Good morning. Concidering a mid-pocket pair

[VivaLaViking]

Consider being dealt pocket 10's. A player acting before you moves "All In" but the good news is he has a much smaller stack than you and he appears to be a loose player.

You begin to calculate whether to call but first you think about him having an overpair and if he does, what is your probability of making trips without him making trips.

Recognizing that there are boards that negate any probability of you winning we focus only on you making trips without him making trips.

First, what are the chances he has an overpair, A's, K's, Q's or J's?

C(4, 2)<-[Him making a pair] * 4<-[Number of pairs better that 10's]
-------------------------------------------------------
C(52, 2)<-[Possible pocket cards]

Last, if you mis-read your opponent and he does in fact have an overpair what are your chances of you hitting trips without him hitting trips? (Math assumes both players have pairs)

C(2, 1)<-[Trips] * C(45,1) * C(44,1) * C(43,1) * C(42,1)
---------------------------------------------------------
C(52,5) <- [Possible boards]

Does this math look correct?

[LetYouDown]

Glanced briefly, there's at least one problem. Your denominators of C(52,5) and C(52,2) are incorrect. You have knowledge of at least 2 cards...so those are impossible on the board.

There are C(50,2) possible hands for him to have. So the odds of him having an overpair to your 10-10 is:

[4 * C(4,2)]/C(50,2) or 24/1225 or about 1.96%.

Assuming he has K-K, the odds that you'll hit one 10, without a K on board should be:

2 * C(44,4)/C(48,5)

271502/1712304 = ~15.86%

Excluded hitting both 10's, as K's are essentially irrelevant at that point. If the board comes 10-10-K-K-X, it's worth the story.

[VivaLaViking]

Good error spotting. Thank you. Are you settled in FL now and are you planning to go to the WPT event in November at Foxwoods. I am going to go to as many satelites as possible starting in October. Note: Some are under $100.

[LetYouDown]

Don't even remember mentioning moving to Florida, but I guess I must have. I'll be in Florida in just over a week. Driving from NY on the 8th of October. Bye bye B&M /images/graemlins/frown.gif.

[VivaLaViking]

Thinking of trading it all in to become a "River Boat Gambler"? lol

[LetYouDown]

I have good sea legs, but I don't think I could play cards on a moving boat. I'll probably never do it. It sucks because I recently started going to a B&M around here, with the softest tables imaginable. If I don't triple my buy-in, it's a bad night. I think I've lost twice in 3 months...and once was because I ran awful (guy rivered a higher boat, I lost an all-in with K-K vs. 7-2 offsuit, etc.). It's been fantastic.