If you have KK there are 50 cards left in the deck. The probability of a single opponent getting dealt AA is 4//50 * 3/49 = .004898.
The probability of single opponent not getting AA is 1 - .004898 = .995102. With 9 opponents the probability that no one holds AA is approximately .995102^9 = .956772.
Therefore the probability that at least one opponent holds AA is .043228. So if you hold KK at a 9 handed game UTG and no one else has acted, there is just over a 4% chance someone else holds AA. At a 10 handed game simply change the 9 to a 10 and get .047914.
This isn't exactly right Sherman because of card removal effects. Also you have confused the 9 and 10 handed scenarios. (.995102)^9 is the 10-handed scenario while (.995102)^8 is the 9-handed scenario since we now have 8 opponents.
How to appropriately calculate the probability is discussed here:
This isn't exactly right Sherman because of card removal effects. Also you have confused the 9 and 10 handed scenarios. (.995102)^9 is the 10-handed scenario while (.995102)^8 is the 9-handed scenario since we now have 8 opponents.
How to appropriately calculate the probability is discussed here:
