RICH119
RICH119
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March 12th, 2024 at 9:07:57 PM permalink
An 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?
unJon
unJon
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March 12th, 2024 at 9:11:05 PM permalink
Quote: RICH119

An 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 race is not always to the swift, nor the battle to the strong; but that is the way to bet.
RICH119
RICH119
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Dieter
March 12th, 2024 at 9:17:38 PM permalink
Either dealt a natural blackjack which the dealer matches with his own blackjack(a push) or you hit until you got a total of 21 and the dealer also hits until they received 21(a push).
aceside
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March 13th, 2024 at 8:45:38 AM permalink
The 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%.
unJon
unJon
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March 13th, 2024 at 9:07:53 AM permalink
Quote: aceside

The 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).
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
SOOPOO
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March 13th, 2024 at 4:00:42 PM permalink
Quote: RICH119

An 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.
ssho88
ssho88
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March 13th, 2024 at 9:26:02 PM permalink
And yet player may need to change their bs strategy(if the bonus justify to do so) and the probability of getting 21 will change as well....
aceside
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March 14th, 2024 at 7:19:47 AM permalink
Deleted.
aceside
aceside
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March 14th, 2024 at 7:21:55 AM permalink
Quote: unJon

Quote: aceside

The 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.
SOOPOO
SOOPOO
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March 14th, 2024 at 10:20:54 AM permalink
Quote: aceside

Quote: unJon

Quote: aceside

The 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.
link to original post



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.
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