The formula for a gambler?

Question

Mathematics

Hello!
There is a task: to calculate the formula for the player so that he wins and loses evenly, not allowing the casino to go into the red and not taking out all the funds so that others can also play

Game data:
- Game bank 1000 rubles - Coefficient from 2X
to 10X at a

the formula can be rendered, given the entire history of the user and all users in this single player game, to output YES or NO?

Answer 1

Nash equilibrium