Improving on bold play when the gambler is restricted
| dc.creator | Schweinsberg, Jason | |
| dc.date | 2004-12-18 | |
| dc.date.accessioned | 2026-07-07T05:15:25Z | |
| dc.date.available | 2026-07-07T05:15:25Z | |
| dc.description | Suppose a gambler starts with a fortune in (0,1) and wishes to attain a fortune of 1 by making a sequence of bets. Assume thay whenever the gambler stakes the amount s, the gambler's fortune increases by s with probability w and decreases by s with probability 1 - w, where w < 1/2. Dubins and Savage showed that the optimal strategy, which they called "bold play", is always to stake min{f, 1-f}, where f is the gambler's current fortune. Here we consider the problem in which the gambler may stake no more than l at one time. We show that the bold strategy of always betting min{l, f, 1-f} is not optimal if l is irrational, extending a result of Heath, Pruitt, and Sudderth. | |
| dc.identifier | https://arxiv.org/abs/math/0412362 | |
| dc.identifier | http://arxiv.org/abs/math/0412362 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73623 | |
| dc.subject | Probability | |
| dc.subject | 91A60; 60G40; 60G42 | |
| dc.title | Improving on bold play when the gambler is restricted | |
| dc.type | text |