7up: When should we surrender against 7?

[7up]

We are told ??Never??, because the chance for dealer??s bust is always higher than 25%.

But this is not the case when the ratio of neutral cards is below 1/13.
An example:
Here is some data from Keith Collins:
dealing from a 6 deck shoe, using a weighted average of all possible subsets relative to Hi-Lo:
Cards in deck = 52 (Running count = +10, no specific removals) : TC = +10

p(2) = 5.79879280021777E-2

p(7) = 7.59376758901768E-2

p(1) = 9.64494664637162E-2

p(10) = 3.85797865854865E-1
Since there are no specific removals -
p(6) = p(5) = p(4) = p(3) = p(2)
p(9) = p(8) = p(7)
p(10) = 4 * p(1)

This gives the chance of dealer??s bust below 25%

[Don Schlesinger]

Hi-Lo indices (you never specified a count) for surrendering against 7 are, according to Wong's "Pro BJ" (approximately):

16: +12
15: +10
14: +16

But, I'm not comfortable with the index for 16 being higher for that of 15. Maybe someone can sim.

Don

[LVBear584]

But, I'm not comfortable with the index for 16 being higher for that of 15. Maybe someone can sim.

Drawing an Ace is more beneficial when you are holding 16 vs. 7 than it is when holding 15 vs. 7.

[7up]

[kc]

> We are told ??Never??, because the chance for
> dealer??s bust is always higher than 25%.

> But this is not the case when the ratio of neutral
> cards is below 1/13.
> An example:
> Here is some data from Keith Collins:
> dealing from a 6 deck shoe, using a weighted average
> of all possible subsets relative to Hi-Lo:
> Cards in deck = 52 (Running count = +10, no specific
> removals) : TC = +10

> p(2) = 5.79879280021777E-2

> p(7) = 7.59376758901768E-2

> p(1) = 9.64494664637162E-2

> p(10) = 3.85797865854865E-1
> Since there are no specific removals -
> p(6) = p(5) = p(4) = p(3) = p(2)
> p(9) = p(8) = p(7)
> p(10) = 4 * p(1)

> This gives the chance of dealer??s bust below 25%

I think the case you listed was for a running count of +10 dealt from 6 decks and to a pen where 52 cards remain -

 

Cards in deck = 52 

    p(2) = 5.79879280021777E-2 

    p(3) = 5.79879280021777E-2 

    p(4) = 5.79879280021777E-2 

    p(5) = 5.79879280021777E-2 

    p(6) = 5.79879280021777E-2 

    p(7) = 7.59376758901767E-2 

    p(8) = 7.59376758901767E-2 

    p(9) = 7.59376758901767E-2 

    p(10) = 3.85797865854865E-1 

    p(1) = 9.64494664637162E-2 

.
This equates approximately to a deck comp of 3,3,3,3,3,4,4,4,20,5. If a 7 is removed and player is assigned a hand of hard 16 his draw win % is .2529 and his stand win % is .2498. So for this one particular run count/pen, the best play would be to hit, followed by surrender, then stand. It is a close decision. Other run count/pens may yield different results. I think the surrender index should be some sort of statistical composite of these.

BTW, surrender vs 7 will be a pretty rare occurrence.

kc

[Norm Wattenberger]

For HiLo, 4.5/6, Half-deck resolution, I get:

vs 7

16 Hit
15 +12
14 +18

[Zenfighter]

4 dks , s17 (same as PBJ) and 75% dealt out

 

Precision: 5 sigma 

Maximum number of pairs of hands at index: 1000 million 

 

 

HARD STANDING 16 versus 7 up 

 

          STAND                     HIT  

 12:  Adv.:-49.829, SEr 0.093  Adv.:-51.211, SEr 0.088  Dif.: 1.382, SEr 0.120 

 13:  Adv.:-50.142, SEr 0.124  Adv.:-51.793, SEr 0.118  Dif.: 1.651, SEr 0.161 

 14:  Adv.:-50.292, SEr 0.151  Adv.:-52.572, SEr 0.142  Dif.: 2.280, SEr 0.195 

 15:  Adv.:-50.449, SEr 0.199  Adv.:-53.443, SEr 0.186  Dif.: 2.994, SEr 0.257 

 16:  Adv.:-50.920, SEr 0.251  Adv.:-54.307, SEr 0.234  Dif.: 3.387, SEr 0.324 

 

Determined surrender index: 13  

 

 

HARD STANDING 15 versus 7 up 

 

          STAND                     HIT  

 12:  Adv.:-49.592, SEr 0.093  Adv.:-50.560, SEr 0.090  Dif.: 0.968, SEr 0.123 

 13:  Adv.:-50.117, SEr 0.125  Adv.:-51.386, SEr 0.120  Dif.: 1.270, SEr 0.165 

 14:  Adv.:-50.184, SEr 0.151  Adv.:-52.537, SEr 0.144  Dif.: 2.353, SEr 0.200 

 15:  Adv.:-50.375, SEr 0.199  Adv.:-53.594, SEr 0.189  Dif.: 3.219, SEr 0.263 

 

Determined surrender index: 13  

 

 

HARD STANDING 14 versus 7 up 

 

Determined surrender index: Never Surrender 

Number of pairs of hands played: 131994720 

 

Well, as you can see here, drawing a card with 16 vs. 7 at TC13 is more expensive than for the other fellow who holds 15 vs. 7.

Sincerely

Zenfighter

[Don Schlesinger]

> For HiLo, 4.5/6, Half-deck resolution, I get:

> vs 7

> 16 Hit
> 15 +12
> 14 +18

Does "hit" imply that it could never be right to surrender? Why would that be? See Zenfighter's post.

Don

[Don Schlesinger]

As I said, my gut told me that something was amiss with Wong's indices.

Don

[7up]

Using ??Dealer Probabilities Calculator?? at qfit.com, with Keith Collins?? data:

Cards in deck = 52 (Running count = +10, no specific removals) : TC = +10
Dealer??s busing chance= 0.2498

Cards in deck = 208 (Running count = +40, no specific removals) : TC = +10
Dealer??s busing chance= 0.2534

Does it mean anything?

Some places offer surrender after double.

[Francis Salmon]

I presume you are Keith Collins.You must have realized your results contradict Zenfighter's who gives standing as the better strategy than hitting for both 16 and 15 v 7 in all double-digit TCs.
I think their is a problem with your method. If I got you right you want to remove the 7 and the two cards of the player's hand only after having established the most probable subset thus removing three more bust cards.This is wrong.When we are facing such a hand, we have already counted the involved cards and there are now 52 cards remaining with an RC of +10.
If you want to remove the 7,you have to do it from the full 312 cards and the resulting frequency of the 7 in the subset of 52 will be 23/6 =3.8 and not only 3 as with your method.Would that explain the difference?

Francis Salmon

[Francis Salmon]

Vs 7
Hit 14 always
Surrender 15 at +18
Surrender 16 at +12

This would make more sense.

[Norm Wattenberger]

Do you count 8,8v7 separately? CVData looks to see if you are also asking for an 88 index. If you are, it excludes 88 from the general index. If not, it includes 88. I get +12 when you also ask for an 88 index. If you gen a general number for all 16v7, CVData says no surrender. So if you exclude 88, I get:

16v7 +12 (Split on 88)
15v7 +12
14v7 +18