Blackjack odds of winning chart
I am looking for a complete table / analysis showing what a player's simple odds of win / lose / push are, immediately after the deal, assuming the player will be proceeding according to basic strategy. I am envisioning a chart that would look just like the classic basic strategy layout, but instead of showing what action the player should take, it would show what the player's percent chance of winning is, assuming the basic strategy is followed.
As a side note, to be complete, I imagine this would probably need to be at least two sets of charts, since knowing the winning % alone for a given hand would not communicate what the chances of losing vs pushing are.
I have seen similar charts including the Wizard's video on the probability of receiving each possible hand, and what the expected value/return of each possible hand are. But I am specifically interested in the winning % chances.
An infinite deck analysis would be fine. In an ideal world, I could see it as it would be under common vegas rules. Perhaps this is published in a book somewhere, but I have been unable to find anything. Any guidance on where I might look would be appreciated. Or if there is a way to back-calculate it from other published data. Thanks!
Are doubles included as two bets or one?
Is surrender occurring?
What about splits?
Multiple splits?
Double after splits?
Blackjack count as 1 win or 1.5 wins?
Anyway, why do you care about the answer to your question? What can you possibly use the answer for?
https://youtu.be/jCF-Btu5ZCk
(Wizard's video on how to calculate basic strategy)
I have no idea what you're up to, but hopefully it's clever. Best of luck.
Quote: SOOPOOYour question does not give enough information to give a simple answer.
Are doubles included as two bets or one?
Is surrender occurring?
What about splits?
Multiple splits?
Double after splits?
Blackjack count as 1 win or 1.5 wins?
Anyway, why do you care about the answer to your question? What can you possibly use the answer for?
link to original post
He is looking for percentage of the hands that a player will win, tie and lose. There is nothing ambiguous. He is not weighing the outcomes by the total amount of money wagered.
A Double Down affects the size of the wager, but if you lose -you lost money on that hand. If you win -you won money on the hand. If you push then its a tie.
When you split - if you win one and lose one -its a tie. If you win both-it counts as a win. if you lose both split hands, then you have lost that hand.
If you surrender, you have lost money on the hand.
A blackjack is a win.
These percentages have been calculated by Wizard and many other people. The win %, lose% and tie % for a typical set of BJ rules are reported on the WOO site -I don't have the time to look for it right now, but perhaps someone will provide the numbers for OP.
(As I remember, a BJ player using basic strategy will win on something like 43.4% of the hands.)
Quote: acesideWizard’s win, loss, tie rates are probably simulation results. I haven’t seen these numbers from exact calculation.
link to original post
aceside,
Bzzzzt! Guess again.
In other words, the EV's shown at
https://wizardofodds.com/games/blackjack/expected-values/
are from Combinatorial Analysis (CA), not from simulation. Thus, you HAVE seen these numbers from exact calculation!
Hope this helps!
Dog Hand
Quote: gordonm888Quote: SOOPOOYour question does not give enough information to give a simple answer.
Are doubles included as two bets or one?
Is surrender occurring?
What about splits?
Multiple splits?
Double after splits?
Blackjack count as 1 win or 1.5 wins?
Anyway, why do you care about the answer to your question? What can you possibly use the answer for?
link to original post
He is looking for percentage of the hands that a player will win, tie and lose. There is nothing ambiguous. He is not weighing the outcomes by the total amount of money wagered.
A Double Down affects the size of the wager, but if you lose -you lost money on that hand. If you win -you won money on the hand. If you push then its a tie.
When you split - if you win one and lose one -its a tie. If you win both-it counts as a win. if you lose both split hands, then you have lost that hand.
If you surrender, you have lost money on the hand.
A blackjack is a win.
These percentages have been calculated by Wizard and many other people. The win %, lose% and tie % for a typical set of BJ rules are reported on the WOO site -I don't have the time to look for it right now, but perhaps someone will provide the numbers for OP.
(As I remember, a BJ player using basic strategy will win on something like 43.4% of the hands.)
link to original post
Ummmm. No!!!! It is AMBIGUOUS. One could EASILY argue that winning one and losing one after splitting is NOT a tie. But rather one win and one loss. Which CERTAINLY results in an overall different percentage of wins/losses/ or ties! And OF COURSE if you surrender you have lost money on a hand. You aren’t able to envision someone counting that as 1/2 a loss???
