Perhaps I can express this in a better way than my first response?
For the purpose of theorizing, the set of hands for self and dealer is 12, 13,14,15, or 16. Therefore, over time, every possible combination will occur equally within that set (for example, my 12 against his 16,15,14,13, or 12). So for practical purposes we can pretend that when I have a 12 he has a 12, when I have a 13 he has a 13....and so on. So we DO "know" what the dealer has for the purpose of examining this hypothetical.
We know that we are equally likely to get 17,18,19, or 20 on a ONE CARD draw. So we can leave that aside.
We know that I have about an 8% chance of 21 on a ONE CARD draw while his probability is 0% (he looked and did not have the ace). So we are left with those instances where we BOTH have 12,13,14,15, or 16.
Knowing he has a 12, I will not draw to MY 12. After all, although he only has 31% chance of breaking on a ONE CARD draw--he also has a 31% chance of being FORCED to draw a second card with even less favourable probabilities. And I am looking at his BEST CASE scenario of beginning with a 12...
Therefore...on his HOLE CARD (using "12" as the starting point) he only has a 38% chance of having 17-20. I am therefore happy to give up my chance for a second draw (which I would not make anyway when he has 12-16 and I have drawn to a ten) for the benefit of an 8% chance of getting 21 outright by drawing an ace...and the benefit of doubling the bet.
If my advantage is .01 % it is monstrous because of the doubled bet...over time. If my disadvantage is .01 % it is monstrous because of the doubled bet...over time. I certainly do not know mathematically which way the cookie crumbles. That is beyond by knowledge and skill. But a depth of experience assures me I am correct. Yet, wrong I may well be!
I think it is close enough that it would only affect a daily player who was playing for a living and experiencing the inevitability of long-term probability. Still, I appreciate that you expressed your opinion. It caused me to think it through and to have some doubt. And I have no desire on this thread to be right! I want to learn and to become a better gambler! This issue is not critical. It is about betting strategies and money management. The house edge is ALWAYS there... |
