non-associativity of heads-up matches
 

Hi a lot of you have probably seen this curious fact regarding the three hands:
{A[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img]}, {7[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/spade.gif[/img]} and {2[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/diamond.gif[/img]}.

In a heads up match:
{A[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img]} is favoured over {7[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/spade.gif[/img]} (57.91% to win)
{7[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/spade.gif[/img]} is favoured over {2[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/diamond.gif[/img]} (52.33% to win)
but
{2[img]/images/graemlins/club.gif[/img], 2[img]/images/graemlins/diamond.gif[/img]} is favoured over {A[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img]} (52.34% to win)

Does anyone know other interesting cases (not trivially similar to the above) where given three hands A, B, and C. A>B, B>C, but C>A?

Thanks. Just curious.

Re: non-transitivity of heads-up matches
 

Among the nonpairs, the best hand is generally determined by which hand has the higher high card. Among pairs, the best hand is determined by the rank. When a pair is favored over a nonpair, any higher pair is also favored. In order to have nontransitivity, you need to have something like a pair over a high nonpair over a low suited connector over the pair, or you need to use some of the exceptions to the ordering of nonpairs.

Here are some examples of the exceptions:

A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/heart.gif[/img] over A[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/spade.gif[/img] over A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/club.gif[/img]

7[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/heart.gif[/img] over 6[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/heart.gif[/img] over 5[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/club.gif[/img]

Re: non-transitivity of heads-up matches
 

non-transitivity... right... oops. Math was a long time ago. Poker is as close as I get to using it these days...