What is the probability that AA beats 66, given that a 6 will flop?

[partygirluk]

I'd like to know to assist with working out implied odds on flopping a set.

Thanks.

[JerseyTom]

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

[binions]

[ 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%

[maurile]

<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]

[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?

[Pokerscott]

[ 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]

[ 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

[binions]

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]

[ 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]

I never excluded an Ace from flopping.