[AaronBrown]

It's not quite 52! for the cards. Only 25 cards are dealt, and order doesn't matter within a hand or within the flop. So it's 52!/[27!*2^10*6] = 1.2*10^36 while 52! is 8.1*10^67. And not all the cards matter for every hand, if it's everyone but the BB folds preflop then the board doesn't matter.

It would not be hard to count all possible betting outcomes by computer program, if you restrict each round to three raises in all cases. If everyone stays in to showdown and every betting round is capped then there are one trillion ways to distribute the raises. The average player makes 11 calls, any one of which we could replace by a fold, which makes 11^10 = 26 billion ways. Not all of those work, for example if everyone folds preflop, there's no one to raise post flop. So, 26 billion trillion, or 2.6*10^22 is an overestimate of the number of possible betting scenarios, I'd knock off a couple zeros to eliminate the cases in which someone folds before they raise, to get something like 10^20. Anyway, it's much less than the number of card combinations.