Quote: CostaAzul
I am looking for a complete table / analysis showing what a player's simple odds of win / lose / push are, immediately after the deal, assuming the player will be proceeding according to basic strategy. I am envisioning a chart that would look just like the classic basic strategy layout, but instead of showing what action the player should take, it would show what the player's percent chance of winning is, assuming the basic strategy is followed.
link to original post
You would need multiple charts. The results will vary depending on shoe composition and rules of the game.
You can use 'The Wizard of Odds Blackjack Hand Calculator' to describe the number of decks and rules to determine the best return for a hand.
Quote: DogHandQuote: acesideWizard’s win, loss, tie rates are probably simulation results. I haven’t seen these numbers from exact calculation.
link to original post
aceside,
Bzzzzt! Guess again.
In other words, the EV's shown at
https://wizardofodds.com/games/blackjack/expected-values/
are from Combinatorial Analysis (CA), not from simulation. Thus, you HAVE seen these numbers from exact calculation!
Hope this helps!
Dog Hand
link to original post
I just followed your link and found Wizard’s EV numbers for a 6-deck Stand-17 game:
For the hand of T, 6 vs T, the stand, hit, and double EV numbers respectively are:
-0.540954, -0.534676, -1.069351.
But these are not them. I guess the OP is asking, what are the win, tie, loss rates of this hand. Like win 18% loss 79% if player hits.
The program prints out charts like this straight out of the box for your choice of rules.
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
Quote: Mental|snip|If you can program (or find someone else to do it), you could easily get it to calculate the numbers you need. But I still have no clue why you would want/need those numbers.
link to original post
1. Maybe OP is designing a sidebet, and needs to know the frequency of ties. Or some sidebet that also has an additional condition that it only pays off when dealer wins. Or when dealer loses.
2. Maybe he is writing a book or an article about blackjack and wants to comment on why a player may often feel that he is losing more hands than he is winning. Because player is indeed losing more frequently than he wins.
3. Maybe he is comparing the win/tie/lose rates of various games:
- In Mississippi Stud and Four Card Poker you win a very low percentage of the time (Four Card poker has something like a 25% win rate)
- In Blackjack you win about 43.6% of the time
- In Ultimate Texas Hold'em, how often do you tie? When you don't tie, you probably lose a hand slightly more frequently than you get paid off, because sometimes you fold a hand that would have won if you had stayed in.
- Player actually wins >55% of the time in the super pai gow poker game played in St Maarten in which the dealer has 8 cards from which to make his front and back hands - but for which player wins the ante bet and pushs the raise bet if one of his two hands (front and back) beats the dealer's analogous hand. This is because many of player's wins are small (+ one unit) and almost all of player' losses are at least 2 units.
Personally, I find this kind of stuff interesting. Perhaps its academic game theory but IMO there's no reason to dismissively challenge someone for asking an intelligent question, the way that the other forum member did.
Quote: gordonm888
- In Ultimate Texas Hold'em, how often do you tie? When you don't tie, you probably lose a hand slightly more frequently than you get paid off, because sometimes you fold a hand that would have won if you had stayed in.
Using Wizard's numbers, I calculated these UTH numbers. Player win 47%, tie 3%, and loss 50%.
Quote: MentalIf you can program (or find someone else to do it), you could easily get it to calculate the numbers you need. But I still have no clue why you would want/need those numbers.
I used your above table data to calculate the hand of T, 6 vs T.
If player hits it, the win, tie, and loss rates are about 21%, 5%, and 74%, respectively.
Yes, there are certainly plenty of situations in BJ where the calculations are easy because you will never draw more than one card. The situations where you are dealt hard 17+ are even easier to run against the dealer percentages. However, the dealer outcome chart does not take into account EOR and is for a specific set of rules. I think the chart I posted was for 8 decks, H17 and no surrender. Eric starts his program output with a summary of rules. I ran it for single deck because I think it is cool how he has a huge set of composition-dependent variations for single deck.Quote: acesideQuote: MentalIf you can program (or find someone else to do it), you could easily get it to calculate the numbers you need. But I still have no clue why you would want/need those numbers.
I used your above table data to calculate the hand of T, 6 vs T.
