A well-known roulette trick, to make a profit for sure, is the following: you stake continuously at one color, for example red, double the bet if you lose, and stop as soon as you win. Because you get twice your bet back if you win, and the ball will once fall on red, you know that you will gain your original bet as profit (you must, however, have an infinite amount of money to be able to double your bet every time when necessary). The expected value for your profit is therefore equal to your original bet.

Assume, however, that there is a maximum stake for the roulette, which means that you can only stake n consecutive times with this trick.

The question: What is the expected value for your profit for this limited roulette?

A hint : The roulette table has 37 squares: eighteen red, eighteen black and one green. For simplicity, assume that you lose your complete bet if the ball falls on green (French roulette and American roulette have different rules for what happens with your bet in this case).

The answer: Click here!