Odds of this in BJ?
October 12th, 2014 at 4:55:39 AM
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A question for the math-heads.
Background: was dealing to a high-end group last night, the usual up and down, some more down than up for being BS challenged. Anyway one hand everyone got paid when I busted. A woman said how that hadn't happened yet. I replied with polite banter but mostly went back to DUAD. But I did think she was right, it was rare.
So, math-wise:
1. What are the odds that a dealer will bust and every player on the 7-seat table gets paid. Assume also that no player has had BJ since we would have paid that already.
2. For fun, what are the odds every player would beat the dealer but the dealer did not bust?4
If it matters, rule is S17 and 4 decks.
Background: was dealing to a high-end group last night, the usual up and down, some more down than up for being BS challenged. Anyway one hand everyone got paid when I busted. A woman said how that hadn't happened yet. I replied with polite banter but mostly went back to DUAD. But I did think she was right, it was rare.
So, math-wise:
1. What are the odds that a dealer will bust and every player on the 7-seat table gets paid. Assume also that no player has had BJ since we would have paid that already.
2. For fun, what are the odds every player would beat the dealer but the dealer did not bust?4
If it matters, rule is S17 and 4 decks.
All animals are equal, but some are more equal than others
October 13th, 2014 at 8:38:50 AM
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Given that each players hands would be more so 'random' you really would be looking at how often the dealer busts with a "bust" card. For example, if the dealer has a 6 up, AND if everyone is playing "basic strategy" then no one should bust out. So assuming no BJ's, and no busts, it would be the table against the dealer. Ignoring situations where people have 20, so they might still win if the dealer has 17 or something, we're just looking for the times where the dealer busts, which will result in a "table win."
Answer to #1: These numbers are all figured by the wizard here.
For #2, this would be quite situationally dependent. Does everyone have 20? Does one person have 20 and another have 13, but standing to dealer 6? In the latter case this would just be the result from answer #1. There's entirely too many combinations of hands. If this would be done it would have to be a simulation of specific situations. I would expect if you were to find an answer to this question it would again be dealer card specific as well.
Answer to #2: It's not worth the time to run simulations of millions of combinations of hands, especially when you're at a BJ table and your bets/bankroll are the only one's that matter mathematically.
Answer to #1: These numbers are all figured by the wizard here.
For #2, this would be quite situationally dependent. Does everyone have 20? Does one person have 20 and another have 13, but standing to dealer 6? In the latter case this would just be the result from answer #1. There's entirely too many combinations of hands. If this would be done it would have to be a simulation of specific situations. I would expect if you were to find an answer to this question it would again be dealer card specific as well.
Answer to #2: It's not worth the time to run simulations of millions of combinations of hands, especially when you're at a BJ table and your bets/bankroll are the only one's that matter mathematically.
Playing it correctly means you've already won.
October 16th, 2014 at 1:37:25 PM
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Answer to 1 (Rough Estimate)
Dealer Busts around 28%
Player Bust slightly less (because of not hitting sriiffs when dealer has 2-6), Do not know the exact % but should be around 25%. So no Bust around 75%.
So 7 Players No Bust, Dealer Bust = 28% * 75%^7 = 4%
So you should see it happen around 2 times an hour (assume 50 hands per hour for full table)
The 2nd question is a lot more difficult to calculate.
Dealer Busts around 28%
Player Bust slightly less (because of not hitting sriiffs when dealer has 2-6), Do not know the exact % but should be around 25%. So no Bust around 75%.
So 7 Players No Bust, Dealer Bust = 28% * 75%^7 = 4%
So you should see it happen around 2 times an hour (assume 50 hands per hour for full table)
The 2nd question is a lot more difficult to calculate.
