Tuesday, February 2, 2010

Bankroll Management vs. Expected Value

Let’s say you start with $100 in you’re account and you can play one of three games.

You can flip a dime 20 times per hour. The dime is weighted so that you win 502 times out of 1000 flips.

You can flip a 50 cent piece 20 times per hour. The 50 cent piece is weighted so that you win 550 times out of 1000 flips.

You can flip a $20 bill. The bill is weighted so you win on Andrew Franklin, which comes up 565 times out of 1000 flips.

If you bust out, something relatively bad happens like you get a wart on your nose and a hangnail for a month.

If you get to $500 playing this game, you have a 60 percent chance of getting to a meaningful dollar amount in your bankroll, say $5,000 or greater over the next 12 months.

Which game would you choose?

I think most gamers would flip the 50 cent piece. It has a pretty high expected value and your chance of busting out, despite the higher variance vs. the dime game, is probably lower given the higher expected value on each flip. The $20 bill game is cool, but you have a relatively high chance of having a wart and a hangnail for a month.

My point is this: The charts, graphs, and hand analysis on each blog are fascinating reading, but where are the graphs, charts, analysis, or at a minimum, intuitive thinking on which game am I constantly beating and where is my expected value the highest?


Marsh, are you a better 4 tabler, 8 tabler, 9 tabler or 2 tabler. Do you know?
Chuck, is your expected value higher at playing .02/.04 NLHE or .02/.04 PLO?
Adam, is your expected value higher from playing .02/.04 NLHE or MTT?
Martin, is your expected value higher from playing micro stakes NLHE, or stud games?
Royal, have you tried low stakes MTT as you enjoy them in person, if not, why not?

The challenge is still early so the stats may not be statistically significant. What I would recommend is that serious challengers at least keep the stats and then play more games at higher expected values.

For the record, the current leader in bankroll as of yesterday is Mike Thomas, who is up about $60 without receiving 10 cents in rakeback money. I know there was some controversy as to whether or not Mike should be allowed to compete as his starting bankroll exceeded $100.00. Mike is completely aware that if he loses the $100 of challenge money he is out. He also has zero $ on himself so he can’t cheat for his own benefit. Martin’s book took Mike out with his parlay auto adjustments but in an odds maker’s book the only fair thing to do was disqualify him with no refunds, or let him play. I decided to let him play and if he wins, Chuck and Jeh will both get good payouts as the odds on Mike were relatively long.

Mike only plays one game. Equal pay sit and goes for the top 5 finishers. He does not play PLO, NLHE ring games or anything else. On Bodog, the stakes are only $7 buyins with a double up to $14 and $14 buyins with a double up to $28. Though these stakes may seem high, the variance is not that bad as an average player will win half the time, eventually losing money to rake.

I would guess that Mike has played 200-300 of these sit and goes and has been very successful, even before the challenge started.

On Cake, they have $2 double up tourneys, $5 ones, and $10 ones. The $10 one runs often, the $5 less often, and the $2 one rarely.

I played in all 3 last night and won 6 out of 9 times. I will say that I ran really good so I am unsure if they are profitable on cake, especially with such a small sample size. The $10 one is probably a bit high in stakes for the challengers’ current bankrolls but the $5 one sure seems manageable.

My only claim to fame with on line poker is that I found a game where the villains sucked and I was better than they. PLO8 was really easy to beat 2 years ago but now my EV is just slightly positive, the players have significantly improved. PLO players have improved as well. Perhaps these double up sit and goes are the new PLO8. We shall see?