AA vs AA with one winning

[BruceZ]

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I was just involved in a hand where I had AA and another guy had AA, but a four-flush(with diamonds) came out and I ended up winning the hand because I had the ace of diamonds....can anyone tell me the odds of this happening? and maybe a short explanation if possible, I'm trying to figure out how to do odds myself...

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Given that you both have AA, the probability that you will win with a flush (incl. str8 flush) is:

2*[C(12,4)*36 + C(12,5)] / C(48,5)

= 45-to-1 =~ 2.17%.

C(48,5) is the total number of boards. C(12,4)*36 is the number of ways to get 4 board cards in one particular suit, and 1 in a different suit. C(12,5) is the number of ways to get all 5 board cards in one particular suit. Then multiply by 2 since we can make a flush in either of 2 suits.