non-associativity of heads-up matches

[chapstick]

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

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

[pzhon]

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/images/graemlins/spade.gif K/images/graemlins/heart.gif over A/images/graemlins/club.gif K/images/graemlins/spade.gif over A/images/graemlins/heart.gif K/images/graemlins/club.gif

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

[chapstick]

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