She Does the Maths

When I first studied poker, I read lots of books on poker written by the smartest people in the game I could find. I don't mean celebraty books, which the market is currently flooded with and are basically just glorified opinion pieces, I mean the people with Ph.Ds in mathematics who studied the game, the probabilities, and the strategies.

There are three such books I consider gold. Most people can't get through them for they do require a strong background in mathematics, like, major in college strong. Nevertheless, I keep them to myself because since most people haven't read them, that gives me an advantage.

However, one book that is well-known (but again, tricky material written by a PhD in maths) is Mason Malmouth's, "Gambling Theory and Other Topics." In it, he spells out the maths for poker, what one can expect in terms of fluctuations, bankroll requirements, and bluffing strategy. It's brilliant. I recently started re-reading my poker books and decided to do the maths for myself.

The result is a bit depressing.

Now I haven't yet recorded enough results from my playing sessions, so I approximated them based on my winnings last year. I came up with a win rate of $28.5/hr and a standard deviation of $305. Now you might think that with a positive win rate, you'll always make money, but that's where the standard deviation comes in. All my results should lie between three standard deviations. That means in any one session I could go home as much as a $1,000 winner or loser, despite having a positive win rate! (Of course statistics doesn't know I'll quit if I'm down more than $400.) The good news though, is that the deviation should go down the more data I collect, assuming my play is consistent.

Believe it or not, it you know your win rate and deviation, there's a forumula you can use to find out how long you need to play in order to guarantee a win! At a $28.5/hour win rate with a $305 standard deviation, I'll need to play for 1,032 hours to assure a win. Ouch! That's like, 1/2 a year of 40 hours/week!

And that's not the depressing part. Taking the derivitive of the above formula and solving for zero finds for you when you can be at your lowest. The lowest point in my bankroll (statistically speaking) can occur at the 258th hour, at which point I'll be $7,357 down.

In other words, to assure I'll never go broke, I'll need just over $7K.

But that's with incomplete data. Hopefully, these numbers will go down (except the win rate, which hopefully will go up!) as I record more sessions. Also, those numbers assume no risk. They go down considerably if say, I am willing to say, "How much money do I need for a 95% chance of never going broke?" then the number of hours required to win drops to five weeks and the bankroll needed to just under $2,000, which amazingly enough, is the amount I wanted to start with.

Math is kewl.