If player hits it, the win, tie, and loss rates are about 21%, 5%, and 74%, respectively.
link to original post
1 deck, H17, DOA, DAN, DAS, SPL3, NRSA, CDP
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 h s s h h h h h
9- 3 | h h s s s h h h h h
8- 4 | h s s s s h h h h h
7- 5 | h s 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 | DH DH DH DH DH H H h h h
6- 3 | DH DH DH DH DH H H h h h
5- 4 | DH 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 | S DS DS DS DS S S h h h
A- 6 | DH 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 DH DH DH H h h h h
A- 3 | H H DH DH DH H H h h h
A- 2 | H H H DH DH 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 ps
8- 8 | Ps Ps Ps Ps Ps Ph ph ph ph ph
7- 7 | ps Ps Ps Ps Ps ph ph h s h
6- 6 | ph Ps Ps Ps Ps ph 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 | ph 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 | 10.445855313
3 | 14.216032812
4 | 19.054182101
5 | 24.395644205
6 | 25.254383035
7 | 15.080827372
8 | 5.740679215
9 | -4.211584755
10 | -17.012106655
A | -38.827569810
---------------------------------
Total | 0.238463297
Up | Probability of outcome of dealer's hand
card | Bust | 17 | 18 | 19 | 20 | 21 |Blackjack
-------------------------------------------------------------------------------
2 | 0.35635 | 0.12978 | 0.13311 | 0.13317 | 0.12562 | 0.12197 | 0.00000
3 | 0.37808 | 0.12353 | 0.13194 | 0.12495 | 0.12421 | 0.11730 | 0.00000
4 | 0.40580 | 0.12279 | 0.11537 | 0.12191 | 0.11779 | 0.11635 | 0.00000
5 | 0.42996 | 0.11666 | 0.12384 | 0.11745 | 0.10524 | 0.10686 | 0.00000
6 | 0.43776 | 0.11611 | 0.11381 | 0.11606 | 0.10962 | 0.10666 | 0.00000
7 | 0.25985 | 0.37234 | 0.13858 | 0.07733 | 0.07890 | 0.07299 | 0.00000
8 | 0.23863 | 0.13086 | 0.36299 | 0.12944 | 0.06829 | 0.06979 | 0.00000
9 | 0.23344 | 0.12189 | 0.10392 | 0.35739 | 0.12225 | 0.06111 | 0.00000
10 | 0.21426 | 0.11442 | 0.11288 | 0.11466 | 0.32888 | 0.03647 | 0.07843
A | 0.14039 | 0.05612 | 0.14095 | 0.14148 | 0.14375 | 0.06358 | 0.31373
-------------------------------------------------------------------------------
Total | 0.28749 | 0.13444 | 0.13969 | 0.13676 | 0.17778 | 0.07557 | 0.04827
Composition-dependent stand/hit strategy variations:
----------------------------------------------------
( 49) Hard 16 vs. A : stand except, 88, 79, 6T, 466, 367, 349, 33T, 277, 268, 259, 24T, 2338, 2266, 2248, 2239, 222T, 22228, A78, A69, A5T, A366, A348, A339, A267, A258, A249, A23T, A2238, A2229, AA77, AA68, AA59, AA4T, AA338, AA266, AA248, AA239, AA22T, AA2228, AA22226, AAA67, AAA58, AAA49, AAA3T, AAA256, AAA238, AAA229, AAA2236, AAA2227
( 69) Hard 16 vs. 7 : stand except, 88, 79, 6T, 556, 466, 457, 448, 367, 358, 349, 33T, 3346, 3337, 277, 268, 259, 24T, 2446, 2356, 2347, 2338, 2266, 2257, 2248, 2239, 22336, 222T, 22246, 22237, 22228, A78, A69, A5T, A456, A447, A366, A357, A348, A339, A3336, A267, A258, A249, A23T, A2346, A2337, A2256, A2247, A2238, A2229, AA77, AA68, AA59, AA4T, AA446, AA356, AA347, AA338, AA266, AA257, AA248, AA239, AA22T, AAA67, AAA58, AAA49, AAA229, AAAA66, AAAA39
( 56) Hard 16 vs. 8 : hit except, 4444, 3445, 3355, 33334, 2455, 23344, 23335, 22444, 22345, 223333, 22255, 222334, 222244, 222235, A555, A3444, A3345, A2445, A2355, A23334, A22344, A22335, A22245, A222333, A222234, AA455, AA3344, AA3335, AA2444, AA2345, AA23333, AA2255, AA22334, AA22244, AA22235, AA222233, AAA445, AAA355, AAA3334, AAA2344, AAA2335, AAA2245, AAA22333, AAA22234, AAA22225, AAAA444, AAAA345, AAAA336, AAAA3333, AAAA255, AAAA2334, AAAA2244, AAAA2235, AAAA2226, AAAA22233, AAAA22224
