When a poker hand goes nuts

Feb 10, 2009 5:03 PM
Back in the Saddle by Johnny Hale |

EDITOR’S NOTE: With Oklahoma Johnny taking a well deserved break, we went back into the GT archives for a 2006 article that still applies in today’s poker rooms.

I recently received a nice note from a reader who related a poker story that many of us can benefit from. Here it is.

Dear OK Johnny,

I dealt poker to you under Jay Nauta at the old Holiday International Casino in 1978, remember that room?

My question is this: I was playing in a 10-handed no limit game, but to make it short three of us went all-in. I had Ks-Qs, and the other players had A-A and A-K. The flop came 2s 6s K.

At this point I believe I have the best draw: I made the nut flush on the turn (with As), but the river came K, which devastated my hand.

What are the odds of fourth and fifth street coming ace, king? Knowing might take some of the sting out of losing to a full house like that. – Mike

Yes, Mike, I remember the old Holiday Casino very well, way back in my salad days; in fact, 1978 was a very good year.

Yours is an interesting question, and it only takes a little basic arithmetic to get to the answer, albeit a painful one!

Mike, here is how you compute the correct odds for this situation.

First, you know there are 52 cards in a standard deck.

You have seen your two cards, plus the other cards that have been played include your opponents’ A-A and A-K, as well as the flop, 2s 6s K, for a total of nine cards already played.

Subtracting the nine cards from the deck leaves 43 cards remaining.

Assume again that the final two cards come in the order you gave, ace and then the king, you would have this result: It is 42-1 that you will catch the As on the turn because of the 43 remaining cards, only one is the ace of spades (thus odds of 42-1).

Revealing the As on the turn leaves 42 cards in the deck, of which only one is the remaining king. Therefore, the odds are 41-1 that you will catch the final K on the river.

The end result of catching this exact order of cards become 42 times 41 or 1722-1!

Indeed, Mike, those are long odds and could be called a bad beat, but it does happen. That is why we play the wonderful game of poker – a lot of different things can and will happen.

Like I sometimes tell folks, it’s going to rain in Oklahoma … get a tub and catch some water. In reality, it may not rain today, but it will rain at some point!

Mike, the mathematical answer of 1722-1 is correct, but so is the somewhat humorous response: the odds are 50-50 that it will happen or not.

Thanks, Mike, for the interesting problem.