Professional betting—whether gambling, investing, or handicapping—is about having an advantage with a positive expected return. If you don’t have any statistical edge, you shouldn’t bet at all. But having a statistical edge is only one part of the equation. The other part of the equation is the delicate issue of bet sizing (or “money management”). And I believe this other part is more delicate and critical than you think.
In fact, you can be the world’s greatest handicapper, but if you can’t manage your money, you’ll end up either broke or way below the potential of your hard work. And the sad fact is that almost any gambler who has an edge but disregards money management goes broke in the long run.
Of course, this requires an explanation.
Let’s say you have an equal bet in which the odds of you winning or losing is 50% and the house takes nothing. You continuously bet a fixed dollar amount in each bet. In such a bet, the mathematical expectation of your wealth change is equal to zero. You are just as likely to win as you are to lose and the statistics say that your wealth should move in a horizontal line.
And often when we think about future expectations, we rely on such statistics. But that is, of course, pure fantasy. In reality, your wealth path would not move in a horizontal line. In reality, your wealth would follow a random walk that gets increasingly chaotic over time.
If we were to extend the wealth line into infinity, it would cross your original bankroll an infinite number of times. You would also go broke an infinite number of times. But this is irrelevant since you can only go broke once and then you’re out of the game. And notice how early bankruptcy happens.
If you were to play a negative expected-return game such as in a casino, the path to bankruptcy would happen even faster. And even if we were to give a small statistical edge such as a 51% win rate, it’s still possible for a persistent gambler to go broke at some point. This is the gambler’s ruin problem.
Knowing this, consider now the foolish betting strategy by the name of martingale. This is the strategy in which you double up your bet every time you lose until you win. Of course, the effect of the martingale system is that it accelerates the gambler’s ruin problem.
The solution to gambler’s ruin—as I think you’ve already figured out—is to bet bankroll proportions instead of fixed dollar amounts so that you bet more as your bankroll increases and you bet less as your bankroll decreases. But even doing that doesn’t shield you from gambler’s ruin if your betting proportions are too aggressive for your statistical edge.
So now the question becomes: How much of the bankroll should you bet? Is there an optimal bet size that assures you to never fall prey to gambler’s ruin while maximizing your long-term wealth?