thinking about spanish 21...
the dealer can bust on 22, 23, 24, 25, and 26.
Are these totals all equally likely? Or does the dealer make say 22 more often than 24?
What about the player?
To bust, the dealer must take a card on a "bustable" hand.
To get to 26 from 16 there is a four (4) card draw from 16.
To get to 22 there is drawing a 10 to a 12, a 9 to a 13, etc.
a "stiff hand" can bust with a variety of hands from 22 to 25
because of multi-card draws of "baby cards."
The reader must take care to note the H17 vs. S17 rule plays into this issue.
A Soft 17 cannot break upon receiving a 3rd card. However, the
Soft 17 may become a Soft 12 though Soft 16, which may bust
on receiving a 5th (or following) card.
The following table shows the probability of the dealer's final total, conditioned on busting (assuming infinite deck since the finite shoe doesn't really affect the gist of the problem):
This is essentially a slightly less elegant version of the following problem: roll a single die repeatedly until the sum of all rolls first exceeds 6000. What is the most likely final total, or are all possible totals (6001, 6002, 6003, 6004, 6005, 6006) equally likely? Intuition might suggest that all totals are roughly, or perhaps even exactly, equally likely. But in fact 6001 is roughly six times more likely than 6006.Code:S17 H17 ====================== 22 0.257907 0.257752 23 0.230067 0.229998 24 0.201117 0.201126 25 0.171048 0.171126 26 0.139861 0.139998
I'm not going to try to work this out. Gut says, since 12 is 25% (approx) more likely than 13,14,15,16, then 22 is most likely bust total.Originally Posted by Meistro123
I note also, and to which I believe Meistro has also alluded to, is that dealer not busting on 22 adds something like 6% to house advantage, where applicable, and which adds credence, right or wrong, to my comments.
I might have a different opinion, however, if I decide to actually figure this out.
It depends; although the dealer's "strategy" is fixed, the player's decisions influence the probabilities of him busting on a given amount (or at all). For example, playing with a "mimic the dealer" strategy, the probability that dealer and player bust with the same amount (conditioned on busting in the first place) is the inner product of the above vector with itself, normalized to sum to 1. Or if there is some sort of side bet motivating this question, the player's strategy may not necessarily be to solely maximize return on the initial wager.
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