Revision
k_c said:
My program computes partial hands. For 6 decks, S17 I get the value of A-A:
Allowed to split aces one time +32.3458%
Allowed to split aces two times +42.7504%
Allowed to split aces three times +44.4513%
Assuming full peek, it is + EV to split aces vs all up cards, so it is it always right to double your bet on the first card. The probability of player being dealt A-A from 6 decks is 24/312*23/311 = .005689
Additional advantage (vs all up cards):
Split(1) +32.3458%*.005689 = .1840%
Split(2) +42.7504%*.005689 = .2432%
Split(3) +44.4513%*.005689 = .2529%
agrees with estimate.
k_c
I'm going to redo the refinement for 1 split from my previous post because I did not take into account that player would lose his original bet only if dealer had an ace up and subsequently had blackjack. You might not want to try this at home, folks
.
EV(1 card to split ace) v A = -26.6858% assuming player loses to dealer BJ
Multiply by 2 because there are 2 hands; -26.6858%*2 = -53.3716%
Dealer probability of blackjack for A-A v A = 96/309 = 31.0680%
Lose only 1 unit on dealer BJ -53.3716%+31.0680=-22.3037%
Therefore overall EV to split aces once v A = -22.3037% (lose to BJ, full peek)
If A-A v A was doubled, player would lose an extra 22.3037%
Prob of A-A v A = 24/312*23/311*22/310 = .0004037
Gain by not doubling A-A v A = 22.3037%*.0004037=.0090
EV(Split once/double A-A vs all up cards) = +32.3458%*.005689 = .1840%
EV(Split once/double A-A vs 2-10 only) = .1840% + .0090% = .1930%
I hope that's right:grin:
k_c