Financial economics/Tutorials: Difference between revisions
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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: | 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 | :::: r = ''(q/p)''<sup>(k/c)</sup> | ||
where p = (1-q), and q ≠ 1/2 | 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) | (for a fuller exposition, see Miller & Starr ''Executive Decisions and Operations Research'' Chapter 12, Prentice Hall 1960) | ||
Revision as of 11:15, 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 = (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)