Financial economics/Tutorials

Gambler's ruin

If q is the risk of losing one throw in a win-or-lose winner-takes-all game in which an amount c is repeatedly staked, and k is the amount with which the gambler starts, then the risk, r, of losing it all is given by:

r = (q/p)^(k/c)

where p = (1-q), and q ≠ 1/2

(for a fuller exposition, see Miller & Starr Executive Decisions and Operations Research Chapter 12, Prentice Hall 1960)