EV of pairs
I would assume that on average, EV would be considerably high since having a guaranteed option to split is a powerful 'Get out of Jail Free' card. But is there an easy way to calculate this besides running a simulation and combing through a bunch of data?
Quote: ChucklesWhat is the expected value of receiving a splitable pair in blackjack? Lets assume 6d h17 DAS NRSA SR and using basic strategy. Any pair of cards is equally likely (10-value cards considered separately, so Q-J wouldn't count) and against any dealer hand.
I would assume that on average, EV would be considerably high since having a guaranteed option to split is a powerful 'Get out of Jail Free' card. But is there an easy way to calculate this besides running a simulation and combing through a bunch of data?
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There are offensive splits that make you money and defensive splits that will cause you to lose less. Not all splits are equal.
Quote: billryanQuote: ChucklesWhat is the expected value of receiving a splitable pair in blackjack? Lets assume 6d h17 DAS NRSA SR and using basic strategy. Any pair of cards is equally likely (10-value cards considered separately, so Q-J wouldn't count) and against any dealer hand.
I would assume that on average, EV would be considerably high since having a guaranteed option to split is a powerful 'Get out of Jail Free' card. But is there an easy way to calculate this besides running a simulation and combing through a bunch of data?
link to original post
There are offensive splits that make you money and defensive splits that will cause you to lose less. Not all splits are equal.
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Indeed! I played blackjack a long time before I learned that splitting 8s merely helps you to lose less in the long run — splitting 8s doesn't enable you to win in the long run.
Quote: smoothgrhQuote: billryanQuote: ChucklesWhat is the expected value of receiving a splitable pair in blackjack? Lets assume 6d h17 DAS NRSA SR and using basic strategy. Any pair of cards is equally likely (10-value cards considered separately, so Q-J wouldn't count) and against any dealer hand.
I would assume that on average, EV would be considerably high since having a guaranteed option to split is a powerful 'Get out of Jail Free' card. But is there an easy way to calculate this besides running a simulation and combing through a bunch of data?
link to original post
There are offensive splits that make you money and defensive splits that will cause you to lose less. Not all splits are equal.
link to original post
Indeed! I played blackjack a long time before I learned that splitting 8s merely helps you to lose less in the long run — splitting 8s doesn't enable you to win in the long run.
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Splitting 8’s against 2-7 ‘enables you to win in the long run’.
Actually, anything that increases your EV ‘enabled you to win in the long run’. Losing less on a single hand ‘enables you to win in the long run’.
The above assumes you were playing a game that the EV was positive, or would be positive with your strategy.
If not, just change my answer to ‘Splitting 8’s ‘enables you to lose less in the long run’.
Quote: SOOPOOQuote: smoothgrhQuote: billryanQuote: ChucklesWhat is the expected value of receiving a splitable pair in blackjack? Lets assume 6d h17 DAS NRSA SR and using basic strategy. Any pair of cards is equally likely (10-value cards considered separately, so Q-J wouldn't count) and against any dealer hand.
I would assume that on average, EV would be considerably high since having a guaranteed option to split is a powerful 'Get out of Jail Free' card. But is there an easy way to calculate this besides running a simulation and combing through a bunch of data?
link to original post
There are offensive splits that make you money and defensive splits that will cause you to lose less. Not all splits are equal.
link to original post
Indeed! I played blackjack a long time before I learned that splitting 8s merely helps you to lose less in the long run — splitting 8s doesn't enable you to win in the long run.
link to original post
Splitting 8’s against 2-7 ‘enables you to win in the long run’.
Actually, anything that increases your EV ‘enabled you to win in the long run’. Losing less on a single hand ‘enables you to win in the long run’.
The above assumes you were playing a game that the EV was positive, or would be positive with your strategy.
If not, just change my answer to ‘Splitting 8’s ‘enables you to lose less in the long run’.
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Sorry, I meant "splitting 8s against a dealer 10 or A" — a defensive split.
Quote: acesideWizard shows the value of pair splitting is 0.57%.
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Thanks! Is there a page or post on this that breaks down the calculation?
The following website from the Wizard of Odds:
https://wizardofodds.com/games/blackjack/rule-variations/
Shows that if splitting is NOT allowed, the change in EV is
"Player may not split -0.57%"
Technically, this is for an 8D, H17, DA2, DAS game, but it is close enough for other shoe games.
I would guess this result is from combinatorial analysis (CA), but I am not certain.
Hope this helps!
Dog Hand
Let us estimate the remaining EV gain. The best pair splitting situation is 8,8 vs 6, where player gains an EV of 0.497. The most marginal pair splitting situation can be 3,3 vs 2, where player gains an EV of 0.
Player splits only when dealer upcard is a 2, 3, 4, 5, 6, or 7, and only when player holds a 2, 3, 6, 7, 8, or 9. Therefore, player splits only about 1/4 of the non-Ace pairs. The EV gain from splitting all non-Ace pairs is
(1/13) x (12/13) x (1/4) x (0.497/2) =0.00441.
Therefore, the overall EV gain from splitting is
0.00441 + 0.0018=0.00621 = 0.621%.
Quote: acesideThis can be estimated. The rules for splitting a pair of Aces differ from those of other pairs. Wizard shows that the EV gain from splitting Aces is 0.18%.
Let us estimate the remaining EV gain. The best pair splitting situation is 8,8 vs 6, where player gains an EV of 0.497. The most marginal pair splitting situation can be 3,3 vs 2, where player gains an EV of 0.
Player splits only when dealer upcard is a 2, 3, 4, 5, 6, or 7, and only when player holds a 2, 3, 6, 7, 8, or 9. Therefore, player splits only about 1/4 of the non-Ace pairs. The EV gain from splitting all non-Ace pairs is
(1/13) x (12/13) x (1/4) x (0.497/2) =0.00441.
Therefore, the overall EV gain from splitting is
0.00441 + 0.0018=0.00621 = 0.621%.
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What about splitting 9s why isn’t that included?
Quote: acesideSplitting 9s is included in the above calculation, but splitting 4s is excluded for the purpose of simplifying calculation. This is just a rough estimation, but it is close enough.
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I was on a business trip with my boss about 28 years ago and we were playing Blackjack. He chastised me for splitting fours against a 6. We argued about the right play and eventually he conceded that I was right. The problem is that we bet $200 on who was correct and he never paid me. At the time hist net worth was probably close to $20 million. I am still pissed about that.
