It may seem odd that Td4c rates equal with AcKc, but the two AK hands are mostly splitting. Another way to think about it is that if only two hands are played against each other, then AcKc is a about a 2-1 favourite over Td4c when AdKd has been removed from the pack.

You may think it a bit unsatisfactory to choose nearly symmetric hands. Here are the best answers if you modify the rules a bit:

Category ----Hands-----     -------Equities(%)------  Best-Worst(%,#boards)
   1     AdKc AcKh AhKd   33.333333 33.333333 33.333333  0.000000    0+0/2
   2     8d4c KhQh KsQs   33.333285 33.333358 33.333358  0.000073    1+0/2
   3     Td4c AcKc AdKd   33.332531 33.334792 33.332677  0.002262   31+0/2
   4     Td2c Th7d Tc7h   33.334501 33.331254 33.334245  0.003246   44+1/2
   5     6c4c 9d5d Qh2d   33.336543 33.340118 33.323339  0.016779  230+0/2

1) Anything goes.

2) The three hands aren't _all_ essentially the same due to changing suits.

3) No two hands are essentially the same due to changing suits, taking into account all three hands (=no "global" suit symmetry; believed to be the rules of the present contest).

4) No pair of hands are essentially the same (suit symmetry) when you disregard the third (=no "local" suit symmetry). In the above example Th7d cannot be transformed to Tc7h, because the first T is the same suit as the second 7.

5) No pair of hands are the same when you disregard the suits altogether.

Here is a complete list of the best triples with up to a 1% difference between best and worst. A few essentially similar ones may be listed twice due to extra symmetries which are not accounted for.

List (510k)
Same but gzipped (155k)