87s/76s/65s vs. AA

[paulish]

According to PokerStove; [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]], [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] wins 22.87% of the time against [A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]]. But [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]] draws 0.37%, [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] draws 0.32% and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] draws 0.30%.

<font color="red">How?</font>

[ajohnson16]

All diamond flush and five straight cards on the board that don't give the other player the nut card (A-5 w/ 65s, 2-6 w/ 76s, 3-7 w/ 87s, (9-K with AA).

Not sure this is totally right but it would make sense?

[Bantam222]

boards like 78910J are when they would draw

the reason 87&gt;76&gt;65 is because...
87 and 67 wins on the 23456 board while 56 splits...
87 wins on the 34567 board while 56 and 67 splits...

[JocK]

[ QUOTE ]
According to PokerStove; [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]], [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] wins 22.87% of the time against [A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]]. But [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]] draws 0.37%, [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] draws 0.32% and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] draws 0.30%.

<font color="red">How?</font>

[/ QUOTE ]

Not sure what you mean by these drawing percentages of 0.30 - 0.37%.

Hands like [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]] draw a flush whenever 3 hearts appear on the board. This happens against [A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]] on ((11x10x9)/(3x2x1)) x ((37x36)/(2x1)) = 109,890 boards. The total number of possible boards is (48x47x46x45x44)/(5x4x3x2x1) = 1,712,304. So the likelihood of a flush draw with 3 hearts on the board is 109,890/1,712,304 = 6.4%. Add to that the likelihood of a flush draw with four hearts on the board, the likelihood of a straight draw, as well as the odds that you hit two pair or a set whilst your opponent does not hit, plus a few other smaller odds, and you get a pot equity well above 20%.

Johannes

[jbones]

[ QUOTE ]
[ QUOTE ]
According to PokerStove; [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]], [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] wins 22.87% of the time against [A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]]. But [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]] draws 0.37%, [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] draws 0.32% and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] draws 0.30%.

<font color="red">How?</font>

[/ QUOTE ]

Not sure what you mean by these drawing percentages of 0.30 - 0.37%.

Hands like [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]] draw a flush whenever 3 hearts appear on the board. This happens against [A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]] on ((11x10x9)/(3x2x1)) x ((37x36)/(2x1)) = 109,890 boards. The total number of possible boards is (48x47x46x45x44)/(5x4x3x2x1) = 1,712,304. So the likelihood of a flush draw with 3 hearts on the board is 109,890/1,712,304 = 6.4%. Add to that the likelihood of a flush draw with four hearts on the board, the likelihood of a straight draw, as well as the odds that you hit two pair or a set whilst your opponent does not hit, plus a few other smaller odds, and you get a pot equity well above 20%.

Johannes

[/ QUOTE ]

Draw = tie

you brutally missed the point

[Eighties21Playa]

The only ties that differ are those due a 5 card board that make a straight or heart flush with all 5 cards higher than the highest card of the suited connector. Since there are more 5 card combinations of A-7 than there are of A-8 or A-9, there are more possible ties for the 65 than the 76 or 87.

[senjitsu]

Those cases, and the cases where there are 5 hearts on the board. FOr example on a board of 9TJQA, all hearts. all three of the hands you mention split with the aces. As the high card in your hand goes up in rank, you arebecome slightly less likely to tie when 5 to a flush hits the board.

[paulish]

[ QUOTE ]
The only ties that differ are those due a 5 card board that make a straight or heart flush with all 5 cards higher than the highest card of the suited connector. Since there are more 5 card combinations of A-7 than there are of A-8 or A-9, there are more possible ties for the 65 than the 76 or 87.

[/ QUOTE ]

[ QUOTE ]
Those cases, and the cases where there are 5 hearts on the board. FOr example on a board of 9TJQA, all hearts. all three of the hands you mention split with the aces. As the high card in your hand goes up in rank, you arebecome slightly less likely to tie when 5 to a flush hits the board.

[/ QUOTE ]

If [6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img]] ties more often when a higher straight or flush hits the board, then [7[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/heart.gif[/img]] and [8[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img]] should win more often…right?

But according to PokerStove they don’t. 22.87% is the win ratio for each of these hands when matched against [A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]]. But the the lower the suited connector, the more "win%" the Aces loses, and the hands draw more often...