#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 |
#8
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Re: What are the odds that someone at a full table has a premium hand?
Interesting method! I'm thinking it can't possibly be sound, though. 1-(450/550) is a shockingly high chance of the tenth hand being *so* special -- even given that the first nine hands were not so special. A 20% chance of the tenth starting hand being a biggish ace or highish pair?! ? |
#9
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Re: What are the odds that someone at a full table has a premium hand?
[ QUOTE ]
Interesting method! I'm thinking it can't possibly be sound, though. 1-(450/550) is a shockingly high chance of the tenth hand being *so* special -- even given that the first nine hands were not so special. A 20% chance of the tenth starting hand being a biggish ace or highish pair?! [/ QUOTE ] Sh*t! You are right. This method is incorrect. I am not accounting for the fact that one a premium-hand card (like an A) could have been used in a non-premium-hand, like A6. I'll keep thinking.... gm |
#10
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Re: What are the odds that someone at a full table has a premium hand?
BTW, our first estimates are a lot closer to each other than I realized: I just now caught a wrong number; there are 4 cards Ten-King, not 5 as I'd used in my counting the biggish aces. I end up with 40.2% as my estimate for at least one player holding a biggish ace. Also, refining a bit on the biggish pairs, I now get 24.06% for at least one player holding. Putting those two results together as if they're independent gives 54.6% as the net estimate for at least one player holding something biggish. I caught the error because I've now been writing little programs to estimate for practical situations: It's folded to you @ 2 off the button, so 4 players left to act. You figure they'll call/raise (fight back at your blind steal in this tournament situation) with any AT+, KQ+, or 77+. What's your risk? |
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