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martypalin
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01-24-2007, 09:38 AM
Post subject: Pair-Overpair odds - why isn't it this?
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#1 (permalink)
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Join Date: Dec 2006
Posts: 64
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I have read the odds are about 4-1 or 80%-20% in favour of the overpair e.g. AA KK or even 33 22 but why statistically isnt it 51%-49%.
Because with both pairs drawing five cards isnt it 50-50 whether either will make a set and the extra percent indicating that the overpair will win if nothing hits?
It's not going to make my world crash down but I was just looking over odds and thought it was a little odd, whenever I throw down an overpair like QQ JJ I certainley dont feel like a big favourite lol.
 forgive the n00b for his stupidity
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arkana
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Full House
Join Date: Mar 2005
Posts: 1,109
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Most of the time the bigger pair will win with both of the hands unimproved since there are only 4 cards in the remaining 48 cards that will give one of the players a set.
For the lower pair to win it has to hit (or make a flush\straight but that won't happen very often either) one of the 2 cards in the 50 unseen cards that will give it a set, with 5 cards to come it will only hit about ~20% of the time.
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Tjorriemorrie
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Join Date: Nov 2006
Location: South Africa
Posts: 57
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Well, I'm not that good with stats, but I think I figured this out.
First, you're right. the chance is the same for both pairs that they will hit. both has 2 cards out of the 50 that will give them the win.
But you're only looking at half of the picture. What of the rest of the 48 cards that won't let him win if it doesn't hit?
Thus, think of the probability like this:
Overpair winning = both 2 cards hit (or 2 cards hit and 1 card hit for underpair), 1 card hit and no card hit for underpair, no cards hit for both pairs (which of there is 46 and is quite a lot).
Now fill in the statistical figure in that equation and you'll get to that 4-1 i think. So both has 1-1 to hit, but not hitting gives the overpair the extra 3 in the odds.
Something like that.
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"Poker is a game of people... It's not the hand I hold, it's the people that I play with." ~ Amarillo Slim
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martypalin
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Join Date: Dec 2006
Posts: 64
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Yeah thanks arkana and Tj thats definately helped me out statistically, I just never feel like a 4-1 when I'm dominating lol. I actually had AA vs TT last night and I was still screaming for an ace just to settle the hand!
Cheers
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