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==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 = n''(q/p)''<sup>(k/c)</sup> | |||
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) | |||
Revision as of 12:07, 23 February 2008
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 = n(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)