( 48) Hard 16 vs. 9 : stand except, 88, 79, 6T, 466, 457, 367, 349, 33T, 3346, 3337, 277, 268, 259, 24T, 2356, 2347, 2266, 2257, 2239, 22336, 222T, 22237, A78, A69, A5T, A447, A366, A357, A339, A3336, A267, A23T, A2337, A2247, A22236, A22227, AA77, AA68, AA4T, AA347, AA266, AA257, AA22T, AA2237, AAA67, AAA3T, AAA337, AAAA66
( 19) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 268, 2266, 22336, 222T, A69, A366, A267, A22236, AA68, AA266, AA22T, AA22226, AAA67, AAAA66
( 15) Hard 15 vs. A : hit except, 456, 366, AAAA56, AAAA47, AAAA38, AAAA344, AAAA335, AAAA29, AAAA245, AAAA236, AAAA2333, AAAA227, AAAA2234, AAAA2225, AAAA22223
( 1) Hard 15 vs. 7 : hit except, AAAA2333
( 9) Hard 15 vs. T : hit except, 555, 456, 366, A455, A356, A266, AA355, AAA66, AAAA56
( 11) Hard 14 vs. A : hit except, AAAAT, AAAA55, AAAA46, AAAA37, AAAA334, AAAA28, AAAA244, AAAA235, AAAA226, AAAA2233, AAAA2224
( 1) Hard 14 vs. T : hit except, 77
( 8) Hard 13 vs. A : hit except, AAAA9, AAAA45, AAAA36, AAAA333, AAAA27, AAAA234, AAAA225, AAAA2223
( 7) Hard 12 vs. A : hit except, AAAA8, AAAA44, AAAA35, AAAA26, AAAA233, AAAA224, AAAA2222
( 7) Hard 12 vs. 2 : hit except, 22224, A56, A22223, AA55, AAAA8, AAAA26, AAAA2222
( 17) Hard 12 vs. 3 : stand except, 39, 2T, 2334, 2235, 2226, 22233, 22224, A2333, A2234, A2225, A22223, AAT, AA2233, AAA333, AAA2223, AAAA233, AAAA2222
( 2) Hard 12 vs. 4 : stand except, 2T, AAT
( 1) Hard 11 vs. 2 : hit except, 22223
( 1) Hard 8 vs. 2 : hit except, 2222
( 6) Soft 18 vs. A : stand except, A7, A34, A25, AA6, AA24, AAA5
( 4) Soft 18 vs. T : hit except, A223, AA33, AA222, AAA23
( 1) Soft 17 vs. A : hit except, AAAA3
( 1) Soft 16 vs. A : hit except, AAAA2
( 1) Soft 14 vs. A : hit except, AAAA
( 19) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 268, 2266, 22336, 222T, A69, A366, A267, A22236, AA68, AA266, AA22T, AA22226, AAA67, AAAA66.
For a player hard 16 vs T, most likely player will hit, so naturally it’s better to list the result in the other way, as follows,
Hard 16 vs T: hit except, what? What? What?
Also, player 88 is not counted as a hard 16. It’s a pair.
I didn't study this part of Eric's code, but this list is auto-generated. I assume the decision to 'hit except X, Y, Z, ...' has a longer list or at least more hands. Otherwise, why would Eric flip it to 'stand except'? You can look at the code yourself or try to ask Eric.Quote: acesideI looked into your spoiler results of composition-dependent strategy, but feel confused, especially about this part:
( 19) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 268, 2266, 22336, 222T, A69, A366, A267, A22236, AA68, AA266, AA22T, AA22226, AAA67, AAAA66.
For a player hard 16 vs T, most likely player will hit, so naturally it’s better to list the result in the other way, as follows,
Hard 16 vs T: hit except, what? What? What?
Also, player 88 is not counted as a hard 16. It’s a pair.
link to original post
The treatment of 88 as an exception here seems overly cautious, but you must agree that you do not stand on 88.
Quote: acesideI looked into your spoiler results of composition-dependent strategy, but feel confused, especially about this part:
( 19) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 268, 2266, 22336, 222T, A69, A366, A267, A22236, AA68, AA266, AA22T, AA22226, AAA67, AAAA66.
For a player hard 16 vs T, most likely player will hit, so naturally it’s better to list the result in the other way, as follows,
Hard 16 vs T: hit except, what? What? What?
