I'm working on something for highschool and I'm stuck at this;
Assume we have a binomial distribution for a fair coin and we flip it 100 times.
Just a standard binomial as pic rel.
Now, assume we have a bettor constantly betting on these 100 coin flips. He has f amount of starting funds in my example f = 100. After each bet, he changes his wager to 1/5 of all his funds. The return on a bet is 1.1/-1.1 based on win or loss. As the bettor always bets the same way, we can essentially assume that the bettor himself is the coin and he only flips on the return so P(Win and return 1.1) = 1/2 and P(Loss and return -1.1)=1/2. Clearly the probability distribution of bettor outcomes will also be a binomial distribution and the distribution of values will be a pareto distribution due to the compounding of wins/losses.
My question is, how do I express the binomial distribution of bettor outcomes and how do I find a function that would return the bettors funds after the 100 bets?
Assume we have a binomial distribution for a fair coin and we flip it 100 times.
Just a standard binomial as pic rel.
Now, assume we have a bettor constantly betting on these 100 coin flips. He has f amount of starting funds in my example f = 100. After each bet, he changes his wager to 1/5 of all his funds. The return on a bet is 1.1/-1.1 based on win or loss. As the bettor always bets the same way, we can essentially assume that the bettor himself is the coin and he only flips on the return so P(Win and return 1.1) = 1/2 and P(Loss and return -1.1)=1/2. Clearly the probability distribution of bettor outcomes will also be a binomial distribution and the distribution of values will be a pareto distribution due to the compounding of wins/losses.
My question is, how do I express the binomial distribution of bettor outcomes and how do I find a function that would return the bettors funds after the 100 bets?
