Probability of Multi-Card Hands
May 23rd, 2020 at 11:49:40 PM
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Hello.
I would like to know the probabilities of receiving certain Multi-card hands. (ie. 11, 10, 9, and 21). The calculations aren't that straightforward because a hand like 2,2 v. 6 will be split before it can be hit again.
Maybe the answer is published somewhere?
Thanks!
I would like to know the probabilities of receiving certain Multi-card hands. (ie. 11, 10, 9, and 21). The calculations aren't that straightforward because a hand like 2,2 v. 6 will be split before it can be hit again.
Maybe the answer is published somewhere?
Thanks!
May 24th, 2020 at 10:28:16 PM
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railer,
Do you have a particular rule set in mind: number of decks, S17/H17, DAS/NoDAS, LS/No LS?
Do you want only hard totals, of do you also want to count soft totals?
Also, you do realize that the results involve some overlap: a 9 can turn into an 11, for example.
I believe the answers can be found by simulation using CVData.
Dog Hand
Do you have a particular rule set in mind: number of decks, S17/H17, DAS/NoDAS, LS/No LS?
Do you want only hard totals, of do you also want to count soft totals?
Also, you do realize that the results involve some overlap: a 9 can turn into an 11, for example.
I believe the answers can be found by simulation using CVData.
Dog Hand
May 25th, 2020 at 3:39:53 PM
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Thanks, DogHand.
The game allows doubling on multiple card hands, so that's what I'd like to evaluate.
The particular game is 6deck, H17, DAS, No LS.
Soft totals would be great.
Regarding overlap...The totals I want are the doubling hands....9, 10, only the 11 is an issue, not a big deal. For soft hands the probability of any 3 card Soft Total (that hasn't been doubled or split already) is good enough.
The probability of all multi-card 21s would help too.
Thanks, DH!
The game allows doubling on multiple card hands, so that's what I'd like to evaluate.
The particular game is 6deck, H17, DAS, No LS.
Soft totals would be great.
Regarding overlap...The totals I want are the doubling hands....9, 10, only the 11 is an issue, not a big deal. For soft hands the probability of any 3 card Soft Total (that hasn't been doubled or split already) is good enough.
The probability of all multi-card 21s would help too.
Thanks, DH!
May 26th, 2020 at 10:02:17 AM
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railer,
While not precisely what you requested, here is the output from Eric Farmer's excellent blackjack7 program for this game:
Hope this helps!
Dog Hand
While not precisely what you requested, here is the output from Eric Farmer's excellent blackjack7 program for this game:
6 decks, H17, DOA, DAN, DAS, SPL3, NRSA, CDZ-
Hard | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
10- 9 | S S S S S S S S S S
|
10- 8 | S S S S S S S s s s
|
10- 7 | s s s s s s s s s s
9- 8 | s s s s s s s s s s
|
10- 6 | s s s s s h h h h h
9- 7 | s s s s s h h h h h
|
10- 5 | s s s s s h h h h h
9- 6 | s s s s s h h h h h
8- 7 | s s s s s h h h h h
|
10- 4 | s s s s s h h h h h
9- 5 | s s s s s h h h h h
8- 6 | s s s s s h h h h h
|
10- 3 | s s s s s h h h h h
9- 4 | s s s s s h h h h h
8- 5 | s s s s s h h h h h
7- 6 | s s s s s h h h h h
|
