Cross post from the probability forum since it's a specific question to PLO and PLO6...

Case 1 - PLO

Say I am holding AQK9 and flop comes out Q Q 9...
Ignoring preflop action and player-specific ranges, what are the odds of my opponent holding the case Q? What about the odds multiway? One of 2 opponents holding the case Q? One of 3 opponents holding the case Q? 4 opponents?

Case 2 - PLO6
Say I am now holding AKQJ97. Flop comes out Q Q 9 again. Same question as case 1... HU? Vs 2 opponents? 3 and 4 opponents?

I know I am asking a lot, but can you show some procedure? I would really like to learn to do this myself so I don't have to ask again and so I can help others with similar questions.

The math is pretty easy in plo4 there are 7 exposed cards, 3 on flop and 4 in your hand so each remaining card = 2.2% so the odds of each opponent having a Q is 8.8%

Plo6 9 exposed cards, each remaining card = 2.3%, odds of each opponent having a Q is 2.3x6 = 14%

This math only works if you assume that opponents are equally likely to hold each card in the deck which isn't true imo

Using your math in plo23 there are 26 exposed cards so each remaining card is 1/26. Odds of having Q is 1/26 * 26 = 100%. And it would go over 100% with more cards.

The way to calculate this is to calculate the odds of them not having the Q

In plo4, odds of not having it are 44/45*43/44*42/43*41/42 = 41/45. This is because there are 45 unknown cards for the first card and 44 are a success (ie not a Q). For the second card there are only 44 unknown cards left. Etc

My method of calculating would still work and would not go over 100%

For example in plo23, 26 exposed cards, each remaining card = 100/26= 3.85%
23x3.85=88.5% so the odds of ur opponent having a Q is 88.5

Actually ur right and im wrong, because my method can go over 100% if lets say theres 2 outs which is impossible.

What about plo40?