I have already read a lot where it’s not possible to beat the casino at roulette, but the prospect of free money is very tempting, so I want to find out more about this issue. I would like to calculate the mat expectation of such a system. I am talking about a system of consistently increasing rates when losing, that is: we start with the minimum bet and put it on the red (red / black does not matter), if we win - again we put the minimum bet, and if we lose, we double the previous one and so, until we win. Increasing the bet twice covers all the previous wins and brings a profit of 1 minimum bet. Who can calculate the mathematical model of such a game?