odds of FLOPPING 2 pair or better in holdem

muckyouraces · #1 06-10-2006, 08:27 PM

does anyone know what the odds of flopping 2 pair or better with a hand like KQ or QJ suited or unsuited

miketurner · #2 06-10-2006, 09:18 PM

I've heard it's 1 in 30. Anyone confirm?

AaronBrown · #3 06-10-2006, 11:03 PM

If you have two different cards in your hand, you can get two pair or better by flopping two or more of the six matching cards in the deck. There are 15 ways to get two of them, with 44 possibilities for the third flop card, and 20 ways to get three. 15*44 + 20 = 680 of the 19,600 possible flops. That's 1 chance in 29.

If the hand is suited, there are also 11*10*9/(3*2*1) = 165 hands that give you a flush, with no overlap to the other hands.

With KQ there are 128 possible straights, QJ has 192. If these hands are suited 2 of the KQ straights and 3 of the QJ are straight flushes, so you don't want to double count them.

This doesn't count hands where there is a non-matching pair or trips on the flop to give you better than two pair.

TaintedRogue · #4 06-12-2006, 02:31 PM

Hello,

You lost me in your 1st para, where you said: "44 possibilities for the 3rd flop card, and 20 ways to get three."

Addressing the 1st part: "44 possibilities"

(6*3)/2 = 9 ways to make Two Pair and then there are 48 remaining cards left that can come up as the 3rd Flop card that could end up giving you either a Full House or just the Two Pair you flopped.

9*48= 432 possible Flops that gives him Two Pair, or a Full House.

Quads: 2 ways

Trips: [(6*2)/2]*44 = 264

19600 - 698 = 18,902/698 = 27.08:1

I don't know what the "20 ways to get three" refers to.

I understand your Flush & Str8 computations.

Alan3 · #5 06-12-2006, 03:22 PM

There are 15 ways to get two pair **or better**.
Select 1 from 6.
Select 1 from the remaining 5.
This will give you either two pair or trips.
Divide by two to get rid of ordering.
(6*5)/2 = 15
Now you have accounted for 2 cards in your hand and 6 cards to improve. That leaves 44 cards possible for the last flop card.

This only accounts for two of your six outs hitting the board. What if you select three cards from the six for flopped quads or boat? There are 20 of these hands (6*5*4/3*2*1=20).