So I am in a casino betting on Black in an American Roulette wheel.
Scenario1: I bet for successive 1000 bets starting with a bet of 1 dollar. If I loose, I bet the double of amount that I bet earlier and if I win, I reset the betting amount to 1 dollar. I also stop betting once I reach 80 dollars and keep my winning as 80 dollars. I also assume that I have infinite amount of bank roll. So I never run out of money to bet.
Scenario2: Same as Scenario 1 but I dont have an infinite bank roll. I have a finite bank roll of 256 dollars. And also I quit once I loose all 256 dollars.
I am trying to calculate the probability of me winning 80 dollars in 1000 successive bets and also the estimated expected value of my winnings after 1000 spins.
I wrote python code to simulate scenario 1 and empherically I never came back without winning 80 dollars. So can I say that the probability of me winning 80 dollars in 1000 spins is 100%?
Similarly, I ran simulation for scenario 2 and found that I lost 38 among 100 "1000 successive spins".
I am trying to calculate the probability mathematically and not able to do so.
Regarding expected value, for 1 spin, my expected value is -0.06 dollars. Is it right to multiply it by 1000 to calculate the expected value for 1000 spins?
Thanks in advance!!