Originally Posted by
aceside
I've done some rough calculation. Consider the player starting hand (3,2,2,2)v6. To reach a 6-card 21 for a 2:1 bonus payout, we have three channels for it, and the resulting player hands and their probabilities are:
(3,2,2,2,2,T), probability=(1/12)*(3/12);
(3,2,2,2,3,9), probability=(1/12)*(1/12);
(3,2,2,2,4,8), probability=(1/12)*(1/12).
The total probability is 5/144 on top of this 4-card hand. For the Spanish 21 hand of 9v6, the Hit EV without bonus is 0.156 and the Double EV is 0.161. If we include the 6-card 21 bonus, the total Hit EV becomes,
EV=0.156x(1+5/144)=0.161.
This means that the critical point TC for the n-card decision is TC=-4. If Kat TC>-4, we double down on a 4-card 9v6; if Kat TC<=-4, we hit on a 4-card 9v6.
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