Odds of your set being counterfeited by larger set?

[carpe2k]

$1-$2 No Limit Cash game. UTG player raises $10. 2 MP players call. Hero in SB calls with 33. Flop is 9h 3d 2h. Hero moves in for his last $65. UTG calls with AhAs. Turn 9. River 9. What are the odds of your set being counterfeited by a larger set? Thanks in advance. [img]/images/graemlins/confused.gif[/img]

[SamIAm]

I think you can do this. How many ways are there for the Turn&River to counterfeit you? How many ways are there for a turn & river to come? What's the first number divided by the second number?
-Sam

[Mark1978]

There is only one overcard on the board, so only one turn/river combination will do it.

45!43!/2 = 990

so 1 in 990, but don't forget that there are many other ways to lose this hand (AA, 45)

[SamIAm]

Dammit, Mark! I was teaching him to fish, and you come in here handing tuna sandwiches to anybody who asks. [img]/images/graemlins/smile.gif[/img]
-Sam

[bigpooch]

In your situation, there are C(3,2) out of C(47,2)=990
ways you can get "counterfeited" or 3 combinations out of
990 when you see running deuces.

In this example, your opponent can also win by hitting an
ace without you hitting the case 3 in 2*42 = 84 combinations
as well as making a flush without the 3 of hearts on
C(8,2) = 28 combinations and a wheel on another 15.

Altogether, you can lose on 130 combinations out of 990 or
about 13.13% of the time.

[Mark1978]

[ QUOTE ]
Dammit, Mark! I was teaching him to fish, and you come in here handing tuna sandwiches to anybody who asks. [img]/images/graemlins/smile.gif[/img]
-Sam

[/ QUOTE ]

But my Tuna sandwiches were off, so learning to fish is a much better prospect.

3 in 990, as BigPooch said (because there are 3 ways of getting two running nines, not one).

[bigpooch]

Also, I mean running nines and not deuces in my post.

[Mark1978]

bigpooch,

There are 139 boards that win for the AA hand (I cheated and used pokenum).

You miscounted the flushes:
C(9,2) = 36

Also you forgot 1 for AA.

That still leaves 3 unaccounted for. What are we missing?

[Mark1978]

Oh yeah, the 3 99 combos. Duh. [img]/images/graemlins/smile.gif[/img].

[Red_Diamond]

This post pisses me off, I've had every set last week except for one counterfeited by a higher one. I prevented the last one from getting busted by banging hard very early so there was no river!! Running bad yes...

I guess it is dumb to slowplay smaller sets, and that's what I get.