Paper Info
Title
How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman
Abstract
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target amount. Specifically, we disprove a 50-year old conjecture of L. Breiman, that there exists a threshold strategy that optimizes the expected number of rounds; that is, a strategy that always bets to try to win in one round whenever the bankroll is at least a certain threshold, and that makes Kelly bets (a simple proportional betting scheme) whenever the bankroll is below the threshold.
Year
Venue
Field
2011
CoRR
Combinatorics,Mathematical economics,Existential quantification,Expected value,Counterexample,Odds,Conjecture,Mathematics
DocType
Volume
Citations 
Journal
abs/1112.0829
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Thomas P. Hayes165954.21