Re: Blackjack Strategy
BJ is not the mathematically easiest game to do Martingale scenarios in, for two reasons:
1) The chance of a win is 46%, chance of a loss 54%, assuming that pushes are simply ignored and another hand played with an unchanged bet, because what else could you do? (MicroBob, your saying a 51% chance of loss is incorrectly giving pushes some value, but they have no effect on the Martingale progression and have to be ignored and replayed). (Also, my BJ days are long over, my memory of the chance of a non-push hand losing being 54% might be wrong, but I think not). A 54% chance of losing is quite different from a 50% chance (not that any casino games offer that). The chance of 15 losses in a row with a 54% chance of losing is 3.2 times higher than with a 50% chance of losing (and 2.4 times higher than your 51%)
2) Many BJ hands are not even-money propositions. If you get a blackjack, you're paid 3:2, so how do you account for that? (assuming the chance of a blackjack is 1-in-21, there's almost exactly a 50% chance of getting at least one within the 15 hands you are proposing). Even worse for hands that offer splits or doubles (or both). These extra bets might win or lose. If they lose, for example, do you quadruple your next wager? Given that, from memory, about 12% of BJ hands are split or doubled (I am very hazy on that number, might be otherwise, but should be similar), again it is likely that your 15 hand sequence will get messed up.
But otherwise your mathematics are fine (although, as I say above, the chance of a 15-loss streak is 2.4 times more than you use (ignoring pushes).
Using equally likely poker examples is a good idea (we've all had successive hands with pocket pairs, so know that does happen enough so that if we had $163k riding on the outcome, we'd be a bit nervous).
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