The Gambler’s Ruin Theory

If you’ve been in the casino game for long enough, you’ll end up hearing the term “Gambler’s Ruin Theory” (probably in hushed tones) at some point. But you are likely to find that even the person using the term doesn’t actually know what it means.

This kind of misunderstanding can possibly cause more damage than mere ignorance if players think that Gambler’s Ruin Theory is some sort of secret to gambling success. In fact, just as its name suggests, Gambler’s Ruin Theory explains how feckless players find themselves in a downward losing spiral that ends with a tapped out bankroll.

Before you can understand Gambler’s Ruin Theory, however, you need to understand one or two related concepts.

Advantage Gambling

Advantage gamblers are the kings of the casino. They are the players who manage to turn the odds in their favour, without breaking any laws. Advantage players are savvy gamblers who use smart strategies and techniques to gain advantage over the casino or other players.

Card games are a particular favourite among advantage gamblers since they provide a certain margin for skill and present a smaller, more knowable number of variables than, say, slot machines. The infamous and impressive practice of counting cards is the best-known example of advantage play. Other examples include shuffle tracking, edge sorting, and hole-carding, among others.

Unfortunately, many inexperienced players fancy themselves as advantage gamblers before they are ready and so fail to see the difference between these legitimate strategies and the countless bogus alternatives out there. The ultimate error in judgement of this nature is the basis of Gambler’s Ruin Theory. But there’s one more related concept to explain before we get to the point.

The Random Walk

Gambler’s Ruin Theory, as you’ll shortly discover, is mathematically based – it’s not just an old wives’ tale. Part of this mathematical theory is the concept of the random walk. Mathematicians use the term “random walk” to refer to the path travelled by a succession of random events toward a certain end point. Like the path of a drunkard trying to cross a street, the random walk may change direction often and unpredictably, but it will always end up in the same place.

What Gambler’s Ruin Theory Really Is

Gambler’s Ruin Theory has two important aspects. When someone (correctly) uses the term, they are referring to the statistical fact that, if a gambler raises his bet by a fixed percentage of his bankroll every time he wins, but fails to reduce his wager similarly when he loses, he is guaranteed to eventually go broke, no matter how positive the expected value of his bets. This is the random walk of gambler’s ruin theory.

An equally significant usage of the term “Gambler’s Ruin” applies when a gambler with a finite bankroll persistently bets against an opponent whose bankroll is infinite. In such a case, in a fair game (i.e. where each bet has an expected value of 0 on both sides), the random walk will see to it that the less wealthy player ultimately gets tapped out.

Finally, Gambler’s Ruin Theory also applies to cases in which a gambler persistently plays a negative expected-value game. According to Gambler’s Ruin Theory, that player will eventually go broke, no matter what betting system is used.

Smart Player Tips

Gambler’s Ruin Theory is not proof that you can predict the outcome of any game. That is simply impossible unless the game is rigged. Smart players use their knowledge of things like Gambler’s Ruin Theory to play a smart but realistic game.

The primary lesson to take from this short overview of Gambler’s Ruin Theory is this: no matter how beneficial the risk, if it is taken persistently over an extended period of time, it will never be beneficial in the end. Don’t push your luck.