Discounted and Rapid Subfair Red-and-Black

A gambler seeks to maximize the expected utility earned upon reaching a goal in a game where he is allowed at each stage to stake any amount of his current fortune. He wins each bet with probability w. In the discounted case the utility at the goal is βnwhere β, the discount factor, is in (0, 1) and...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of statistics 1977-07, Vol.5 (4), p.734-745
Main Author: Klugman, Stuart
Format: Article
Language:English
Subjects:
60G35
93E99
bold strategy
Expected utility
Gambling
Gambling problem
Games
Integers
Optimal strategies
optimal strategy
red-and-black
stop rule
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A gambler seeks to maximize the expected utility earned upon reaching a goal in a game where he is allowed at each stage to stake any amount of his current fortune. He wins each bet with probability w. In the discounted case the utility at the goal is βnwhere β, the discount factor, is in (0, 1) and n is the number of plays used to reach the goal. In the rapid case the utility at the goal is 1 and the gambler seeks to minimize his expected playing time given he reaches the goal. Here all optimal strategies are characterized when w ≤ 1/2 for the discounted case and when$w < \frac{1}{2}$for the rapid case. It is shown that when$w < \frac{1}{2}$the set of rapidly optimal strategies coincides with the set of optimal strategies for the discounted case.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176343896