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Old 06-23-2005, 05:10 PM
pzhon pzhon is offline
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Join Date: Mar 2004
Posts: 66
Default Re: unique showdown probabilities for two preflop hand matchups

[ QUOTE ]

Part 3h: Consider hand B unpaired unsuited in the two suits of A. There are 11*10/2[no shared ranks]+12[share rank with lower card of A in high card suit]+11[share rank with higher card of A in low card suit but no double count of shared lower card of A in high card suit] such hands.

[/ QUOTE ]
My count agrees with yours except in this step. Suppose hand A is A [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/heart.gif[/img]. When B has no shared rank, you can still distinguish Q [img]/images/graemlins/spade.gif[/img] J [img]/images/graemlins/heart.gif[/img] from Q [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/spade.gif[/img]. I think you undercounted by 55*78.

Actually, this example is flawed, since those matchups give the same w/l/t probabilities. However, A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/heart.gif[/img] vs. Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/heart.gif[/img] is different from A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/heart.gif[/img] Q[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/spade.gif[/img].


http://twodimes.net/h/?z=138760
cards win %win lose %lose tie %tie EV
A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] 1114667 65.10 588268 34.36 9369 0.55 0.654
Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/heart.gif[/img] 588268 34.36 1114667 65.10 9369 0.55 0.346

http://twodimes.net/h/?z=121452
cards win %win lose %lose tie %tie EV
A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] 1114667 65.10 588268 34.36 9369 0.55 0.654
J[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/heart.gif[/img] 588268 34.36 1114667 65.10 9369 0.55 0.346


http://twodimes.net/h/?z=1047170
cards win %win lose %lose tie %tie EV
A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/heart.gif[/img] 951868 55.59 752043 43.92 8393 0.49 0.558
J[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/heart.gif[/img] 752043 43.92 951868 55.59 8393 0.49 0.442

http://twodimes.net/h/?z=318619
cards win %win lose %lose tie %tie EV
A[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/heart.gif[/img] 951910 55.59 752000 43.92 8394 0.49 0.558
Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/heart.gif[/img] 752000 43.92 951910 55.59 8394 0.49 0.442
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