What probability distribution applies?

[elmarsur]

Homework Statement

Peter and Paul bet one dollar each on each game. Each is willing
to allow the other unlimited credit. Use a calculator to make a
table showing, to four decimal places, for each of p = 1/10, 1/3,
.49, .499, .501, .51, 2/3, 9/10 the probabilities that Peter is ever
ahead by $10, by $100, and by $1000. (p is the probability of Peter winning the game)

Homework Equations

I don't know.

The Attempt at a Solution

I don't know what distribution applies, or how to choose the variables.

Thank you very much for any help.

 

[elmarsur]

If winning is in streaks of 10, 100, 1000 then each p is raised to those powers.
But if it is done haltingly (e.g., to win 10 games ahead of Paul, Peter wins 7 in a row, then loses 2, then wins again 5 in a row) how could this be represented?

Thank you, if anyone still looks here.