Also, player 88 is not counted as a hard 16. It’s a pair.
link to original post
I changed one character in Eric's source code to flip the list to the way you think is more natural.
< bool hit = (2 * hitHands > numHands);
---
> bool hit = !(2 * hitHands > numHands);
After recompiling:
Composition-dependent stand/hit strategy variations:
----------------------------------------------------
(127) Hard 16 vs. T : hit except, 556, 457, 448, 4444, 358, 349, 3445, 33T, 3355, 3346, 3337, 33334, 277, 259, 24T, 2455, 2446, 2356, 2347, 2338, 23344, 23335, 2257, 2248, 22444, 2239, 22345, 223333, 22255, 22246, 22237, 222334, 22228, 222244, 222235, A78, A5T, A555, A456, A447, A357, A348, A3444, A339, A3345, A3336, A258, A249, A2445, A23T, A2355, A2346, A2337, A23334, A2256, A2247, A2238, A22344, A22335, A2229, A22245, A222333, A22227, A222234, AA77, AA59, AA4T, AA455, AA446, AA356, AA347, AA338, AA3344, AA3335, AA257, AA248, AA2444, AA239, AA2345, AA2336, AA23333, AA2255, AA2246, AA2237, AA22334, AA2228, AA22244, AA22235, AA222233, AAA58, AAA49, AAA445, AAA3T, AAA355, AAA346, AAA337, AAA3334, AAA256, AAA247, AAA238, AAA2344, AAA2335, AAA229, AAA2245, AAA2236, AAA22333, AAA2227, AAA22234, AAA22225, AAAA57, AAAA48, AAAA444, AAAA39, AAAA345, AAAA336, AAAA3333, AAAA2T, AAAA255, AAAA246, AAAA237, AAAA2334, AAAA228, AAAA2244, AAAA2235, AAAA2226, AAAA22233, AAAA22224
Clearly, Eric chose the more concise method even if you think it is naturally better to list the result as 'hit except'.
Admittedly, I don't expect to see AAAA22224 vs. T in my lifetime. But if your aim is to be comprehensive, then 'stand except' is a shorter list.
To clarify several comments/questions: what I am after is *not* the expected values or returns of a given hand. Also I have seen the overall win%, but I have not seen it on a per-hand basis, including in the Wizard’s videos and appendices. If what I am after can be calculated from the published EVs per hand, I can’t figure out how.
I kept my original post short and did not specify exact rules, because if the data I am seeking was available in some form somewhere, which I assumed it was, I would have been happy to accept whatever rules (assuming representative of a reasonable playable table in Vegas) were chosen to calculate the percentages that win/lose/tie by hand.
I was/am willing to go with an infinite deck analysis, because I assume this increases my likelihood of finding the data (easier to calculate). But to provide specifics, if helpful, in order to best tie to an infinite deck I would probably go with commonly available/reasonably favorable:
6 decks, S17, double after splitting, resplitting aces
This was the intention of my original vague “standard Vegas rules” reference – apologies.
Surrender:
I would be fine assuming surrender is not possible. I don’t think surrender rules change the spirit of my request. If I wanted to add in surrender rules, it would be an easy overlay because the outcome of a surrender is known and guaranteed.
Double Down:
The size of the wager relative to the base wager is irrelevant to my request.
Note if the rules require a given situation to only receive one more card, then those rules must be followed. However it would not change the fact that by following the rules and the basic strategy each hand will still have *some* certain % chance of win, lose, and tie.
Splitting:
I am not completely sure how to think about this. When I wrote my original post I assumed this data was out there and whoever published it would have provided a mathematically correct explanation for how splits should be considered. I welcome others’ thoughts. But I think: Since both post-split hands will have equal percent chances to win/lose/tie in an infinite deck, that the proper answer would be based on analyzing the % chance of a single given card (i.e. 2,3,4,6,7,8,9,A) to win/lose/tie against each dealer upcard, following the next steps required by blackjack/basic strategy. And then, calculating each of the six unique possibilities (win-win, loss-loss, tie-tie, win-loss (x2), win-tie (x2), loss-tie (2x). For my purposes, I was assuming a win-win = win, a win/loss = tie, and a loss-loss = loss, but I see how others could interpret differently) for each of the base single cards and then rolling up those answers to give “The” *pre-split* correct values for “% win, % lose, % tie” of the dealt parent pair hand. [I realize there is additional complexity from the chances of re-splitting the split, but I assume that could be easily accounted for.]
