Odds for flopping two pair?

[Huhmare]

what are the odds for flopping two pair with TJ for example? and what about KQ when villain is holding AK?

[PygmyHero]

Okay, here's the situation: you have two random cards that are NOT of the same rank and you do not know any other cards out. In all the below situations I am taking the number of made hands then dividing it into 50C3 = 19,600 which is the number of possible flops. This give us the percentage chance, which I have also converted to odds. The odds of flopping two pair (but not better) are:

3C1 * 3C1 * 44C1 = 396

That would be about 2% of the time, or 48.5:1 against.

In case you're interested, the odds of flopping EXACTLY trips is (see below for full house and quads):

2 * 3C2 * 44C1 = 264

This is 1.3% or 73.2:1 against.

Full house:

2 * 3C2 * 3C1 = 18

0.09% or 1087.9:1 against.

Quads:

2 * 3C3 = 2

0.01% or 9799:1 against

So adding it all up (two pair, trips, full house, AND quads), I have 680 ways of flopping these hands.

That's 3.5% or 27.8:1 against.

Please note that this calculation did NOT take into account unfavorable flops such as you hold JT and the flop comes T J Q - you have two pair but there's at least a straight draw if not a made straight out against you. It likewise does not account for scenarios when the flop comes with two suited cards or (worse) three.

If you know some other cards that are out you can remove them from your hypothetical deck. In your example, if you put someone on AK, and you still have the JT, repeat all of these calculations, but it would be 42C1 instead of 44C1 (in the two pair and twips caluculations - do NOT alter the full house and quads equations). The other thing you have to do is reduce the number of possible flops since we normally expect 50C3 = 19,600 to be the number of flops. Now the number would be 48C3 = 17,296.

If you have KQ and they have AK and you know this, you really shouldn't play the hand as you're totally dominated. Although its equally true you'll probably get a lot of action if you do out-flop him (but what if he KNOWS you have KQ?). But anyway, here we go.

Basically you remove his cards from the hypothetical deck (as above), and you also need to account for the fact that one of the kings (one of the cards you want) is out. So, for two pair:

2C1 * 3C1 * 43C1 = 258 (1.5% or 66:1 against)

Trips:

2C2 * 43C1 = 43 for trip kings - notice in this case you would be hurting - drawing to only three outs

3C2 * 43C1 = 129

So 0.99% for trips (but again, keep in minds that about a quarter of these are really bad), or 99.6:1 against.

Full house:

2C2 * 3C1 = 3 (for kings full of queens)

3C2 * 2C1 = 6 (for queens full or kings)

Quads are only possible for queens and it should be fairly obvious that there's only one way to flop quads (if not, see calculation above).

So adding it all up that's 440 'hands' - 2.5% or 38.3:1 against.

Hope that helps!

[Huhmare]

Thanks alot!! /images/graemlins/smile.gif

[gamble4pro]

The event to be measured is "flopping two pair". I think this should also include two pair with new pair on the flop. Your calculation was only made for two pair using both of hole cards.
So: if you hold two different cards (as value) - let's name them AB, the favorable flops for two pair (no higher) are:
ABx - 3*3*44
Axx - 3*C(4,2)*11
Bxx - 3*C94,2)*11 (x different from A and B - as value)
Totally, 792 favorable combinations from 19600 possible. Probability: 792/19600 = 4.04%

[gamble4pro]

sorry, typing error : C(4,2) instead of C94,2)

[Ponts]

always good info to know, but probably not was original poster was after. I think he wanted to come ahead of AA with KQ for example which means he need to have both hole cards paired and not the table. (any trips or above ignored here)

/Ponts

[jpg7n16]

Just in case you are wondering about your hole card probability stuff...

http://www.texasholdem-poker.com/calculator.php

Gives you the odds (in percentage, odds, ratio or probability) or hitting every hand possible on the flop and...

http://www.twodimes.net/poker/

or

some other site was better because it had the ability to do a random hand but I lost the link

give you the odds of beating other hands, PF or Post-flop