Odds of a Push: Three Card Poker

With no hierarchy of suits, what are the odds of a push in 3-Card Poker where the cards of any player and the dealer match, e.g. K,7,2 against K,7,2?

The probability that the hand ends with 0 units being won or lost is 0.000612. First you have to choose to Play in order to have a push, so hands like J,6,2 off-suit can never push (even if the cards match). Second, if your hand is (for example) 6,7,8 then properly speaking it doesn't push a dealer 6,7,8 because you win 1 unit. So, the only hands that can push are in the range Q,6,4 off-suit up to A,K,J suited. Also, it is not just that the cards match, they have to both be suited or both unsuited.

Man, I'm going to regret this - but how did you get that answer? I see the logic - but the math escapes me.

Quote: ukaserex

I see the logic - but the math escapes me.

I don't see any logic, I just see an answer. I got the answer by running a cycle:

Quote: ukaserex

I see the logic - but the math escapes me.

Flush tie: (COMBIN(13,3)-12)*4*3 = 3288
Pair Tie: 13*COMBIN(4,2)*12*4*3 = 11232
A High Tie Using 2 suits: (COMBIN(12,2)-2)*4*3*3*(3*3*3-2) = 57600
A High Tie Using 3 suits: (COMBIN(12,2)-2)*4*3*2*(3*3*3-1) = 39936
K High Tie Using 2 suits: (COMBIN(11,2)-1)*4*3*3*(3*3*3-2) = 48600
K High Tie Using 3 suits: (COMBIN(11,2)-1)*4*3*2*(3*3*3-1) = 39936
Q64 to QJ9 Tie Using 2 suits: (COMBIN(10,2)-9)*4*3*3*(3*3*3-2) = 32400
Q64 to QJ9 Tie Using 3 suits: (COMBIN(10,2)-9)*4*3*2*(3*3*3-1) =22464