[ohnonotthat]

If you have AQ and another player at the table has QQ the odds against seeing the case Queen will flop are 15-1 against; put another way, the Queen will flop 6.25% of the time.

QQ will flop a set approximately 12% of the time when both Queens are in the deck so it seems reasonable that with only one Q the set will show up roughly half as often.

Notes:

1. Despite the fact that it worked out in this instance this method is NOT the correct one for doing calculations of this sort (although in most cases it comes fairly close); the reason should be obvious. If there were 16 Queens left in the deck the chances of flopping one when you held AQ and your opponent held QQ would obviously not be 100%.

2. You asked what the chance(s) were of flopping the Queen IF ONE OF YOUR OPONENTS HELD QQ WHILE YOU HELD AQ. You did not the question that would be more appropriate (to me anyway), "If I hold AQ and a Q flops what are the odds against my opponent having QQ" ?

Do you see why knowing this figure is more useful than the one you asked ?

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If I were invited to attend an event and knew that "Joe" had also been invited and I did not wish to see "Joe", knowing the odds of him attending are of little use once I run into him !

However, if on the way in I am told that there are is male in the room whose first name begins with "J" out of 20 people with this initial who were invited it's not difficult to determine that the chances of that person being "Joe" are 1 in 20.

If I am then informed that the person in question has red hair and I know that only 14 of the 20 "J's" have red hair I can then lower the likely odds to 1 in 14 (although some allowance must be made for the possibility that Joe has dyed his hair since I last saw him).

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Do you see the idea ?

If your opponent raised before the flop and you know from past sessions with him (or you make the very plausible assumption if you've never played with him before) that he will raise in this exact situation (same position, same number of callers, etc.) with

AA, KK, QQ, AKs and AK/off

you can proceed knowing that if a Queen does flop there is only one chance in 22 that he has QQ. (I am assuming for purposes of simplification that there are no Aces or Kings on the flop).

He can have QQ 1 way, AA 3 ways, KK 6 ways AKs 3 ways and AK/off 9 ways.

- You want to be able to do these calculations in your head rapidly and accurately, because if you can you'll be one of about a dozen people in the world who can. [img]/images/graemlins/wink.gif[/img]

- Seriously though, if you can at least guestimate the individual chances for each of the possiblities you can make more informed choices regarding how and whether to continue with your hand. But do not forget to adjust for what you see as the hand progresses. If the flop comes Q-7-2 rainbow and a tight player continues to contest the pot you can pretty much rule out JJ or AK/off and AK/s becomes a little less likely. A tight player will usually not push AKs without flopping som e sort of draw.

I hope that helped.

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BTW, I stand by the math and the info it provides you but you're on your own regarding how you use it. Don't get too attached to your initial assesment of his possible holdings. This particular [tight] opponent may have chosen to add 77 to his raising hands causing you to incorrectly measure not only his chances of having QQ but more importantly your chances of winning the hand. (Tight player raises 77 = Joe dyed his hair)
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To those who think this answer was far too f---ing long [img]/images/graemlins/smile.gif[/img] . . .

This is a complex topic for someone who has no backround in probability and I thought it best to illustrate it as clearly as possible.

Or, to put it another way, [censored] me; I did the best I could. (LOL)

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Best wishes,

- Chris