In summary, I am looking for the discrete distribution for each possible player hand vs dealer card, immediately after the deal, showing:
% chance of winning the hand
% chance of losing the hand
% chance of tying the hand
Thanks!
Quote: CostaAzulThanks for the many replies.
To clarify several comments/questions: what I am after is *not* the expected values or returns of a given hand. Also I have seen the overall win%, but I have not seen it on a per-hand basis, including in the Wizard’s videos and appendices. If what I am after can be calculated from the published EVs per hand, I can’t figure out how.
I kept my original post short and did not specify exact rules, because if the data I am seeking was available in some form somewhere, which I assumed it was, I would have been happy to accept whatever rules (assuming representative of a reasonable playable table in Vegas) were chosen to calculate the percentages that win/lose/tie by hand.
I was/am willing to go with an infinite deck analysis, because I assume this increases my likelihood of finding the data (easier to calculate). But to provide specifics, if helpful, in order to best tie to an infinite deck I would probably go with commonly available/reasonably favorable:
6 decks, S17, double after splitting, resplitting aces
This was the intention of my original vague “standard Vegas rules” reference – apologies.
Surrender:
I would be fine assuming surrender is not possible. I don’t think surrender rules change the spirit of my request. If I wanted to add in surrender rules, it would be an easy overlay because the outcome of a surrender is known and guaranteed.
Double Down:
The size of the wager relative to the base wager is irrelevant to my request.
Note if the rules require a given situation to only receive one more card, then those rules must be followed. However it would not change the fact that by following the rules and the basic strategy each hand will still have *some* certain % chance of win, lose, and tie.
Splitting:
I am not completely sure how to think about this. When I wrote my original post I assumed this data was out there and whoever published it would have provided a mathematically correct explanation for how splits should be considered. I welcome others’ thoughts. But I think: Since both post-split hands will have equal percent chances to win/lose/tie in an infinite deck, that the proper answer would be based on analyzing the % chance of a single given card (i.e. 2,3,4,6,7,8,9,A) to win/lose/tie against each dealer upcard, following the next steps required by blackjack/basic strategy. And then, calculating each of the six unique possibilities (win-win, loss-loss, tie-tie, win-loss (x2), win-tie (x2), loss-tie (2x). For my purposes, I was assuming a win-win = win, a win/loss = tie, and a loss-loss = loss, but I see how others could interpret differently) for each of the base single cards and then rolling up those answers to give “The” *pre-split* correct values for “% win, % lose, % tie” of the dealt parent pair hand. [I realize there is additional complexity from the chances of re-splitting the split, but I assume that could be easily accounted for.]
In summary, I am looking for the discrete distribution for each possible player hand vs dealer card, immediately after the deal, showing:
% chance of winning the hand
% chance of losing the hand
% chance of tying the hand
Thanks!
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Your question is clear now. Just curious…. why does this matter to you? I’m not being ‘dismissive’ like the Administrator implies, rather, the answer may lead to a more interesting discussion.
The Wizard breaks out the full distribution for every result from -8 units to +8 units in these charts. This is needed to calculate the exact variance of a random starting hand.
OP just wants something similar for every particular starting three cards. Obviously, he is not using it to calculate variance. Eric's program recursively plays out each hand every possible way that it can play out. He returns the EVs and probabilities. What is needed for OP's question is to carry back not just the EV, which is an average, but the entire distribution of results. It would not be easy to modify the code to do this.
As an example for this hand of T, 6 vs. T, they are roughly
21% chance of winning,
74% chance of losing,
5% chance of tying.
For a finite deck game, the calculation of basic strategy is still problematic, as far as I know. How is it possible you can get these numbers?
Is this question directed to me? For a finite deck game, the calculation of basic strategy is solved by enumerating every possible reachable state and seeing whether it is a win, tie, loss, or BJ. Then, you carry this information back to the previous state and see which decision has the higher EV. This takes a fraction of a second. BJ is really a simple game with very few game states. Infinite deck is the same except that it is slightly easier to get the probabilities for each branch in the decision tree.Quote: acesideI don’t quite understand this question, but for an infinite deck, these numbers can be calculated.
As an example for this hand of T, 6 vs. T, they are roughly
21% chance of winning,
74% chance of losing,
5% chance of tying.
For a finite deck game, the calculation of basic strategy is still problematic, as far as I know. How is it possible you can get these numbers?
