I flopped a K high flush, opponent flopped an A high flush. What are the chances of this happening? Thanks.
there is a about a 25% chance that you get dealt suited cards. (12/51 ~ 23.5% to be exact)
given that you already hold 2 suited cards, there is a 4.4% chance that your opponent also get dealt 2 cards of the same suit (11/50 * 10/49 any 2 cards ace or not) and a .4% chance that they hold 2 cards of the same suit where 1 card is an ace.
there is about a 6% chance of flopping a flush if you hold 2 suited cards, so the odds of you getting 2 suited cards, your opponent getting an ace and another card of that suit, and flopping a flush is pretty small. to be exact:
.25 * .004 * .06 = .00006 or .006%
I did not account for that fact that one of your cards is the king of the given suit. My math is off in a few other ways too but this should give you an idea.
It is more important to just realize that this is extremely unlikely, rather than the exact numbers. You got coolered an that happens from time to time, better to focus on things that are in your control.
The other answers answer "what are the odds of me flopping a flush and my opponent also flopping a flush", and the quite-low odds of flopping a flush in the first place skew the results. But I think the question you're more interested in might be: once I've flopped a flush, what are the odds of my opponent also flopping a flush.
If I've flopped a flush, what are the odds of your opponent also having a flush?
We've seen 5 cards of this suit, and there are 8 left out of the 47 cards we haven't seen. So his two cards have the odds of 8/47 and 7/46 respectively, which combine to
8/47 * 7/46 = 2.59% (If you want to understand how to combine them, see my other answer).
But there's usually more than one opponent, which significantly alters the odds. Each opponent has a 2.59% chance of flopping a flush separately, and we can combine the odds:
- For two opponents,
2.59% + ((1-2.59%)*2.59%) = 5.11%
- For three opponents,
2.59% + ((1-2.59%)*2.59%) + ((1-2.59%)*(1-2.59%)*2.59%) = 7.57%
- For four opponents,
2.59% + ((1-2.59%)*2.59%) + ((1-2.59%)*(1-2.59%)*2.59%) + ((1-2.59%)*(1-2.59%)*(1-2.59%)*2.59%) = 9.96%.
- For five opponents, 12.30%
- For six opponents, 14.57%
- For seven opponents, 16.78%
- For eight opponents, 18.94%
- For nine opponents, 21.04%
In short, if you flopped a flush and have multiple opponents, odds that are at least one of them would also hit a flush right there aren't that low, and that's without even considering the turn and the river.