Chances of at least one ten...
September 20th, 2012 at 8:02:16 PM
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The chances of getting a ten with one card is 16 out 52, or 30.7%. What are the chances of at least one ten with the first two blackjack cards? It can't just be double 30.7%, that seems unrealistic. What about if you played 3 hands, what are te chances of at least one ten?
I did some guerilla math and came up with 40.38%. I know my method is wrong, but can anyone tell me the right answer, and how you got it? Thanks.
I did some guerilla math and came up with 40.38%. I know my method is wrong, but can anyone tell me the right answer, and how you got it? Thanks.
September 20th, 2012 at 8:19:45 PM
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Last edited by: sodawater on Oct 1, 2018
September 20th, 2012 at 8:22:50 PM
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And here are my results, which depend a little on the number of decks used:
decks P( >0 tens in two cards) P( >0 tens in six cards)
1 52.49% 90.43%
2 52.28% 89.70%
4 52.17% 89.34%
6 52.14% 89.23%
8 52.12% 89.17%
September 20th, 2012 at 9:40:27 PM
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It's easier to work out the chances of not getting a ten. If you're dealing with infinite decks, that would be (9/13)^2 = 47.929%, for a 52.071% chance of getting one. If you're dealing with a single deck, it'd be (34 choose 2)/(52 choose 2) = 42.308%, for a 57.692% chance of getting one. It's always going to be somewhere between those two.
In general, though, yeah, work out the chances that every single card comes from the pool of not-tens, remembering they're not replaced. It's going to be ([number of cards that are not tens] choose [number of cards drawn])/([number of cards] choose [number of cards drawn]); you don't have to know what the "choose" operator is (it's basically an index on Pascal's triangle, or more concretely the factorial of the first number divided by the product of the factorial of the second and that of the difference), since Google calculator has it.
In general, though, yeah, work out the chances that every single card comes from the pool of not-tens, remembering they're not replaced. It's going to be ([number of cards that are not tens] choose [number of cards drawn])/([number of cards] choose [number of cards drawn]); you don't have to know what the "choose" operator is (it's basically an index on Pascal's triangle, or more concretely the factorial of the first number divided by the product of the factorial of the second and that of the difference), since Google calculator has it.
The trick to poker is learning not to beat yourself up for your mistakes too much, and certainly not too little, but just the right amount.
September 20th, 2012 at 11:00:57 PM
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You are all wrong. The chances of getting at least one ten in two cards 14.79%.
The chances of getting at least one ten, jack, queen, or king with two cards is 52,07%.
You all need to improve either your assertions or your math.
The chances of getting at least one ten, jack, queen, or king with two cards is 52,07%.
You all need to improve either your assertions or your math.
At my age, a "Life In Prison" sentence is not much of a deterrent.
September 20th, 2012 at 11:14:10 PM
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In blackjack, every face card is as well understood as a "ten".
September 20th, 2012 at 11:40:35 PM
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Last edited by: sodawater on Oct 1, 2018
September 21st, 2012 at 8:51:21 AM
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@ DRich... Please learn the rules of blackjack before you start insulting people. A ten value is any face card.
