unique showdown probabilities for two preflop hand matchups

[pzhon]

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However, while your way of organizing the permutations is nice on paper, it looks problematic from an algorithmic perspective.

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I still don't see what difficulties there are and what alternative you offer.

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For example, given the matchup:

A1K1 vs. Q1J1

the "switch two suits" permutation doesn't apply. There aren't two suits to switch.

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There are always 4 suits. You can always apply all 24 permutations of the 4 suits.

[img]/images/graemlins/spade.gif[/img] <-> [img]/images/graemlins/heart.gif[/img] applied to A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/spade.gif[/img] vs. Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img] results in A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img] vs. Q[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/heart.gif[/img].

[img]/images/graemlins/diamond.gif[/img] <-> [img]/images/graemlins/club.gif[/img] applied to A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/spade.gif[/img] vs. Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img] results in A[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/spade.gif[/img] vs. Q[img]/images/graemlins/spade.gif[/img] J[img]/images/graemlins/spade.gif[/img].

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The idea here is to quickly discover all members of each equivalence class for the N-way case. Counting the classes was just a sanity check on my method.

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You can always apply the 24 permutations of the suits to get a complete list of equivalent match-ups. Sometimes there will be only 3 distinct match-ups repeated 8 times. Sometimes there will be 24 distinct collections of hands.