• Anne

The expected value of Roulette

Can you really win at Roulette?

This morning I woke up and felt like crunching some probabilities on the game of Roulette and calculating expected value for each bet you can make!

My specialty in graduate school was game theory (actual games, not economics or decision theory), so this stuff has always been a passion of mine. Let’s see what you can expect when you play American Roulette.

I’ll break it down by types of bets and find the probability and expected value for each. If you’re unfamiliar with Roulette, congratulations: you’re likely not a gambler. You can learn more about it on this video.

Here I go, breaking out the spreadsheets on you again! Please focus on the expected value column - that is what you can expect to earn for each dollar you bet in that way.

The results

Wow, isn’t it amazing that on average, you lose 5¢ for every $1 you bet? It’s so mathematically interesting that the loss is so subtle, especially with such a volatile distribution, that people don’t notice that they are playing a losing game in the long run.

All gambling is mathematically calculated to make sure that the house wins. Do you think it’s an accident that the payoffs and probabilities matched up to 5¢ for every single one of these? Food for thought.

In the end, all bets are equally valued, so no one bet is better than the others.


I don’t really have much of a conclusion - I was just thinking about the game and I’ve always wanted to play around the math with it, so this gives me a nice chart to show my students. The moral of the story is don’t gamble! If you do, plan to lose the money you spend, because the casinos are probably better at math than you (no insult to you - they are pros).


Watch out for creative impulses and follow them! This morning I could have consumed something, and I probably will soon (like breakfast), but I created first. Of course I’m not the first person to answer this Roulette question, but the point is I used my own interests and thoughts to do this. Try to find a creative impulse you have and follow it, however small of unimportant it is!


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