Quote:RICH119An online casino has a promotion where you receive a bonus if you push on 21, whether you are dealt a natural blackjack or receive more than 2 cards. What are the odds of pushing on a 21?

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Are you saying that if you are dealt a natural and the dealer hits to 21 that’s a push and not a 3:2 win?

The probability of a dealer non-blackjack 21 is 7.3%, but that of a player 7.2%. With these numbers, we have

4.7%^2 +7.3%x7.2% = 0.75%.

Quote:acesideThe probability of a dealer or player blackjack is 4.7%;

The probability of a dealer non-blackjack 21 is 7.3%, but that of a player 7.2%. With these numbers, we have

4.7%^2 +7.3%x7.2% = 0.75%.

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That’s going to be close, but there is correlation between dealer non BJ 21 and player non BJ 21. Chance of player non BJ 21 is much lower with a dealer upcard of 2-6 (limited only to splits and doubles).

Quote:RICH119An online casino has a promotion where you receive a bonus if you push on 21, whether you are dealt a natural blackjack or receive more than 2 cards. What are the odds of pushing on a 21?

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Not directly answering your question, but if the bonus is big enough you would hit certain hands that you wouldn’t necessarily hit if the bonus didn’t exist. ‘Basic strategy’ would change depending on how big the bonus is.

Quote:unJonQuote:acesideThe probability of a dealer or player blackjack is 4.7%;

The probability of a dealer non-blackjack 21 is 7.3%, but that of a player 7.2%. With these numbers, we have

4.7%^2 +7.3%x7.2% = 0.75%.

link to original post

That’s going to be close, but there is correlation between dealer non BJ 21 and player non BJ 21. Chance of player non BJ 21 is much lower with a dealer upcard of 2-6 (limited only to splits and doubles).

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I thought about this again. When the dealer up card is a Deuce, and both the player’s up cards are Deuces, both the dealer and player are more likely to get a non BJ 21 at the same time. Good point. So, the push % number is a little complicated.

Quote:acesideQuote:unJonQuote:acesideThe probability of a dealer or player blackjack is 4.7%;

The probability of a dealer non-blackjack 21 is 7.3%, but that of a player 7.2%. With these numbers, we have

4.7%^2 +7.3%x7.2% = 0.75%.

link to original post

That’s going to be close, but there is correlation between dealer non BJ 21 and player non BJ 21. Chance of player non BJ 21 is much lower with a dealer upcard of 2-6 (limited only to splits and doubles).

link to original post

I thought about this again. When the dealer up card is a Deuce, and both the player’s up cards are Deuces, both the dealer and player are more likely to get a non BJ 21 at the same time. Good point. So, the push % number is a little complicated.

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You can’t even begin to do a reasonable calculation until you know the ratio of the base bet to the bonus. If you are betting $10 and the bonus is $10,000 you will keep hitting until you get 21 or you bust. If the bonus is a penny your calculation is probably correct.