2004/12/18 by Jason Schweinsberg, Schweinsberg, Jason
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · Psychology · #60G40 #60G42 #91A60 #FOS: Mathematics #Gambling Behavior and Treatments #Organizational Management and Leadership #Probability (math.PR) #Sports Analytics and Performance #math.PR #msc:60G40 #msc:60G42 #msc:91A60
paper · pdf · doi:10.48550/arxiv.math/0412362
arxiv created 2004/12/18 · openalex publication_date 2004/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 minf, 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 minl, f, 1-f is not optimal if l is irrational, extending a result of Heath, Pruitt, and Sudderth.