[shday]

How about calculate the number of permutations based on the number of cards used. All the randomness left in the unused part of the deck wouldn’t matter.

The size would be further reduced because the order of cards doesn’t matter for each players hand and for the 3 cards of the flop. Then the equivalency of the suits would cut it down more.

For heads-up the total number of effectively unique shuffles would be close to (in case I missed something):

P(52,4)/4*C(48,3)*47*46/4!

or 2 530 869 413 800

I think this is very close to what you get using Seigmunds calculation from above (I didn't have a way to accurately calculate 52! at hand).