railer
railer
Joined: Mar 2, 2012
  • Threads: 8
  • Posts: 17
May 23rd, 2020 at 11:49:40 PM permalink
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!
DogHand
DogHand
Joined: Sep 24, 2011
  • Threads: 1
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Thanks for this post from:
ksdjdjrailer
May 24th, 2020 at 10:28:16 PM permalink
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
railer
railer
Joined: Mar 2, 2012
  • Threads: 8
  • Posts: 17
May 25th, 2020 at 3:39:53 PM permalink
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!
DogHand
DogHand
Joined: Sep 24, 2011
  • Threads: 1
  • Posts: 381
May 26th, 2020 at 10:02:17 AM permalink
railer,

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
railer
railer
Joined: Mar 2, 2012
  • Threads: 8
  • Posts: 17
May 27th, 2020 at 1:00:05 AM permalink
Very useful! Thanks a lot!

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