el_jefe: late surrender variation

[el_jefe]

I?m wondering what the effect of allowing late surrender at any point in the player?s turn (even after hitting or doubling) would have on the basic strategy expectation for a 1D, H17 game. I took a rough crack at the calculation below, and I would appreciate any feedback.

Basically, it seems like this rule would benefit the player in two ways.

1) After doubling 11 v 8, 9, T, or A or 10 v 8 or 9 the player would be allowed to surrender if he doesn?t make a hand totaling 17 or more. In each case this would be the correct play based on the EV?s in Appendix A of BJA3 (EV for standing is less than ?0.5). (Note, the correct play is to surrender 17 v A, but it is such a close play that it should have little effect on the overall EV.)

The effect of this can be quantified from the following (summed for all 6 of the above plays):

frequency of occurrence x prob. total will be less than 17 x EV gain from surrender

for example the 11 v A case would be:

(0.0026)x(5/13)x(0.09)=0.000090

and the total of the 6 cases would be 0.00044

2) Hands initially totaling less than 15 v T or A could become 15 or 16 after hitting (at which time the correct play would be to surrender).

This effect can be quantified from the following (summing for all plays):

prob. initial total < 15 x prob. dealer total equals specific value x prob. hand becomes 15 or 16 x EV gain from surrender

for example the 15 or 16 v A case would be:

(0.4)x(1/13)x(2/13)x(0.09)=0.00043

(I realize these values are not exact, but should be a reasonable estimate)

and the total of both cases would be 0.0010

Thus making the total EV gain for this rule (both 1 and 2) roughly 0.00144 or 0.144% (less than I had expected)

I assume this would also reduce the variance (and increase the SCORE), but it?s beyond my present ability to calculate that.

I also have a couple specific questions for anyone who is still with me:

The gain would probably be even larger for an AP, care to guess by what amount?

Index numbers would be needed for the surrender after doubling plays. I doubt the count would ever be large enough to make it correct to stand against an A (since the EV gain from surrender is initially about 0.09), but index plays might occur when doubling against a dealer T since the initial EV gain is only about 0.03. Any comments on this? I?m not sure if the index number would be positive or negative let alone what the magnitude would be.

Thanks,
el_jefe

[Zenfighter]

With the late surrender rule in effect, it is correct to surrender any stiff after doubling down against 8,9,T and Ace.

An increase of 0.1% in EV will be a fairly estimate of the gain available, when this exotic rule applies. My guess, is that you?re not too wrong with your estimate. (Due mainly to the difference between a shoe-game and a hand-held one)

Now your SCORE question can be answered knowing that:

DI^2 = SCORE that?s the same like

((W/100) / SD)^2

For the sake of simplicity let?s keep the SD fixed and wary only the %w/l. Given that we have here a squaring factor, your SCORE will increase in an exponential way. That?s the main reason, why meagre increases in win rate can achieve acceptable ones in SCORE.

An example:

Assume you have a healthy 1.30% advantage. Now raising ?only? by 0.1% means the SCORE increasing by:

(1.40/1.30)^2 ?1 = 15.98% which is a wonderful jump.

My two cents for your questions.

Sincerely

Zenfighter