The number of bets isn't important, because the vast majority of the bets are relatively small, and have little effect on the bottom line.
Satoshi Dice's overall profit is bigger than it 'should' be thanks to a very rich player who bet huge amounts of money on the site earlier this year and ended up stopping after a bad run of luck.
It's possible to run 'provably fair' poker games using a system where each player encrypts each card in the deck and shuffles it before passing it on to the next player. That way nobody can see cards they aren't supposed to. You can read about it here: http://en.wikipedia.org/wiki/Mental_poker
One problem with such a scheme is that if any player drops out of the game mid-hand then the game stops, because every player is needed to decrypt the cards. Another problem is the bandwidth needed to pass all the cards around continually for encryption. I think. Maybe it was CPU, I forget...
There is a 1-in-2^256 chance of finding another secret with the same hash each time they try. That's as close to 0-in-1 as you can imagine. It would take trillions of years to cheat a single time. It's harder for SatoshiDice to cheat by finding an alternative daily secret than it is for them to break the security of Bitcoin itself.
Edit: Maybe I'm not being clear. They have a lot of combinations to run through, but *none of them have the correct hash* so we would know immediately that they're cheating if they used a different secret than the one that has the hash they published in advance.