# Tag Archives: expected value

## The most profitable roulette

Last weekend I attended Riaza’s local festivities with some friends who have a house there. Riaza is a small and beautiful village in the province of Segovia famous for its main square.

One of my friends raised to me the issue of a game being organized by some locals. It was a kind of casino roulette, but very much simplified…

Instead of 36 numbers plus zero, there were only six. Instead of using an actual roulette, they used just a six-sided die and small cup. Instead of casino coins, bets were placed directly with cash, starting from one euro. Instead of using a green clothed table they used a small wooden board with the images of 6 Spanish playing cards; with numbers 1 to 6.

Prize. We did not know how they came up with the amount of the prize, but it was perfectly established to maximize their benefits and attract as many players as possible. In case you bet for the right number, they gave you 4 times the amount you bet plus your stake, i.e., you bet 1 euro and are lucky, you then walk away with 5 euros.

If they had offered more money, the expected value for the organizers would have been zero or a loss. Have they offered less (e.g., to just double the bet) and not so many people would have been tempted by the game.

Offering 4 times the stake to the players, means  to them a mathematical expectation of -0,17 € for a one-euro bet. For the organizers means the opposite: a business with an expected profit of 17% of all the amounts at stake.

Compare this to the business of a casino with a French roulette, with 37 numbers, in which the expected profit for the casino is 2.7% (where the prize for hitting the number is 35 times the amount you bet). This local game is 6 times more profitable than the casino!

The next question is: how much money could they make out of it? I first saw them at 2:30 am of Sunday morning. At 3:30 am they were still there, though at 4:30 am they were not. Let me assume they hold the village-casino for about 8 hours a day (from 20 pm to 4 am, being conservative, i.e., assuming they are not out there during most of day time).

The highest amount we witnessed at the table at one single round was in excess of 40 € (including a 20€ note), but I assume they had some collaborators among the crowd. The lowest amounts were around 6-8 euro per round. Let’s assume the average to be around 10€ per round.

Each round we witnessed lasted very short time: less than a minute, though we did not measure it. Let’s assume there was exactly a minute, and that they kept that rhythm during the 8 hours…

• They would have earned about 1.67€ per round.
• About 100€ per hour (33€/hour per person, taking into account that they were three organizers).
• 800€ per day.

By organizing the game for four or five days during the festivities they managed to take home their monthly salaries for the three of them out of this simple game.

Some times it is surprising how easy a business can be.