charts for counters is the effect of the hand on the count. A good example is a single deck game where 8 vs. 5 and 8 vs. 6 are double down hands using Basic Strategy. But in a neutral count they are hit hands. The reason is that most counters recalculate before every decision and if you have one of those hands 3 low cards had to have been dealt out.

It's kind of paradoxical that if you are playing SD and you get one of those hands, and for some reason you forget the index and use the BS play in a neutral count, it will be the wrong play. It took me a while to figure this out when I was making an index chart for someone and saw a positive index number on what should be a BS double... what the heck???

KenSmith said:

QFIT answered this already, but I wanted to make sure the answer is clear... Yes, modern basic strategy charts use full combinatorial analysis and consider every possible composition of a particular total, weighted by the appropriate probability of that composition's appearance.

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Sorry guys, I'm still a bit unclear. Would this mean that standing 2/2/3/A against a dealers 10 could still be the best option due to the fact that this particular composition would have a much lesser probability of appearance, so therefore may not have been considered as much as other S18 compositions in BS calculations averages? or does it still not matter?

Also back to the original point, BS still doesn't take into consideration the composition of other players hands. There must be a cut off point where further deviations from BS must be made when further key cards are out of play? As an extreme example, what if I knew there were no more A's 2's or 3's left in the game? Should I still hit my S18 v 10 and hope for two further cards to improve the hand?

Composition Dependent Plays

Below is directly from Shackleford's site. There are additional 1 deck examples here: http://wizardofodds.com/blackjack/appendix18.html

There are only a few exceptions for 2 to 8 decks, as follows.
Always: Stand on 16 vs 10 with 3 or more cards.
Two decks, dealer stands on soft 17: Stand soft 18 vs A with 3 or more cards.
Four or six decks, dealer stands on soft 17: Stand soft 18 vs A with 4 or more cards.
BW

jay28 said:

Would this mean that standing 2/2/3/A against a dealers 10 could still be the best option due to the fact that this particular composition would have a much lesser probability of appearance, so therefore may not have been considered as much as other S18 compositions in BS calculations averages? or does it still not matter?

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Sure. Everything matters, and yes there are situations where using a total-dependent basic strategy yields slightly incorrect decisions. For example, in single deck you should stand with A78 vs ten, but hit A69 vs ten. (There are actually four 3-card 16vT hands that should be hit: A69, 268, 367 and 466. Stand with all the others.)

Also back to the original point, BS still doesn't take into consideration the composition of other players hands. There must be a cut off point where further deviations from BS must be made when further key cards are out of play? As an extreme example, what if I knew there were no more A's 2's or 3's left in the game? Should I still hit my S18 v 10 and hope for two further cards to improve the hand?

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As others have indicated, if you're interested in playing this accurately, learn to count cards and use the appropriate strategy index numbers. That's what they are for. Search the board for references to the Illustrious 18.

KenSmith said:

As others have indicated, if you're interested in playing this accurately, learn to count cards and use the appropriate strategy index numbers. That's what they are for. Search the board for references to the Illustrious 18.

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Thanks for the info/advise, I have been counting & also shuffle tracking a while now and am fully aware of I18, Although, I'm not quite a pro yet However, as well as live play, I'm also building my backroll by bonus hunting online casinos, as you know, counting isn't possible in this situation. I usally play 5+ hands at once on very low stakes to compromise between ROR and time to complete the WR. Like everybody else, I want to be playing my best game possible at all times and think having good knowledge of table composition would help.

KenSmith said:

QFIT answered this already, but I wanted to make sure the answer is clear... Yes, modern basic strategy charts use full combinatorial analysis and consider every possible composition of a particular total, weighted by the appropriate probability of that composition's appearance.

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Thanks for making that clear. I better get modern lol.

In other words, something like always hit a soft 18 total vs Ace, regardless of the number of cards that comprise it, in a 2D S17 game can never be wrong even though, simultaneously, something like "always stand on any multi-card soft 18 total vs Ace", is also always the right thing to do.

Like your EV would be slightly improved by doing that compared to always hitting any soft 18 but just because it's true for multi-card hands doesn't mean you should stand on A,7 .

Wow, doing splits to 4 hands must be a freakin' nightmare