Re: Doubling soft 21

[EMAIL PROTECTED] (Bob R) wrote, "Let's say I'm playing blackjack at a
table and the dealer's hole card has been accidentally exposed to reveal
he has a hard 16. The pit knows the card is up so I don't have to be
fearful of making outrageous plays. I have two tens, so I split them. On
one of them I get an ace. Do I double? I am guessing yes."

You're right to double.  Your EV for a 21 is 12/13, and your EV for
doubling is 14/13.  Below is the derivation.  (In fact, there's a
similar game called "double exposure" in which both dealer's cards are
face up.  When the dealer has hard 16 the player should split a pair of
tens and double on any resulting soft 21's, if allowed to.)

Probablity of dealer getting various totals after hitting hard
16________________________:
dealer21:  1/13
dealer20:  1/13
dealer19:  1/13
dealer18:  1/13
dealer17:  1/13

Player's EV=1-2prob(lose)-prob(push):
player21:  12/13
player20:  10/13
player19:  8/13
player18:  6/13
player17:  4/13
player<17:  3/13

EV for player doubling soft 21 =
2x(4x12/13+10/13+8/13+6/13+4/13+5x3/13)/13
=14/13