Trading and Poker

I'm fascinated by the number of traders who also dabble in game playing. Ugly loves chess and games of chance. Chris Perruna thinks that poker has some parallels to trading. Warren Buffet loves to play bridge. And Dr. Van K Tharp enjoys poker playing as well.

I played a few poker games with my brother and a few friends of his at a recent birthday party. It was the first time I had played since playing on my Mattel Intellivision back in the mid-80's. I'm guessing that most StockPunk readers don't even know what an Intellivision is. Whippersnappers. I digress.

I think there are many lessons that poker teaches that can be integrated into a trading system. Issues like drawdowns, bet size, risk, ruin, and probabilities are common to both trading and poker.

One StockPunk reader sent me an interesting and math-intensive article he wrote that utilizes a computation called the Kelly Criterion for poker. The Kelly Criterion is also found in many books about trading systems. The writer asked me to use his cryptic poker playing name which is Moneysuckle.

The Kelly Criterion and Bankroll Management for the Live NL Cash Game Player

By Moneysuckle

After reading Fortune’s Formula, Phil Laak’s interview and Al Kratz’s article in the July issue, I decided to explore the application of the Kelly Criterion http://en.wikipedia.org/wiki/Kelly_criterion to bankroll management for the live cash game no limit hold’em player. 2+2 poster Pzhon illuminated my way.

Here is the formula, in layman’s terms:

((Odds * Chance of winning) - chance of losing) / Odds

Most live game players keep records by session. It is quite easy to figure out:

1. How often you log a winning session,
2. What your average winning session is, and
3. What your average losing session is.

Let's say Player A wins 60% of his sessions, and loses 40% at 5-10 NL. He buys in for $1000 and his average winning session is $2000 while his average losing session is $1200 (because he brings more than one buy-in).

Player A’s odds are 2000:1200 or 1.67:1. In other words, on average, he risks losing $1200 to win $2000. Employing the formula, ((1.67 * 60) – 40) / 1.67 = 36%. So, under the Kelly Criterion, Player A’s bankroll * 36% should equal his average loss ($1200). We use average loss because that's the denominator we used to figure the odds payoff. Player A therefore needs a $3333 bankroll under the Kelly Criterion if these are his true winning stats. At 5-10, this would be three buy-ins!

The problem with full-Kelly is that you have a 13.53% risk of ruin. See http://www.bjmath.com/bjmath/proport/riskpaper1.pdf This risk of ruin is too high for a player dependent on poker for income. If you double the bankroll ("half-Kelly"), you get risk of ruin down to 1.83%. If you quadruple the bankroll (“quarter-Kelly”), then your ROR is down to 0.03% with only a 2% chance of ever losing half your bankroll. Quarter-Kelly bankrolls are therefore conservative and considered appropriate for professional players. But Player A’s quarter-Kelly bankroll for his 5-10 game with these stats would be $13,333 or ~13 buy-ins of $1000!

Bottom line, the wives’ tale advice you hear about having 20-30 buy-ins for a given game is very conservative for a top winning player. Of course, no amount of bankroll is big enough for a losing player, while marginally winning players need much larger bankrolls than solid winning players -- or the customary 20-30 buy-in advice. An example:

Player B plays 5-10 NL too. He buys in for $1000, and wins 52% of his sessions. Player B’s average win is $2000 while his average loss is $1900.

His odds are 2000:1900 or1.05:1. Using the formula, ((1.05 * 52) – 48) / 1.05 = 6.3%. So, at full-Kelly, $1900 (average loss) should be 6.3% of Player B’s bankroll. Bankroll therefore equals $30,158. But full-Kelly has 13.5% risk of ruin. Player B’s quarter-Kelly bankroll would be $120,632 or ~120 buy-ins!

There you have it. Using quarter-Kelly, the top player can operate with 13 buy-ins while the marginal winning player needs 120 buy-ins for the same game.

In reality, most top players operate at bankrolls far greater than quarter-Kelly would require of them, while most marginally winning players operate at bankrolls far short of their quarter-Kelly requirements. This is why many marginally winning players go broke from time to time – they take too much risk of ruin, especially if they like to take shots at bigger games.