Heads Up Odds

[Evil Monkey35]

Can anyone help me? My brother and friend were playing heads up Hold'em the other night and I wanted to know if anyone knew the probablitly of this hand. My friend was dealing and dealt my brother pocket aces and my friend dealt himself pocket twos. Then the flop came ace, two, two. My brother flopped a full house and my friend flopped four of a kind. I know that the probability of flopping a full house with a pair in your hand is 1%, and flopping 4 of a kind with a pair in your hand is 0.02%. Does anyone have any idea of the probabliltiy of both of those coming on the same hand in a heads up game??? We think my friend was cheating because a 1% chance and a 0.02% chance happening on the same hand seems a little odd. Please reply with any answers or comments you have. Thanks.

[Adamm]

Getting dealt a pocket pair: 5.88%
You both getting a different pocket pair: 0.35%
Getting dealt two aces in the pocket: 0.45%
Getting dealt two twos in the pocket: 0.45%
You getting aces, other guy getting twos: 0.0022%
Getting a boat when you hold a pocket pair: 0.98%
Getting quads when you hold a pocket pair: 0.245%
Given your aces and twos, getting that exact flop: 0.00385%
Getting screwed over by your friend: Priceless

Might be wrong on that last figure.
So I'd think it'd be the "both getting a different pocket pair" times "getting that exact flop", because it could've came KK and 77 and still would've been the same thing.
So I guess that's a 0.0013475% chance of that happening or so?

[K-rug]

Oddly enough, this exact hand happened to my brother. My brother was dealing and delt himself pocket A's and a friend pocket 2's. However, my brother did not go all-in or make a large bet. If memory serves me he checked trying to sucker my friend in. Of cousre, my friend with pocket 2's checked. Flop, A, 2, 2,. My brother goes all in with his full-house my friend goes all in with his four of a kind. My brother learned something that day...

So the moral of the story is that it can and will happen. It also has happened with those exact cards too.