While I'm at it, I'm going to test this, as well:
To test this, I'm going to run 100,000 hands (10 players each) with the AAA flop and simply see how many times someone has flopped quads (meaning they were dealt the case Ace). According to MB, the expected answer here should be either 37% or 74%. I'm not sure - please clarify, MB.
According to me, it should be 20%, as per this:
Whooops. Looking at that again now, I think I made a (big) mistake.
This would be if each player was only holding one hold card. Because each player is holding 2 hole cards, I think we need to multiple that all by 2: 1/49*20=40.8%. But that can't be right, because to do that with 0 Aces on the flop, we'd have a greater than 100% chance of someone holding an Ace.
Ok, I've definitely confused myself here. But dammit, I still want to run some simulations!!!