How the Kelly Criterion works

The Kelly Criterion is a universal way of determining how much risk exposure a casino should take on per game: here’s how it works.

Kelly betting

In 1956, J. L. Kelly Jr, who can best be described as a game theory scientist, came up with something called the Kelly Criterion. It may seem narcissistic, but mind you he had a PhD in Physics. The Kelly Criterion is a set of rules governing how much of your bankroll you should bet on an outcome if you have an edge in the situation. This can be applied to international stock markets, and most beautifully to casinos. The calculus behind Kelly betting is even more beautiful, but that’s for a different time and a different audience.

The rules of the game

The Kelly betting style is supposed to work when you have an edge. This usually happens when you’re playing against stupid people, like gamblers. (Note: gamblers aren’t always stupid, but most of them are.) The idea is to take as much money as you can from an irrational participant without accidentally going bankrupt.

Let’s think about a simple scenario. A friend offers to flip a coin: if it’s heads, he will pay you $6. If it’s tails, you pay him $4. Mathematically, you have a 10% house edge here, which is excellent. If you play this game infinite times, you are guaranteed to make infinite profit, as are the rules that govern this crazy universe in which you were gifted such a giving friend. Sadly, you don’t have unlimited money to back this up. If you have $1,000, it may work, but you probably have only $50 tops. You are still likely to win, but you may not. You may get screwed pretty easily. This is where Kelly steps in to help.

If you bet your whole bankroll in one bet, you have a 50% chance of losing everything. Sure, it’s a smart bet, but not really great if you’re a casino. If betting safe is betting low, why not bet $0.01? Well, it’s a waste of time, you’ll barely make any profit, and eventually your friend will realise he’s an idiot, just like many gamblers eventually do. You need Kelly to help you take as much money as is possible from your friend within the shortest timeframe possible, while also not busting everything you have.

Kelly says you should bet (2P(X)-1) of your bankroll each time, with P(X) being your odds of winning each match. For the sake of simplicity, let’s say your odds of winning are 60% (0.6). This means that (2P(X)-1) is (2*0.6–1), which is (1.2–1), which is 20%. So, if you have $100, the Kelly Criterion says it’s safe to bet $20. As your bankroll grows and shrinks, the percentage you should bet doesn’t change, but the bet amount does. If you lose money, you should bet smaller, and if you win money, you should bet bigger. It’s sort of the opposite of what martingalers do: maybe that’s why martingalers always lose and the house always wins.

As mentioned earlier, this is merely a surface-level explanation of what the Kelly Criterion tells you to do. If you want to learn more, delve deeper into the mathematics of it: it is as fascinating as it is rewarding. You also know why flashflip has a maximum profit per game capped at 0.75% of the current bankroll. Thanks, Kelly! We owe you one.