Poker Talk

Last week was the annual World Series of Poker "Big One" in Las Vegas, and while the tournament won't be shown on ESPN until later this year, a lot internet sites have been reporting some or all of the action that's taken place.

I happened to read about one hand which really blew my mind:

Two guys have about the same amount of chips, one has pocket 5's and the other pocket 9's. On the flop comes two 5's and another low card, giving the one guy 4-of-a-kind, and the other guy an overpair with his 9's. So they both go all in (I don't know in what order, but it doesn't really matter), and you gotta think, the guy with the four-of-a-kind pretty much has the hand locked up, going against a measly one-pair with his four-of-a-kind and only 2 cards to go. Nope, the turn and river were both 9's, which gave the second guy four 9's to beat four 5's.

All of us who play poker have plenty of bad beat stories to tell, but it really doesn't get any worse than that. Literally, it's the worst bad beat possible if you do the math. It's one thing for a guy to hit running cards against you (like hitting a running straight or flush), cause even then, you have a bunch of possible combinations out there. But with 2 cards left to flip in that hand, the guy needed those two exact cards in the deck to win, and he got them. Something like 0.05% probability. So the next time anyone feels like complaining about bad luck in our $10 home games, think about the guy who flopped four-of-a-kind against one pair, and still ended up losing, in what was probably the biggest tournament of his life.

I was thinking about the math of no-limit tournaments and decided to do some calculations, just for kicks and giggles. Let's say that you only go all in pre-flop with the best possible starting hands (A-A, K-K, A-K, Q-Q). Usually, your winning percentage if you play these hands out is gonna come out to somewhere between 70-80% on average. For the sake of my math, I just estimated that you will win 75% of the time with these hands if you go all-in pre-flop.

By the way, 75% is pretty damn good odds. Consider for example:

- A-A is at best about 90% against certain hands (including 2-7 offsuit, the worst possible hand), and about 80% against any underpair
- K-K is also about 80% against underpairs and then about 70% against any hand with an Ace (except pocket Aces of course)
- Q-Q is pretty much the same as K-K, except you are only around 55% against A-K.
- A-K is about a 70% winner against any hand except pocket pairs and A-K. Believe it or not, whether you're up against A-Q suited or 2-7 offsuit, you are never much more than a 70% favorite.

These are all assuming that you're not going against another top hand (which is usually the case if you are called on an all-in bet). So even if you are the tightest player ever, or even if you make all the right reads, the best you can realistically hope for is to average 75% pre-flop odds for all the times you go all-in.

Anyways, in a tournament like the WSOP, say you decide to go all-in for all your chips, only in those situations where you have the top hands I listed. If you have A-Q, J-J, 10-10, A-J, etc., you fold if someone bets you for all your chips. Using the 75% number, if you risk all in:

3 times - You'll survive the tournament 42% of the time (0.75^3)
5 times - You have a 24% survival rate (0.75^5)
10 times - You have a 5% chance of staying in the tournament (0.75^10)

Think about that: even if you get your money in with the best odds every single time for only 3 times throughout the entire tournament, the numbers are still against you winning in the end (you have a 58% probability of losing at least one of those 3 times and getting eliminated). True, this is also assuming the other guy has more chips than you all 3 times, but if you've been playing that tight, you'll definitely be going against larger stacks more often than not. And if you ask me, 3 times is a very low estimate for that situation to come up in a tournament (I think even 5 or 10 would be a conservative number).

Moral of the story: it's better to be lucky than good in a poker game.

Of course, that doesn't mean that skill is worthless - pros will still win more money in the same game than amateurs in the long run. But these calculations tell us that if you want to win a tournament, you definitely can't win it on skill alone.

* If any of you are interested in how I got the numbers for those odds, www.cardplayer.com has an applet that lets you calculate odds in Hold'em. The rest of the calculations are high school math.