How many strategically distinct flops exist?

[CallMeIshmael]

ok, cool. 1755 was also what I go.


Im reading up on Polya counting, thanks for the mention.

[pzhon]

[ QUOTE ]

Im reading up on Polya counting, thanks for the mention.

[/ QUOTE ]
Polya counting is actually overkill, unless you are looking at much more complicated problems. This can be done with Burnside's lemma. You might look at actions of S_4 on possible flops, and then for each conjugacy class of S_4, count how many flops are fixed by that symmetry. The identity fixes everything, 4-cycles fix nothing, 3-cycles fix flops that are monotone in the 4th suit or trips in the moving suits, etc. It's not too bad, but not easier than a direct computation here.

[JABoyd]

There are 19,600 possible flops for each of the 1,326 starting hands.