Can you help me make an estimation...

[CallMeIshmael]

Given this information:

AKo vs 66

Hand 1: 45.0113 % 44.82% 00.19% { AcKd }
Hand 2: 54.9887 % 54.79% 00.19% { 6c6s }


AKo vs 98s
equity (%) win (%) tie (%)
Hand 1: 59.6167 % 59.42% 00.20% { AcKd }
Hand 2: 40.3833 % 40.19% 00.20% { 9s8s }


98s vs 66
equity (%) win (%) tie (%)
Hand 1: 50.1147 % 49.67% 00.44% { 6c6s }
Hand 2: 49.8853 % 49.44% 00.44% { 9s8s }


Is there a way to derive an estimate for

AKo vs 98s vs 66?

If so, can it be used with 4+ hands. And, how accurate is it?

[pzhon]

No, there isn't a good way to derive such an estimate at all from the pairwise data.

Suppose any pair of hands is 50-50. Together, it is possible that hand A wins 60%, and hands B and C win 20% each:

http://twodimes.net/h/?z=1052536
T[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/heart.gif[/img] 0.596
5[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/diamond.gif[/img] 0.202
5[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 0.202

It could be 56-22-22:

http://twodimes.net/h/?z=1052533
5[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 0.562
T[img]/images/graemlins/spade.gif[/img] 9[img]/images/graemlins/heart.gif[/img] 0.219
T[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/diamond.gif[/img] 0.219

It could be 33-33-33:

A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/spade.gif[/img] 0.333
A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img] 0.333
A[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/diamond.gif[/img] 0.333

It could be that hand A is a favorite heads up against B and C, and an underdog in a 3-way pot:

http://twodimes.net/h/?z=1052539
A[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/club.gif[/img] 0.279
6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 0.298
J[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 0.422

and vice versa:

http://twodimes.net/h/?z=1052541
6[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img] 0.384
J[img]/images/graemlins/diamond.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 0.308
J[img]/images/graemlins/spade.gif[/img] T[img]/images/graemlins/spade.gif[/img] 0.308