2 simple math questions

[ajmargarine]

1. In HE, if you have a pocket pair, and your card hits on the flop, what are the chances you will get a boat or quads by the river? (and how is that computed)

2. Also HE, it's said if you have KK, there's a 5% chance of running into AA in someone else's hand. Is that correct first of all? I guess that assumes full table. My question then is if you have QQ, what are the chances of running into KK or AA; and if you have JJ, what are the chances of running into AA, KK, or QQ?

EDIT: (Doh: I now see #2 has been asked in the last 24 hours...and I am sure #1 has been asked many times)

tyvm,

aj

[AaronBrown]

For your first question, I assume you mean you get one match to your pair on the flop, and two other cards, not the same. So after the flop you have three of a kind, not four or a full house.

There is one card that gives you a four and six that will pair one of the cards on the flop. There are 47 unknown cards, so you have a 7/47 chance to get your hand on the turn. If you don't get it on the turn, you have ten possible winning cards out of 46 for the river. So you do:

7/47 + (40/47)*(10/46) = 722/2,612 = 33%.

There are other ways to compute the same number, but they should give the same answer. There are 47*46/2 = 1,081 possible combinations of turn and river card. You could match your set and combine with any of 46 other cards. You can add up how many of those give you quads or a boat, there are 361 of them.