Out of curiosity because of the last thread about the odds of dealer busting with 14 (S17), I've tried doing the same with 13 and was surprised - there is ~ 52% for the dealer to bust with it. Of course, the edge is very small and trying to guess if the dealer's gonna have 3 after showing up the 10 upcard, or 10 with the 3 upcard is never a good idea, however, just for the sake of probability, can you check if I'm doing it right?
Possible outcomes (x means bust and next to it is the probability of that happening):
13 > x 5/13 (Hitting on 13 and busting)
13 > 14 > x 1/13 * 6/13 (Hitting on 13, getting A, hitting on 14 and busting)
13 > 14 > 15 > x 1/13 * 1/13 * 7/13 (Hitting on 13, getting A, hitting on 14, getting A, hitting on 15 and busting)
13 > 14 > 15 > 16 > x 1/13 * 1/13 * 1/13 * 8/13 (Hitting on 13, getting A, hitting on 14, getting A, hitting on 15, getting A, hitting on 16 and busting)
13 > 14 > 16 > x 1/13 * 1/13 * 8/13 (Hitting on 13, getting A, hitting on 14, getting 2, hitting on 16 and busting)
13 > 15 > x 1/13 * 7/13 (Hitting on 13, getting 2, hitting on 15 and busting)
13 > 15 > 16 > x 1/13 * 1/13 * 8/13 (Hitting on 13, getting 2, hitting on 15, getting A, hitting on 16 and busting)
13 > 16 > x 1/13 * 8/13 (Hitting on 13, getting 3, hitting on 16 and busting)
So:
5/13 +
(1/13 * 6/13) +
(1/13 * 1/13 * 7/13) +
(1/13 * 1/13 * 1/13 * 8/13) +
(1/13 * 1/13 * 8/13) +
(1/13 * 7/13) +
(1/13 * 1/13 * 8/13) +
(1/13 * 8/13)
~ 52%
Is this right?
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