Wednesday, May 28, 2008

Wednesday Math, Vol. 25: Better than the rake

This is Doyle Brunson. Known by the nickname Texas Dolly, due to a misspelling of his name in a newspaper story many years ago, Brunson won the World Series of Poker back in 1976 when only a few people would dare to put up $10,000 and sit in on a game with the best players in the world. Doyle Brunson hasn't worked a regular job for a very long time, being an honest to goodness professional poker player. He made a nice amount of money writing a very useful book on poker in the 1970s called Super System, which improved the level of poker play around the world. But to be a professional poker player, you don't just have to be one of the best players at the table. In the long run, you have to be better than the rake.

Poker has changed dramatically over the past few years. It used to be that you had to go to a poker room to play for money, or go to a home game, which is technically illegal in some states. In California, it's a city by city decision as to whether or not there can be poker rooms, and in the Bay Area only a few cities, including San Jose, Palo Alto, Emeryville and Hayward, decided to allow poker rooms. The rooms make their money by effectively charging rent to play, taking a little money out of every pot. This is called the rake, and it means that the average player at any table is losing money to the house, and you have to be better than average to make any money at all.

Nowadays, many people play poker online. Some have never seen real cards dealt at a real table. The online poker rooms have the same business model as the brick and mortar places, taking a rake from every pot, but the speed of the game has dramatically increased, and because tournament poker is the popular method seen on TV, the online rooms have lots of tournaments. In person, tournaments are rare, maybe only one or two a day at a big club. In online poker, they run continuously, especially the Sit 'n' Go tournaments, known as SnG to save on typing.

Lemme 'splain. You sign up on a waiting list to play in a tournament that will have only one table full of players. For most tournaments, that means nine players, but there are tournaments set up short handed for six players or eight players if the game is a stud game, or even games with two players.

In these games, you pay an entry fee and your money is turned into tournament chips. Instead of a rake of every pot, only part of the entry fee goes into the prize pool, and every player pays an extra fee which goes to the casino. Not every game is charging the same rate. Here are some examples from Full Tilt Poker.

$6 to the prize pool, $.50 to the house. Here, the extra amount is 8.3% of the money you have a chance to get back. For a cheap game, this is the big bargain.

$5 to the prize pool, $.50 to the house. This is the standard at a lot of games, paying a 10% rent for the table. If you play in a $50 tournament for example, it's a $5 extra, so the percent is the same.

$1 to the prize pool, $.25 to the house. This is a truly horrible game. Some people play in the cheap games because they don't have much money, but at 25% rent, almost no one will win in the long run.

Let's define "the long run".

I ran a computer simulation of 100 players playing poker tournaments constantly. When a simulated player ran out of chips in one tournament, that player was put on a waiting list for the next available game.

After 90 games:
$6+.50 tournaments:
44 players are seeing a profit, 56 are in the red.
$5+.50 tournaments: 40 players are seeing a profit, 60 are in the red.
$1+.25 tournaments: 29 players are seeing a profit, 71 are in the red.

Well that's not so terrible. In the better games, it's not completely fair 50-50, but it's not that bad. Well, the long run might actually be a little longer than that.

After 900 games:
$6+.50 tournaments:
33 players are seeing a profit, 67 are in the red.
$5+.50 tournaments: 32 players are seeing a profit, 68 are in the red.
$1+.25 tournaments: 7 players are seeing a profit, 93 are in the red.

After 9000 games:
$6+.50 tournaments:
7 players are seeing a profit, 93 are in the red.
$5+.50 tournaments: 4 players are seeing a profit, 96 are in the red.
$1+.25 tournaments: 0 players are seeing a profit, 100 are in the red.

In the long run, the real long run, the "play poker your whole life" long run, it's the very rare person who is ahead. Ahead enough to make your living at it, that's a completely different matter. Personally, I play online poker, but I keep tabs of how much I win (or lose) and how time I spend playing. In these little tournaments for small stakes, even if I was as good as Doyle Brunson, I couldn't make hourly minimum wage winning these things. To make a living, I'd need a much larger bankroll than the paltry amount of cash I'm willing to risk.

I'd also need more skill at the game. I've seen a profit several times, but usually I'm in the red.

This reminds me of an old joke about the business of sports, a joke which is no longer true, but still is a well crafted ancient trinket of comedy gold.

You know how you can make a small fortune owning a baseball team?

First, you start with a large fortune.


CDP said...

Very interesting! I had no idea how this worked. (and I love the joke about the baseball team) said...

After spending ten years in the casino business, and a few years playing poker for living, these are things that every person who wishes to play for profit has to take into account. The rake, the tip, tips for waitress, brushes and the like.

There are strategies that take into account beating the rake but it is true that the higher you play the less effect the rake has.

This is the reason most beginners get discouraged because it is almost impossible to beat the rake in a low limit game. People that don't understand math don't realize how big of a difference there is between 5% of a 50 dollar pot and 5% of a 500 dollar pot.

Oh well, that's why we call them fish.


Matt said...

Interesting simulation. I was wondering if you had one focused strictly on single table sit n go's? With the proper strategy, I have found the single table SnG's to be the most profitable.

dguzman said...

So I guess the good old days of being a riverboat gambler and making a good living at it are pretty much over. Shit.

Matty Boy said...

Hey, sitngo. Yes, the simulation focused on simulating an online poker room where players knocked out of a single table tournament immediately signed up for another tournament, and the simulation would end after a certain number of tournaments were played. The simulation was completely random, not assuming that any players in the pool of 100 were any better than any other players. I have an idea for how to simulate a "top 10%" that I'll program into my computer this weekend.