#1
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probability of overcards flopping in Hold\'em
<<I posted this in Probability but have not heard a word, so figured I'd also post here since may apply and hope to find a helpful responder>>
Specifically, I was trying to calculate the probability of overcards flopping to specific Pocket Pairs in Hold'em. For example, % of time overcards would flop against someone holding pocket 3's. For the first card of the flop, I calculated the % of an overcard as such: 44/50 = 88% But how do I extend this for the following two cards to come with an total flop %? Independently, flop card one is 44/50, two is 44/49, three is 44/48? And then how would I arrive at the total %? Thanks. |
#2
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Re: probability of overcards flopping in Hold\'em
Are you looking for the probability of one overcard, or that all three cards will be overs?
All three cards are not overcards = 6/50 * 5/49 * 4/48 = 0.15% (i.e. you calculate the chances of an overcard not appearing each time and multiply together to get the chance of it happening each time.) So chances of at least one over = 99.85% |
#3
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Re: probability of overcards flopping in Hold\'em
[ QUOTE ]
AAll three cards are not overcards = 6/50 * 5/49 * 4/48 = 0.15% [/ QUOTE ] When I perform that calculation I get 0.10%?? |
#4
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Re: probability of overcards flopping in Hold\'em
Probability of Flopping at least one over card:
(AND you do not hit a set) KK: .21 QQ: .38 JJ: .52 TT: .63 99: .72 88: .78 77: .82 66: .85 55: .87 44: .88 33: .88 22: .88 |
#5
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Re: probability of overcards flopping in Hold\'em
This is obviously when you hold a pocket pair^
Not exactly what you were looking for but close enough. |
#6
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Re: probability of overcards flopping in Hold\'em
[ QUOTE ]
This is obviously when you hold a pocket pair^ Not exactly what you were looking for but close enough. [/ QUOTE ] A player holds a pocket-pair. What are the chances the flop contains at least one overcard to the pair? As I ran the numbers, I came up with the following: 22 = 100% of at least 1 overcard 33 = 99% at least 1 overcard 44 = 99 55= 98 66=96 77= 92 88 = 86 99 = 79 tt = 69 jj = 56 qq = 41 kk = 22 % AA = 0% But I thought my formula was flawed, therefore my calculations were errant. And I'm still not sure [img]/images/graemlins/confused.gif[/img] |
#7
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Re: probability of overcards flopping in Hold\'em
[ QUOTE ]
(AND you do not hit a set) [/ QUOTE ] Yes [img]/images/graemlins/smile.gif[/img] I see. |
#8
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Re: probability of overcards flopping in Hold\'em
KK
There is 1 overcard. 4 aces in the deck. 3 hits. = 4/50 + 4/49 + 4/48 There are two overcards. 4 kings and 4 aces in deck = 8/50 + 8/49 + 8/48 etc etc |
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