This might be a fairly standard question to some MTT players, but as a cash player I have no idea, and I was discussing it with a few good tournament players recently, and no one knew the answer. Everyone had a rough estimate, but the math is actually quite complicated to figure out, so I assume someone has a simulator or something.

Question: (as title states obviously): You're at a 9-handed MTT table. What is the odds that at least one of the opponents has TT, JJ, QQ, KK, AA, AQ, or AK? Assume that no players have acted yet (this is relevant because if you're in CO or something and its folded to you, obviously no one has these hands).

Not sure if it's exactly the right answer but close enough: 220:1 to get dealt AA, 220:9 1 person gets dealt AA, multiply by 5 for TT-AA and by another 5.5 or so for AK/AQ, so seems to be close to half the time for somebody to get TT+/AQ+.

Odds somebody has a TT+: (4/52*3/51)*5
Odds somebody has AQ/AK: 2*(4/52*4/51*2)
Odds that no opponents has that = (1-((4*3/52/51)*5+(4/52*4/51*2*2)))^8 or 68.176%
Odds that at least one opponent has it = 31.824%

Really for probablity forum 4.7% that any one opponent has TT+/AQ+. The chances that on of 8 players has one of those hands is 1 - .953^8 = 32%. Now it is slightly higher, because if one doesn't have it, more likely others do as high cards are live. Also, you own hand could have blockers. In anycase, someone has a premium hand pretty often, so raising or pushbotting light from early position may not be good.

pretty sure this is correct, that is why you can profitably open raise tens at a nine handed table but you will lose money raising a ten handed Tble with same hand

Wat

I'm fairly certain its at least under 1/3, and that 1/2 is way too much.

QED

This might be the worst interpretation of probability in poker I've seen

I'd scrap the "in poker" bit of that statement

I really would like an answer to this question

haha yeah I was sure it was a level

then read betgo's answer

To get an exact answer, you would probably have to do a simulation, because the fact that several earlier players didn't have TT+/AQ+ makes it more likely a later one will. Also, it is more likely that someone has TT+/AQ+ if you have 77 than if you have AJ, because with AJ you have blockers.

No I don't think so, at time #1 , when ur utg w/ 77 it is 1 - .953^8 = 32%.

But let's say ur mp with 5 behind and its folded to u the probability is slighty bigger than 1 - .953^5 = x