#1
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What is the probability that AA beats 66, given that a 6 will flop?
I'd like to know to assist with working out implied odds on flopping a set.
Thanks. |
#2
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Re: What is the probability that AA beats 66, given that a 6 will flop
Well if a 6 flops (and I'm assuming an A doesn't flop?), the only way AA wins is:
- A on turn or river - runner-runner flush - runner-runner straight (unless, of course, the 66 fills up or quads up). (All numbers below from twodimes.net ) The "best" board for AA vs a set of 6's might be something like: 6[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/club.gif[/img] vs A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img] Flop: 6[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] AA is about 35.6% to outdraw on this board. Slightly more common will be boards which provide AA with only backdoor draws): Flop: 6[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] AA draws out about 14.3% of the time here. The overwhelming majority of the time, however (rainbow drawless board), AA will be drawing to 2 outs: Flop: 6[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/club.gif[/img] AA outdraws less than 9% of the time here. If you want something more exact, you'd have to calculate the relative probability of the above "flop types" (plus freakish boards like 6QQQQ) and I don't know how to do that (or if any online resources exist to let you do that type of analysis). Best guess, AA average pot equity with a 6 on the board is probably 9-10% (i.e. slightly higher than the most common "worst case"). Does this help? Tom |
#3
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Re: What is the probability that AA beats 66, given that a 6 will flop
[ QUOTE ]
Well if a 6 flops (and I'm assuming an A doesn't flop?), the only way AA wins is: - A on turn or river - runner-runner flush - runner-runner straight (unless, of course, the 66 fills up or quads up). (All numbers below from twodimes.net ) The "best" board for AA vs a set of 6's might be something like: 6[img]/images/graemlins/spade.gif[/img] 6[img]/images/graemlins/club.gif[/img] vs A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img] Flop: 6[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] AA is about 35.6% to outdraw on this board. Slightly more common will be boards which provide AA with only backdoor draws): Flop: 6[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] AA draws out about 14.3% of the time here. The overwhelming majority of the time, however (rainbow drawless board), AA will be drawing to 2 outs: Flop: 6[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/club.gif[/img] AA outdraws less than 9% of the time here. If you want something more exact, you'd have to calculate the relative probability of the above "flop types" (plus freakish boards like 6QQQQ) and I don't know how to do that (or if any online resources exist to let you do that type of analysis). Best guess, AA average pot equity with a 6 on the board is probably 9-10% (i.e. slightly higher than the most common "worst case"). Does this help? Tom [/ QUOTE ] Sometimes you will have A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/heart.gif[/img] And the board will be 6[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] Here, against a set of 6s, you will have 4 outs twice - 17.2% |
#4
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Re: What is the probability that AA beats 66, given that a 6 will flop
<font class="small">Code:</font><hr /><pre>Text results appended to pokerstove.txt
3,210,570 games 1.110 secs 2,892,405 games/sec Board: 6c Dead: equity (%) win (%) / tie (%) Hand 1: 17.9305 % [ 00.18 00.00 ] { AA } Hand 2: 82.0695 % [ 00.82 00.00 ] { 66 }</pre><hr /> |
#5
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Re: What is the probability that AA beats 66, given that a 6 will flop
[img]/images/graemlins/blush.gif[/img]
sorry, I don't buy it. 8.5% is more right. where is 18% coming from? good thing that program doesn't cost money. anyone disagree? |
#6
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Re: What is the probability that AA beats 66, given that a 6 will flop
[ QUOTE ]
<font class="small">Code:</font><hr /><pre>Text results appended to pokerstove.txt 3,210,570 games 1.110 secs 2,892,405 games/sec Board: 6c Dead: equity (%) win (%) / tie (%) Hand 1: 17.9305 % [ 00.18 00.00 ] { AA } Hand 2: 82.0695 % [ 00.82 00.00 ] { 66 }</pre><hr /> [/ QUOTE ] That looks like the board can still flop an ace. That looks to me like the difference between 8% and 18%. Pokerscott |
#7
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Re: What is the probability that AA beats 66, given that a 6 will flop
[ QUOTE ]
[img]/images/graemlins/blush.gif[/img] sorry, I don't buy it. 8.5% is more right. where is 18% coming from? good thing that program doesn't cost money. anyone disagree? [/ QUOTE ] Of course 18% is too high. He only told pokerstove that there was a 6 on the flop. Unfortunately, there is no way to tell pokerstove that there is NOT an A on the flop. So, that 18% figure includes the flops which are A6X |
#8
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Re: What is the probability that AA beats 66, given that a 6 will flop
AA has 2 outs for sure. With 45 unseen cards, that's 8.8%. Throw in the rare miracle flushes, miracle straights, and bigger full houses, and AA probably has a ~10% chance with 2 to come.
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#9
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Re: What is the probability that AA beats 66, given that a 6 will flop
[ QUOTE ]
<font class="small">Code:</font><hr /><pre>Text results appended to pokerstove.txt 3,210,570 games 1.110 secs 2,892,405 games/sec Board: 6c Dead: equity (%) win (%) / tie (%) Hand 1: 17.9305 % [ 00.18 00.00 ] { AA } Hand 2: 82.0695 % [ 00.82 00.00 ] { 66 }</pre><hr /> [/ QUOTE ] I don't think the OP wants to exclude an A from flopping, so maurile has it correct. |
#10
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Re: What is the probability that AA beats 66, given that a 6 will flop
I never excluded an Ace from flopping.
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