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Blackjack - Composition-Dependent Strategy

First of all, I would like to add my name to the growing list of people who love your web site. Your information is quite valuable to both the beginning and expert gambler, and you present your findings in a pleasant, understandable, and even humorous manner. I always check out your site before I head to Las Vegas or Lake Tahoe just to remind me how to play smartly.

Anyway, on to my question. Well, more of an observation: when the dealer pulls a 5 on a 16 for their sixth consecutive win, there's always someone who gets up and leaves the table, muttering that the dealer is a mean cruel heartless soul, and goes in search of a "hotter" table. But is there any truth in this? Obviously the dealer is inconsequential to the cards dealt (I like to say the dealer is "simply a messenger of the cards") but are streaks in an 8-deck shoe inevitable, and even predictable? Or is it more like your roulette example, where the odds of each new round are exactly the same? Thanks once again for your web site.

Dave K. from Beverly Hills, California

Thanks for your kind words. Streaks, such as the dealer drawing a 5 to a 16, are inevitable but not predictable. Blackjack is not entirely a game of independent trials like roulette, but the deck is not predisposed to run in streaks. For the non-card counter it may be assumed that the odds are the same in each new round. Putting aside some minor effects of deck composition, the dealer who pulled a 5 to a 16 the last five times in a row would be just as likely to do it the next time as the dealer who had been busting on 16 for several hours.

Appendix 3b: Composition dependent exceptions to double deck basic strategy where the dealer stands on soft 17. Do these apply to multiple (4, 6 and 8) deck games or is there NO variation from Basic Strategy on these?

Trevor from Northampton, United Kingdom

No, these exceptions should not be used for 4-8 decks. There are a few exceptions in 4-8 deck games but they are so border line that it isn’t worth the bother to learn them. An interesting rule of thumb for all numbers of decks is that with 16 vs. 10, where the 16 is composed of 3 or more cards, in general the odds favor standing.

I have reviewed your blackjack site and FAQ, and I have a question about your Blackjack House Edge Calculator. From your description of methodology: "The program played each hand according to the correct basic strategy for those rules without regard to composition dependent exceptions." Can you explain how you determined total-dependent strategy (e.g., that which maximizes expected value)?

anonymous

First, to those who don’t know, composition dependent strategy considers each and ever card in the player’s hand. Total dependent strategy only cares about the total, whether the hand is soft or hard, and whether it is a pair. So the basic strategy is total dependent. However the analysis of blackjack is generally composition dependent. The way derive the basic strategy charts is to take every composition of an initial two card hand and weight the expected value of each play by the probability of the composition. Let’s look at the case where the dealer stands on a soft 17 and the player has a 13 against a 2. The following table shows the composition dependent expected return of standing and hitting of all ways to compose a 2-card 13. The final column is the conditional probability of each compostion.

Expected values of 13 agaisnt 2

Player Cards Stand EV Hit EV Conditional Probability
7,6 -0.265046 -0.331966 0.142857
8,5 -0.264895 -0.331281 0.142857
9,4 -0.285726 -0.293008 0.142857
10,3 -0.31239 -0.304215 0.571429

If we take the weighted average of standing and hitting we get the following expected values:

Stand: -0.29503
Hit: -0.31045

Although hitting 10,3 is the better play overall standing has the greater expected value and is thus the better play.

Thank you for your composition dependent basic strategy exceptions. However in The Theory of Blackjack Peter Griffin says the player should stand on 4+4+4+4 against an 8 in single deck. Is he wrong or did you overlook this play?

anonymous

Griffin is of course correct. The expected value of hitting is -0.552613 and standing is -0.535787. Some plays I don’t list because they are either so obscure I didn’t find them or so unlikely I didn’t bother to list them.

First, great site. Second, sorry if this is in the wrong category, I did my best. Finally, Appendix 3B mentions a program used to come to all of the composition dependant strategy. I was wondering if this program was available for purchase or if you could just give me the formula used to determine what any given hand’s optimal play would be given the removal of any number of other cards (lise the perfect play calculator at gamblingtools.net). Thanks.

Chuck from Spring, TX

Thanks. My program is not very user friendly. I would recommend you use the blackjack calculator at gamblingtools.net, which will give you perfect advice for any situation and deck composition.