Poker Probabilities
July 21st, 2013 at 8:11:41 PM
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Was looking at this site:
hold'em poker probabilities
It says the probability of flopping a set while holding a pocket pair is 11.8%. This agrees with other numbers I have seen published on other sites. When I try to calculate the number myself I get 11.3%. Don't know where the difference comes from.
The other number given is the odds/probability of flopping a set or better= 10.5%. Something seems off here. I would expect the odds to be higher, not lower since we are now including additional events. You should add the 0.73% for the full house and 0.25% for the quads to give a number closer to 12.6%. Seem reasonable?
Still like to know why I get only 11.3% though.
hold'em poker probabilities
It says the probability of flopping a set while holding a pocket pair is 11.8%. This agrees with other numbers I have seen published on other sites. When I try to calculate the number myself I get 11.3%. Don't know where the difference comes from.
The other number given is the odds/probability of flopping a set or better= 10.5%. Something seems off here. I would expect the odds to be higher, not lower since we are now including additional events. You should add the 0.73% for the full house and 0.25% for the quads to give a number closer to 12.6%. Seem reasonable?
Still like to know why I get only 11.3% though.
July 21st, 2013 at 8:40:28 PM
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I think the 11.8% number is just 1-(combin(48,3)/combin(50,3)). That would mean that no adjustment has been made to subtract the odds of getting quads or a full house that includes a set. If you made that correction when you got to 11.3%, that may be the source of the difference.
I don't understand the 10.5% number at all. All I have is that it'd be a pretty easy double-fat-finger on a 10 key to hit the 0 and 5 instead of 1 and 8 and wind up with 10.5 instead of 11.8...
I don't understand the 10.5% number at all. All I have is that it'd be a pretty easy double-fat-finger on a 10 key to hit the 0 and 5 instead of 1 and 8 and wind up with 10.5 instead of 11.8...
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
July 21st, 2013 at 9:10:44 PM
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You are likely using:
1 - (50/52)(49/51)(48/50) = 11.3% which is incorrect because your hole cards cannot appear on the flop. You must base the flop calculation on the remaining 50 cards.
This is the correct (and easiest) way to calculate the likelihood of flopping a set (or better) with a pocket pair:
1 - (48/50)(47/49)(46/48) = 11.8%
Now as for the probability of flopping exactly 3 of a kind from a pocket pair is a little more tricky:
Let's consider flops better than 3 of a kind:
Quads: both remaining cards that rank-match your hole cards must be chosen along with any of the 48 remaining cards: (48 combos)
Full house: 1 of 2 cards that rank match your hole cards must be chosen along with a pair from the 12 remaining ranks. Each rank has 4*3/2 = 6 combos to make a pair. 2*12*6 = 144 combos
The total number of possible flops is:
50*49*48/(3*2*1) = 19600
So the probability of flopping quads is: 48/19600 = 0.25%
And the probability of flopping a full house is: 144/19600 = 0.73%
And the number of combinations to just flop 3 of a kind only would be all the possible choices for a flop with EXACTLY one rank-matched card (i.e. choose the other two cards from 48 cards only) AND subtract all the full house combos: 2*48*47/2 - 144 = 2112 combos
Probability of exactly flopping 3 of a kind: 2112/19600 = 10.8%
Sum all three of the possibilities together:
(2112 + 144 + 48)/19600 = 2304/19600 = 11.8% (checks with the "easy formula")
He is off because he flipped the spots of the words and messed up the "3 of a kind only" calculation. People screw up, obv.
1 - (50/52)(49/51)(48/50) = 11.3% which is incorrect because your hole cards cannot appear on the flop. You must base the flop calculation on the remaining 50 cards.
This is the correct (and easiest) way to calculate the likelihood of flopping a set (or better) with a pocket pair:
1 - (48/50)(47/49)(46/48) = 11.8%
Now as for the probability of flopping exactly 3 of a kind from a pocket pair is a little more tricky:
Let's consider flops better than 3 of a kind:
Quads: both remaining cards that rank-match your hole cards must be chosen along with any of the 48 remaining cards: (48 combos)
Full house: 1 of 2 cards that rank match your hole cards must be chosen along with a pair from the 12 remaining ranks. Each rank has 4*3/2 = 6 combos to make a pair. 2*12*6 = 144 combos
The total number of possible flops is:
50*49*48/(3*2*1) = 19600
So the probability of flopping quads is: 48/19600 = 0.25%
And the probability of flopping a full house is: 144/19600 = 0.73%
And the number of combinations to just flop 3 of a kind only would be all the possible choices for a flop with EXACTLY one rank-matched card (i.e. choose the other two cards from 48 cards only) AND subtract all the full house combos: 2*48*47/2 - 144 = 2112 combos
Probability of exactly flopping 3 of a kind: 2112/19600 = 10.8%
Sum all three of the possibilities together:
(2112 + 144 + 48)/19600 = 2304/19600 = 11.8% (checks with the "easy formula")
He is off because he flipped the spots of the words and messed up the "3 of a kind only" calculation. People screw up, obv.
