A3 vs A2. Baffled by the percentages here.

[Toddy]

I always figured this was dead even and I was baffled when I saw A3 is a 28-22% favorite. How is this a 6% favorite. Any cards that come out other than a 2 or 3 will create a tie. Is the odds so different because the possibility that a 2 AND a 3 will come?

I believe so, yes.

[TomCollins]

Small advantage for A3-
5 flush board with a deuce in the suit of the 3. A2 cannot

4567A= 4*4*4*4*2 = 256 ways
45672= 4*4*4*4*4 = 512 ways
45674= 6*4*4*4 = 384 ways
45675= 6*4*4*4 = 384 ways
45676 = 6*4*4*4 = 384 ways
45679 = 4*4*4*4*4 = 1024 ways
4567J = 1024 ways
4567Q = 1024 ways
4567K = 1024 ways
6016 wins
2456(non 3 x) = Win for A3
Should be about 6016 wins


These two should negate each other:
245(non 3&A) = Win for A3
345 = win for A2

So this might be some of it. I didn't enumerate how many ways this can happen, although there may be a few cases where flushes will determine the winner, which may make a difference what suits you choose.

This makes about 1% of a difference.