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#1
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What are the odds that someone at a full table has a premium hand?
Presuming ATo and 99 or better?
Ten people at the table. I have no clue but would guess 75% chance at least one person has it? Feel free to ballpark it... I just want a rough idea. |
#2
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Re: What are the odds that someone at a full table has a premium hand?
[ QUOTE ]
Presuming ATo and 99 or better? [/ QUOTE ] Not specific enough. For example, would KJo qualify? KJs? What about QJs? KQo? You need to actually list all the ranges. For example: AA-99 ATo-AKo KQ-KJ etc... gm |
#3
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Re: What are the odds that someone at a full table has a premium hand?
ATo-AKs and 99-AA only. So something that can flop TPTK or a high pair. QKs would not qualify.
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#4
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Re: What are the odds that someone at a full table has a premium hand?
[ QUOTE ]
ATo-AKs and 99-AA only. So something that can flop TPTK or a high pair. QKs would not qualify. [/ QUOTE ] AT-AK: 16 hands each, 64 hands total AA-99: 6 hands each, 36 hands total So 100 hands are in the range you're concerned with. Because the inter-player hand dependence is loose, the following is an accurate approximation to the answer you want: 1 - (1226/1326)^10 = .54 So over half the time at least one person will have a hand in these ranges. gm |
#5
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Re: What are the odds that someone at a full table has a premium hand?
Awsome. I bow down to you!
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#6
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Re: What are the odds that someone at a full table has a premium hand?
Neat question. I estimate about 60.6%, quite a bit higher than Gaming Mouse's quick 54%.
This method should handle the interdependences a little cleaner: 1) The biggish aces. For each ace, 20/52 that it's in a starting hand. Then, 4(5)/51 that it's a ATo+. So, 15% for each of the 4 aces. (1-(1-.15)^4) for none of the 4 aces being out there as biggish aces. Roughly 48% for at least one biggish ace being out there. 2) The highish pocket pairs: 6 of them. 10/(13*17) for each. The (1-(1-... method gives a 24.3% of at least one highish pocket pair being out there. Combining the aces & the pocket pairs as rather independent events, meaning using the (1-(1-... method again, gives 60.6% for at least one qualifying starting hand among the ten players. |
#7
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Re: What are the odds that someone at a full table has a premium hand?
[ QUOTE ]
Neat question. I estimate about 60.6%, quite a bit higher than Gaming Mouse's quick 54%. [/ QUOTE ] That's not right either, but you are right that my assumption about the interhand dependence not being significant was wrong. The correct answer is about 71%: ncr(52,2)=1326 ncr(50,2)=1225 ncr(48,2)=1128 ncr(46,2)=1035 ncr(44,2)=946 ncr(42,2)=861 ncr(40,2)=780 ncr(38,2)=703 ncr(36,2)=630 ncr(34,2)=561 1 - (1226/1326)*(1125/1225)*(1028/1128)*(935/1035)*(846/946)*(761/861)*(680/780)*(603/703)*(530/630)*(461/561)=.7148 Next time I shouldn't be so lazy [img]/images/graemlins/smile.gif[/img] gm |
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