S Yama posted this in another thread: This is a convenient rule of thumb, and I've always assumed it was true in infinite deck. In finite decks, it's not always true, though the cases where it is false may always be extreme. As an illustration, let's say that you have a hard 12, you have only the low, and your opponent has 19. If winning your bet is enough to beat your opponent's push, this is a free-hit situation. Now let's impose an outlandish constraint. The remaining deck is composed of nothing but sixes. Hitting means making 18, and hitting twice means busting. Thus, the usual optimal strategy here (hit to 20) is exactly as effective as standing with 12. (Remember the bust costs you nothing.) However, if your hand total were 14 instead of 12, the usual optimal strategy of hit to 20 does provide an improved chance of advancing. So, at least in this case, we see that standing with 12 is optimal (at least tied with other strategies), yet hitting 14 is better. --------------------------------------------------------------- Follow-ups: 1) Can we create a scenario where standing with 12 is better (not just tied) with hitting, but hitting 14 is better than standing? I'm guessing the answer is yes, if we involve a third player and retain the effects of deck composition. 2) Can an anomaly like this exist in the world of infinite deck? I'm guessing no, but this is an interesting question.
Apples and cherimoyas. What I posted is not just a rule of thumb, it is an optimal strategy for a specific set of information available, or for a specific level of skills even with much richer information. Finite decks? What is it? The full set of cards from the number of decks used minus cards making the hand in question and the dealer upcard? Ken, I think that you got two different techniques slightly mixed up. You should calculate “hitting to” for more than one total only if you are planning to analyze a fixed set of cards, be it the infinite deck, or a specific subset of cards, and only when you are not going to include the newly created deck composition. Then, it will remain the optimum play. If you have more information and capability to process it, you have to use different approach. With a better precision you have to include effects of removal. Then, we must deal with the specific changing subset of cards that have to be recalculated after every card is gone. In that case we always deal with “hit once” and recalculate, time after time. There would be no comparable hit to x or hit to x+1, as the whole set of circumstances changes. Would you say that standing on hard sixteen against the dealer five in a regular blackjack game is a bit more that just a rule of thumb? Even more so, if you knew that the dealer’s hole card is a ten? It would be irrelevant to basic strategy “rules of playing” that you also might have known that in some extreme cases the remaining cards were nothing but fives. Less experienced players could be left under the impression that “the rule” I posted was incorrect, so I allowed myself a broader explanation. When we deal with blackjack tournament playing strategies we may be looking for rules, characteristics, mechanics, patterns, etc., that govern situations within the given circumstances. We find out strategies that statistically offer best results, they are the ones that work most of the time considering most common conditions. A set of these strategies becomes a rule, a generic one, nevertheless, useful one for the existing situation. We could try to include more information to come up with more precise rules (though, they still might remain unchanged) if more information was available. We need to keep in mind possible tradeoffs of precision and impractical complexities. Assumption of the infinite deck is the accepted method of finding correct playing decisions. Basic strategy is based on assumption of dealer’s outcomes for the specific number of decks and removal of cards used to make the hand that is analyzed and the dealer upcard. We aslo may come up with an optimal playing strategy that includes removal of cards of other players in that round. Even better, using a counting system from the very beginning of the shuffle. This still may be improved by using multilevel, multiparameter systems. Then, we can invent some specific subsets of cards left, or even know exactly what the next cards are. This can have a great anecdotal effect: Can you believe it! What’s the chance! All of the above would be creating strategies, and set of them would comprise a set of “rules”, that’re specific for individual situation. Consider a statement: I had a Ten and a four, the dealer showed a Ten -I should hit. But the hi-lo True Count was plus fourteen, so I should stand. But I also knew that the remaining 26 cards consisted of two fives, nine Tens, and fifteen sevens, so I should hit. But as the dealer prepared to deal the next card he exposed it partially and from the pips I could tell it wasn’t a seven. So I stood. It was a five, and the dealer had a seven in the hole, so I lost. This statement invokes four ever-changing rules. The rules are never wrong at any level of available information; they get more and more precise, yet, they still may not work. Ken, I think that there would be no problem if you phrased your question more in the style of: I wonder if what S. Yama posted “xx” holds true for all possible subset of cards? It does if you don’t change the situation in the middle of the play, or if you calculate the chances as the situation changes. You shouldn’t try to negate rules for a specific set of circumstances, then change the situation but keep the rules to prove that there is a better play. It is a bit ironic, that I found myself defending a more universal analysis, while I am one of the very few stating that adjustments for precise changes in deck composition are absolutely necessary for a “professional level” tournament player. Even mixing the two techniques can be okay in practice, but not to make theory comparisons. S. Yama
Yama, you seem to have perceived my post as personal criticism, when it wasn't intended that way at all. The key phrase in my post was "though the cases where it is false may always be extreme." I agree that two of my choices of phrases were subject to misinterpretation... "convenient rule of thumb" is far too timid a phrase to describe the postulate in question, because it's probably true in every single case in the real world. Also, "finite decks" didn't accurately convey the idea that I'm talking about specific compositions of small numbers of cards. I apologize for the possible confusion.
No problem. I will try to find a few additional intersting angles to this subject later this week. Take care, S. Yama
