13 card chances
August 11th, 2010 at 4:54:11 PM
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If you deal out 13 cards to 4 stacks, is it easier to 6 pairs and an extra card or no face cards? (10s included in the no face card)
August 11th, 2010 at 9:18:08 PM
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If I deal them face up, it will be equally easy to do either.
The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw
August 12th, 2010 at 4:48:45 AM
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the probability of not getting any face cards in 13 drawn out of a single deck is
36/52*35/51*34/50 ... * 23/39 = (36!*38!)/(22!*52!) = 0.002146
I am a little confused about the other condition. Why are we drawing to 4 stacks? Does it mean that we can only pair up the top cards in the stacks? For example if the first four cards are 2 3 4 5, and the next for are 5 4 3 2, is this four pairs or none?
36/52*35/51*34/50 ... * 23/39 = (36!*38!)/(22!*52!) = 0.002146
I am a little confused about the other condition. Why are we drawing to 4 stacks? Does it mean that we can only pair up the top cards in the stacks? For example if the first four cards are 2 3 4 5, and the next for are 5 4 3 2, is this four pairs or none?
"When two people always agree one of them is unnecessary"
August 12th, 2010 at 5:46:52 PM
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Quote: weaselmanthe probability of not getting any face cards in 13 drawn out of a single deck is
36/52*35/51*34/50 ... * 23/39 = (36!*38!)/(22!*52!) = 0.002146
I am a little confused about the other condition. Why are we drawing to 4 stacks? Does it mean that we can only pair up the top cards in the stacks? For example if the first four cards are 2 3 4 5, and the next for are 5 4 3 2, is this four pairs or none?
Your formula is for 14 cards not 13. 36 to 23 is 14 cards.
I assume your are delt 13 cards from a 52 card deck for both:
there are combin(36,13)ways to get no faces 2310789600
there are combin(13,6)*pow(6,6)*28 ways to get 6 pairs and a single card 2241727488
If you are counting quads as 2 pair and/or trips as a pair and the single card, there are more ways. I'll calculate tem if you need them.
“Man Babes” #AxelFabulous
August 12th, 2010 at 6:33:53 PM
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Quote: mipletYour formula is for 14 cards not 13. 36 to 23 is 14 cards.
Indeed. Today must be one of my "off by one" days :) For 13 cards, I get 0.00364.
"When two people always agree one of them is unnecessary"
August 13th, 2010 at 12:41:53 PM
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basically this is for 13 card poker or commonly called 13 card chinese poker, im a little confused on some bonus bets that are given. It seems like with 13 cards its easier to get no face cards than it is to get 6 pairs with an extra card.
August 13th, 2010 at 12:54:07 PM
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For six pairs and a singleton:
Combinations = COMBIN(13,6)*7*6^6*4 = 2241727488
Probability = 0.003530204.
No face cards:
Combinations = COMBIN(40,13) = 12033222880
Probability = 0.018949553.
Combinations = COMBIN(13,6)*7*6^6*4 = 2241727488
Probability = 0.003530204.
No face cards:
Combinations = COMBIN(40,13) = 12033222880
Probability = 0.018949553.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 13th, 2010 at 6:38:05 PM
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Why 40? Aren't there 36 non-face cards, counting 10s?
"When two people always agree one of them is unnecessary"
August 13th, 2010 at 7:09:16 PM
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I suppose it depends on whether you consider the ace a "face" card.
August 13th, 2010 at 8:27:19 PM
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Quote: weaselmanWhy 40? Aren't there 36 non-face cards, counting 10s?
I didn't count 10s or aces. There aren't faces on either of them.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 13th, 2010 at 8:55:22 PM
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If there aren't faces on them, they are non-face cards, aren't they? I take it, that you meant to say you DID count them (or else, you should have gotten even fewer non-faces). I am also guessing, that, like Doc said, you also counted aces as non-face - that would explain the discrepancy I am after.
"When two people always agree one of them is unnecessary"
August 13th, 2010 at 9:55:55 PM
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Correct, I don't count aces as face cards either. Only jacks, queen, and kings have faces on them. That leaves 40 cards without faces.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 16th, 2010 at 11:46:26 AM
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thank you wizard! I didn't want you to add the aces or 10's