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Quote: MentalQuote: acesideI looked into your spoiler results of composition-dependent strategy, but feel confused, especially about this part:
( 19) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 268, 2266, 22336, 222T, A69, A366, A267, A22236, AA68, AA266, AA22T, AA22226, AAA67, AAAA66.
For a player hard 16 vs T, most likely player will hit, so naturally it’s better to list the result in the other way, as follows,
Hard 16 vs T: hit except, what? What? What?
Also, player 88 is not counted as a hard 16. It’s a pair.
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I changed one character in Eric's source code to flip the list to the way you think is more natural.
< bool hit = (2 * hitHands > numHands);
---
> bool hit = !(2 * hitHands > numHands);
After recompiling:
Composition-dependent stand/hit strategy variations:
----------------------------------------------------
(127) Hard 16 vs. T : hit except, 556, 457, 448, 4444, 358, 349, 3445, 33T, 3355, 3346, 3337, 33334, 277, 259, 24T, 2455, 2446, 2356, 2347, 2338, 23344, 23335, 2257, 2248, 22444, 2239, 22345, 223333, 22255, 22246, 22237, 222334, 22228, 222244, 222235, A78, A5T, A555, A456, A447, A357, A348, A3444, A339, A3345, A3336, A258, A249, A2445, A23T, A2355, A2346, A2337, A23334, A2256, A2247, A2238, A22344, A22335, A2229, A22245, A222333, A22227, A222234, AA77, AA59, AA4T, AA455, AA446, AA356, AA347, AA338, AA3344, AA3335, AA257, AA248, AA2444, AA239, AA2345, AA2336, AA23333, AA2255, AA2246, AA2237, AA22334, AA2228, AA22244, AA22235, AA222233, AAA58, AAA49, AAA445, AAA3T, AAA355, AAA346, AAA337, AAA3334, AAA256, AAA247, AAA238, AAA2344, AAA2335, AAA229, AAA2245, AAA2236, AAA22333, AAA2227, AAA22234, AAA22225, AAAA57, AAAA48, AAAA444, AAAA39, AAAA345, AAAA336, AAAA3333, AAAA2T, AAAA255, AAAA246, AAAA237, AAAA2334, AAAA228, AAAA2244, AAAA2235, AAAA2226, AAAA22233, AAAA22224
Clearly, Eric chose the more concise method even if you think it is naturally better to list the result as 'hit except'.
Admittedly, I don't expect to see AAAA22224 vs. T in my lifetime. But if your aim is to be comprehensive, then 'stand except' is a shorter list.
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There is something incorrect about this list. How can anyone have a hard 16 that is AAAA22224 without having a soft 19-21 or a very unattractive soft 18 which should be stood on? By "very unattractive" I mean a soft 18 in which many of the 2's and Ace's are gone.
The best way to make a soft 18 with these cards is 2-2-2-A-A vs T. Presumably, you would then draw a 4 to give you a hard 12 and then proceed to make a hard 16 with more aces and deuces. However a single deck '2-2-2-A-A vs T' is Stand EV= -0.1982; Hit EV= -0.2004. So AAAA22224 shouldn't be on this list.
The same is true of other extreme hands on this list such as AAAA2334. You can't make a hard 16 wth these cards without inbcorrectly hitting a soft 18 (and drawing the 4). Ex: single deck Soft 18: AA33 vs T is Stand EV= -0.1107; Hit EV = -0.1735. So its massively incorrect to hit such a soft 18 on the way to making a hard 16.
The rules in Eric's list are correct. I agree that some rules are superfluous because you cannot reach that decision point employing correct strategy. If it bothers you, write some code to cull the list and post it here or send it to Eric.Quote: gordonm888
There is something incorrect about this list. How can anyone have a hard 16 that is AAAA22224 without having a soft 19-21 or a very unattractive soft 18 which should be stood on? By "very unattractive" I mean a soft 18 in which many of the 2's and Ace's are gone.
The best way to make a soft 18 with these cards is 2-2-2-A-A vs T. Presumably, you would then draw a 4 to give you a hard 12 and then proceed to make a hard 16 with more aces and deuces. However a single deck '2-2-2-A-A vs T' is Stand EV= -0.1982; Hit EV= -0.2004. So AAAA22224 shouldn't be on this list.
The same is true of other extreme hands on this list such as AAAA2334. You can't make a hard 16 wth these cards without inbcorrectly hitting a soft 18 (and drawing the 4). Ex: single deck Soft 18: AA33 vs T is Stand EV= -0.1107; Hit EV = -0.1735. So its massively incorrect to hit such a soft 18 on the way to making a hard 16.
