Let's imagine a coin-flip game, which uses an unbiased coin.
Starting with X dollars, your total increases 50% every time you flip heads. But if the coin lands on tails, you lose 40% of your total. You can play this game N times. On each turn, you must bet the total amount you had on the last turn.
Is it worth betting on this case? How can we formalize this in order to have this answer in the general case?
Is it easier to formalize this for a specific value of X and N? Let us assume, for example X = 100 dollars and N = 100 turns.
PS: This scenario appears in an article discussing some ideas of Ole Peters, a theoretical physicist who is claiming that Everything we know about modern economics is wrong.