View Full Version : What is the probability that AA beats 66, given that a 6 will flop?
partygirluk
02-04-2005, 01:27 PM
I'd like to know to assist with working out implied odds on flopping a set.
Thanks.
JerseyTom
02-04-2005, 01:58 PM
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 (http://www.twodimes.net/poker/) )
The "best" board for AA vs a set of 6's might be something like:
6/images/graemlins/spade.gif 6/images/graemlins/club.gif vs A/images/graemlins/heart.gif A/images/graemlins/diamond.gif
Flop: 6/images/graemlins/diamond.gif K/images/graemlins/diamond.gif Q/images/graemlins/diamond.gif
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/images/graemlins/heart.gif K/images/graemlins/diamond.gif Q/images/graemlins/diamond.gif
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/images/graemlins/heart.gif K/images/graemlins/diamond.gif 2/images/graemlins/club.gif
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
binions
02-04-2005, 03:11 PM
[ 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 (http://www.twodimes.net/poker/) )
The "best" board for AA vs a set of 6's might be something like:
6/images/graemlins/spade.gif 6/images/graemlins/club.gif vs A/images/graemlins/heart.gif A/images/graemlins/diamond.gif
Flop: 6/images/graemlins/diamond.gif K/images/graemlins/diamond.gif Q/images/graemlins/diamond.gif
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/images/graemlins/heart.gif K/images/graemlins/diamond.gif Q/images/graemlins/diamond.gif
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/images/graemlins/heart.gif K/images/graemlins/diamond.gif 2/images/graemlins/club.gif
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/images/graemlins/club.gif A/images/graemlins/heart.gif
And the board will be 6/images/graemlins/club.gif 7/images/graemlins/heart.gif 7/images/graemlins/diamond.gif
Here, against a set of 6s, you will have 4 outs twice - 17.2%
maurile
02-04-2005, 03:40 PM
<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 />
chadash
02-04-2005, 04:35 PM
/images/graemlins/blush.gif
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?
Pokerscott
02-04-2005, 05:55 PM
[ 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
binions
02-04-2005, 05:59 PM
[ QUOTE ]
/images/graemlins/blush.gif
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
binions
02-04-2005, 06:04 PM
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.
reubenf
02-04-2005, 06:42 PM
[ 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.
partygirluk
02-04-2005, 07:31 PM
I never excluded an Ace from flopping.
partygirluk
02-04-2005, 07:32 PM
Thanks Maurile, that is perfect.
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