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Quote: gordonm888Quote: MentalQuote: acesideI looked into your spoiler results of composition-dependent strategy, but feel confused, especially about this part:
( 19) Hard 16 vs. T : stand except, 88, 79, 6T, 466, 367, 268, 2266, 22336, 222T, A69, A366, A267, A22236, AA68, AA266, AA22T, AA22226, AAA67, AAAA66.
For a player hard 16 vs T, most likely player will hit, so naturally it’s better to list the result in the other way, as follows,
Hard 16 vs T: hit except, what? What? What?
Also, player 88 is not counted as a hard 16. It’s a pair.
link to original post
I changed one character in Eric's source code to flip the list to the way you think is more natural.
< bool hit = (2 * hitHands > numHands);
---
> bool hit = !(2 * hitHands > numHands);
After recompiling:
Composition-dependent stand/hit strategy variations:
----------------------------------------------------
(127) Hard 16 vs. T : hit except, 556, 457, 448, 4444, 358, 349, 3445, 33T, 3355, 3346, 3337, 33334, 277, 259, 24T, 2455, 2446, 2356, 2347, 2338, 23344, 23335, 2257, 2248, 22444, 2239, 22345, 223333, 22255, 22246, 22237, 222334, 22228, 222244, 222235, A78, A5T, A555, A456, A447, A357, A348, A3444, A339, A3345, A3336, A258, A249, A2445, A23T, A2355, A2346, A2337, A23334, A2256, A2247, A2238, A22344, A22335, A2229, A22245, A222333, A22227, A222234, AA77, AA59, AA4T, AA455, AA446, AA356, AA347, AA338, AA3344, AA3335, AA257, AA248, AA2444, AA239, AA2345, AA2336, AA23333, AA2255, AA2246, AA2237, AA22334, AA2228, AA22244, AA22235, AA222233, AAA58, AAA49, AAA445, AAA3T, AAA355, AAA346, AAA337, AAA3334, AAA256, AAA247, AAA238, AAA2344, AAA2335, AAA229, AAA2245, AAA2236, AAA22333, AAA2227, AAA22234, AAA22225, AAAA57, AAAA48, AAAA444, AAAA39, AAAA345, AAAA336, AAAA3333, AAAA2T, AAAA255, AAAA246, AAAA237, AAAA2334, AAAA228, AAAA2244, AAAA2235, AAAA2226, AAAA22233, AAAA22224
Clearly, Eric chose the more concise method even if you think it is naturally better to list the result as 'hit except'.
Admittedly, I don't expect to see AAAA22224 vs. T in my lifetime. But if your aim is to be comprehensive, then 'stand except' is a shorter list.
link to original post
There is something incorrect about this list. How can anyone have a hard 16 that is AAAA22224 without having a soft 19-21 or a very unattractive soft 18 which should be stood on? By "very unattractive" I mean a soft 18 in which many of the 2's and Ace's are gone.
The best way to make a soft 18 with these cards is 2-2-2-A-A vs T. Presumably, you would then draw a 4 to give you a hard 12 and then proceed to make a hard 16 with more aces and deuces. However a single deck '2-2-2-A-A vs T' is Stand EV= -0.1982; Hit EV= -0.2004. So AAAA22224 shouldn't be on this list.
The same is true of other extreme hands on this list such as AAAA2334. You can't make a hard 16 wth these cards without inbcorrectly hitting a soft 18 (and drawing the 4). Ex: single deck Soft 18: AA33 vs T is Stand EV= -0.1107; Hit EV = -0.1735. So its massively incorrect to hit such a soft 18 on the way to making a hard 16.
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I don’t agree with your assumption. If you start with a 2 and 4 Then hit to get a 2 then another 2 then another 2 you have a 12. Then you keep hitting and drawing 4 aces getting yourself to a 16. You never had a soft total.
Quote: unJon
I don’t agree with your assumption. If you start with a 2 and 4 Then hit to get a 2 then another 2 then another 2 you have a 12. Then you keep hitting and drawing 4 aces getting yourself to a 16. You never had a soft total.
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D'oh. You're right and I'm wrong. I had missed that! Seems so obvious in retrospect.
Although, the incredibly thin path to get to hard 16 makes these hands even less probable to occur.
If you are playing with a Charlie bonus, you can also get to hands that would be incorrect for a different game.
