What is the probability of someone having a Ace high flush when I have a King high flush. or when I have AA someone having KK? how can I calculate these probabilities. Does these probabilities change vs. getting a 10 high vs 9 high? or getting pocket Jacks vs Queens?

If you have the flush at the flop, I believe the chance someone else among 8 opponents was dealt the Ace-high flush hand in that suit is:

16/47 * 8/46 = 5.92%

The first number is the chance the Ace is among the 16 cards dealt to your opponents. The Ace is 1/47 but we dealt 16 cards, i.e. 16 chances for that card to have come out. The second number is the chance that player has another card in that suit given he has the Ace (8 of that suit remaining).

Note that this is only the chance the hand was dealt, not that the player is still in the hand. The chance someone folded Ax preflop will vary. And no, the rank of your cards is irrelevant, we only care that you don't have the Ace.

And if you hit the flush on a later street than the flop, just adjust the unknowns in the denominator accordingly.



For your other question, I think you meant if you have KK what is the chance someone else has AA, but it's the same answer.

For that type of problem you can do an approximation that is very close. Given your hand, there are 1225 other possible starting hands your opponents can hold, from C(50,2). And there are 6 ways to make AA. So the chance a player does not have AA is 1 - (6/1225). And to approximate the chance one of 8 opponents does have it:
1 - (1 - (6/1225)^8 = 3.9%

This is a very close approximation, because if we scale the exact 10 player answer from http://people.math.sfu.ca/~alspach/mag88/ we get
4.39% * 8/9 = 3.9%.

What is the probability of someone having a Ace high flush when I have a King high flush? This is dependent on number of players, their hand ranges and board texture. One example, you decide to call a raise with kdjd against a loose player who opens (any suited cards+, 22+, jt+) {457 total combos vs kdjd} and the flop comes td4d6d. For this flop his open range can only have 7 higher flushes (adxd about 1.53%) and 21 lower flushes (qdxd- about 4.59%) out of his 457 opening combos. Also, be aware that 9 combos (1.97%) are drawing to a higher flush.

Higher flush example number two; you call a raise with kdjd against a very tight player who opens (at suited+, 77+, aq+) {71 total combos vs kdjd} and the flop comes 8d4d6d. For this flop his open range can only have 2 higher flushes (adqd & adtd, or about ~ 2.81%) out of his 71 opening combos. Also, be aware that 9 combos (12.67%) are drawing to a higher flush (3-adkx, 3-adqx & 3-adax).

Here's another take on OP's questions
OP didn’t specify the conditions – number of opponents remaining, which street, number of flush cards on the board, and opponent read.

Assume one opponent and three flush cards after the river with you hitting a king high flush with the river card. The chance your one opponent has two of the flush suit with one of them being the ace is

2* 1/45 * 7/44= 0.007

1/45 is for holding the right ace and 7/44 is for having one of the remaining flush cards out of the 44 remaining deck cards. The 2 multiplier is for two possible orderings; Ax or xA. This result should be modified to account for opponent tendencies. For example, if he is very tight, the fact that he is still in the hand may well indicate he had a flush draw after the turn with a high card, perhaps the ace, so this result is too low.

If you have KK the chance someone holds AA depends on the number of players. Using a pretty good approximation, the probabilities that at least one opponent has AA are as follows:

1 Opponent 0.5%
3 Opp 1.5%
5 Opp 2.4%
7 Opp 3.4%
9 Opp 4.3%

The same answers apply for any comparison TT vs JJ, etc. However, if you have a pair of tens you are more interested in villain having jacks or higher, not just jacks. This increases the chances significantly, roughly by a factor of k, where k is the number of higher ranks.

How about, if I have a 8 high flush and someone having the same suit flush and higher, than my flush in HU in a full ring game? and would it make a significant difference, if it was a multi-way pot? btw, thx, for the reply.

You asked a similar question in the Poker Theory forum. See my response there where I used a simulation program to get results of at least one of 8 players having suited cards of same suit of yours but with a higher rank.

Axs vs Kxs according Flopzilla 0.65%.

AA vs KK it happens 0.02% of all hands. Every 44th times 6max or 27th times when you hold AA or KK.