Apologies if this is pretty basic, but I would appreciate some help.
Suppose we have a game that cost $1 to play. The game is a fair coin toss. You get returned $2 if the coin lands on heads (win $1) and returned $0 if it lands on heads
I understand that after 1000 trials the EV of the game is still 0, you should be breaking even.
My question is, what is the probaility that you are $100 up after 1000 and 10000 trials respectively?
Now applying this to a wider context, suppose a die is rolled. If it lands on an odd number, you win an amount equal to that number and vice versa for odd number. The average gain for this game is calculated at -0.5 per roll. What is the probaility you are $20 up after 1000 trials and 10000 trails respectively.
Thanks in advance.