The Tall Tale of Martingale (Part 2)

In the last post I mentioned, “while rare, extreme losing streaks do occur.” This is an important detail worthy of extra time.

One of the best bets in a casino is found in the game of Craps. The table I presented in the last post assumed even money bets, which are very hard to find in the real world. Casinos make their money on the house edge. Betting the pass line in Craps offers a 49.29% probability of winning, which translates to a low 1.41% house edge.

Consider a simple Martingale betting system with $1 as the standard bet. Suppose I have $2,047, which can cover up to 10 consecutive losses. Here is a table of outcomes:

Looking at the probability column tells us just how rare those extreme losing streaks can be. The chance of five consecutive losses is about 1.6%. The chance of 10 consecutive losses is 0.055% or one out of every 1818 times. The chance of being struck by lightning (based on number of people hit each year) is one out of three million. The odds of winning a million dollar lottery are roughly one in 10-12 million. Compared to these numbers, then, the odds of 10 consecutive losses are pretty good!

How scary is that?

That there is any chance of an extreme losing streak means the Martingale betting system favors shorter play over longer play. The longer I play, the more likely I am to encounter such a losing streak. If I knew how many rolls per hour occurred in a particular Craps game then I could calculate the odds of experiencing one based on playing time.

Regardless of duration, the ultimate arbiter of whether I will “live to play another day” lies in the hands of Chance.

I will write more on Martingale betting systems in the next post.