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.
"My life is spent in one long effort to escape from the commonplace of existence. These little problems help me to do so." -- Sherlock Holmes
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.
"My life is spent in one long effort to escape from the commonplace of existence. These little problems help me to do so." -- Sherlock Holmes
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.
"My life is spent in one long effort to escape from the commonplace of existence. These little problems help me to do so." -- Sherlock Holmes
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
