Open Archive 7

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Re: "ES"

Posted by Cyrus on 7 February 2000, at 10:49 a.m., in response to Re: "ES", posted by Garry Baldy on 7 February 2000, at 12:33 a.m.

"According data from tables I should NOT to early surrender 3,2 v. A or 9,3 v. A or 8,6 v. A... How can it be?"

Cacarulo's tables list the EV's for composition-dependent plays (T6 is examined separately from 97). To get the standard BS Early Surrender table, with total-dependent hands (i.e. not 32vA but 5vA, etc), you should get the EV's for each combination of the hand, weigh the EV's with each hand's probabilities and add to get the weighted EV for the generic total. You need also to adjust for the probability that the dealer may also draw to a natural. (See Cacarulo's post below.)
Example:

Hand          Stand       Hit     Probability    

 62         -0.6627    -0.2016      0.000919      0.4034

 53         -0.6649    -0.2001      0.000919      0.4034

 44         -0.6649    -0.1987      0.00044       0.1932

                                                  1.0000
Weighted    -0.6640    -0.2004

The probability of a dealer natural in this case is 96/309=0.31068, where you lose your full bet. The probability of a dealer non-natural is 1.00-0.31068=0.68932 and taking this into account it's

Standing
(-0.6640 bets)*(0.68932 non-natural) + (-1 bet)*(0.31068 natural)
= -0.7684

Hitting
(-0.2004)*(0.68932) + (-1)*(0.31068)
= -0.4488

So you're better off Hitting 8vA, instead of Surrendering it Early. If you do the same thing for your 14vA, you'll see that you should use ES off the top (and subsequently for any HiLo TC above -9; Wong has the ES HiLo indices in p91 Pro BJ - that's all you'll need instead of all these damn calculations!)...

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