10- 2 | h h s s s h h h h h
9- 3 | h h s s s h h h h h
8- 4 | h h s s s h h h h h
7- 5 | h h s s s h h h h h
|
9- 2 | DH DH DH DH DH DH DH DH DH DH
8- 3 | DH DH DH DH DH DH DH DH DH DH
7- 4 | DH DH DH DH DH DH DH DH DH DH
6- 5 | DH DH DH DH DH DH DH DH DH DH
|
8- 2 | DH DH DH DH DH DH DH DH H H
7- 3 | DH DH DH DH DH DH DH DH H H
6- 4 | DH DH DH DH DH DH DH DH H H
|
7- 2 | H DH DH DH DH H H h h h
6- 3 | H DH DH DH DH H H h h h
5- 4 | H DH DH DH DH H H h h h
|
6- 2 | H H H H H H h h h h
5- 3 | H H H H H H h h h h
|
5- 2 | h h H H H h h h h h
4- 3 | h h H H H h h h h h
|
4- 2 | h h h H H h h h h h
|
3- 2 | h h h H H h h h h h
|
Soft | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
A- 9 | S S S S S S S S S S
A- 8 | S S S S DS S S S S S
A- 7 | DS DS DS DS DS S S h h h
A- 6 | h DH DH DH DH H h h h h
A- 5 | h H DH DH DH h h h h h
A- 4 | h H H DH DH H h h h h
A- 3 | H H H DH DH H H h h h
A- 2 | H H H H H H H h h h
Pair | Dealer's up card
hand | 2 3 4 5 6 7 8 9 10 A
-----------------------------------------------------------
A- A | PH PH PH PH PH PH PH Ph Ph Ph
10-10 | S S S S S S S S S S
9- 9 | PS PS PS PS PS S PS ps s s
8- 8 | Ps Ps Ps Ps Ps Ph ph ph ph ph
7- 7 | ps ps Ps Ps Ps ph h h h h
6- 6 | ph ph Ps Ps Ps h h h h h
5- 5 | DH DH DH DH DH DH DH DH H H
4- 4 | H H H PH PH H h h h h
3- 3 | h ph Ph PH PH ph h h h h
2- 2 | ph Ph PH PH PH Ph h h h h
-----------------------------------------------------------
S = Stand
H = Hit
D = Double down
P = Split
Uppercase indicates action is favorable for the player
Lowercase indicates action is favorable for the house
When more than one option is listed, options are listed from left to right
in order of preference.
Up |
card | Overall expected value (%)
---------------------------------
2 | 9.599268103
3 | 12.965222329
4 | 16.758000634
5 | 20.833490329
6 | 24.394635229
7 | 14.741993579
8 | 5.957821867
9 | -4.011606427
10 | -17.256011289
A | -37.227971003
---------------------------------
Total | -0.385630040
Up | Probability of outcome of dealer's hand
card | Bust | 17 | 18 | 19 | 20 | 21 |Blackjack
-------------------------------------------------------------------------------
2 | 0.35666 | 0.13007 | 0.13598 | 0.13161 | 0.12566 | 0.12002 | 0.00000
3 | 0.37696 | 0.12590 | 0.13193 | 0.12666 | 0.12218 | 0.11637 | 0.00000
4 | 0.39847 | 0.12246 | 0.12541 | 0.12262 | 0.11783 | 0.11322 | 0.00000
5 | 0.41963 | 0.11809 | 0.12304 | 0.11822 | 0.11243 | 0.10859 | 0.00000
6 | 0.43926 | 0.11506 | 0.11457 | 0.11504 | 0.11018 | 0.10588 | 0.00000
7 | 0.26194 | 0.36921 | 0.13793 | 0.07843 | 0.07868 | 0.07382 | 0.00000
8 | 0.24369 | 0.12894 | 0.35995 | 0.12872 | 0.06922 | 0.06947 | 0.00000
9 | 0.22924 | 0.12031 | 0.11735 | 0.35185 | 0.12037 | 0.06088 | 0.00000
10 | 0.21247 | 0.11191 | 0.11167 | 0.11194 | 0.34001 | 0.03482 | 0.07717
A | 0.13915 | 0.05727 | 0.14282 | 0.14294 | 0.14328 | 0.06586 | 0.30868
-------------------------------------------------------------------------------
Total | 0.28576 | 0.13346 | 0.14120 | 0.13568 | 0.18153 | 0.07487 | 0.04749
Composition-dependent stand/hit strategy variations:
----------------------------------------------------
( 24) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 33T, 268, 2266, 2239,
22336, 222T, 222226, A69, A366, A267, A23T, A2229, A22236, AA68, AA266,
AA22T, AA22226, AAA67, AAAA66
-----
24
Hope this helps!
Dog Hand
