WSOP, bad beats, great hands

MGM wrote:

I've been playing about 1 year now. Here is my worst beat.

At MGM in Vegas. 1-2 no limit. On BB with $250 in front of me. A weak player in first position raises pre-flop to $15. Amazingly, 6 people call. I look down at A/9 off suit. Pot odds, good enough to call $13 more to win $105, if I was to happen to flop a monster hand.

Flop: A K 9

I check. 1st position (woman) bets $30. Amazingly, 4 people call the $30. Pot now stands at $225. I raise $100, thinking the 4 people were on some ridiculous draws and the woman caught her weak Ace. She looks confident and reraises me all in. (She had nearly $1000 in front of her from exceptional luck through out the night). After some considerable thought, I call. The pot now stands at $675.

Her hand: K 9

My hand: A 9

Turn: 2

River: K

I was dizzy for a week.

mcgato wrote:

The statistician in me just had to answer this. To calculate the probabilities in question, you have to consider all the possible scenarios:

Case 1: KK. The probability of getting KK on the final two cards is (2 kings/47 cards left)(1 king/46 cards left)=0.000925. Remember that once the first king comes out, there is only one left in the deck.

Case 2: K then something not an ace or king. (2 kings/47 cards left)(41 non king or ace cards/46 cards left)=0.037928.

Case 3: Something not an ace or king then a king. (41 non king or ace cards/47 cards left)(2 kings/46 cards left)=0.037928.

So those three cases will result in a win for the K9. Add up the probabilities, and you get 0.076781, or 7.6781%. I think I did that right. Of course it gets more complicated when flushes come into play, but the idea is the same, namely what are the possible scenarios and the probability of that scenario.