Optimal policies for playing variable wager HI-LO

Abstract

Use of the HI-LO procedure by the gaming industry is ubiquitous—hence playing strategies of interest to gamblers and machine providers alike. Players’ tactics necessarily depend on goals being pursued and consistent with these, a variety of schemes ranging from the ‘aggressive’ to the ‘timid’ have evolved. Characteristics of the some of the best known of these—as far as they are applicable to a variable wager version of the HI-LO routine—are considered and contrasted. Of interest, results for a relatively risk-aversive scheme, played over a finite number of rounds are reconciled with those obtained asymptotically when maximizing capital growth is the priority.

Keywords:

• gaming
• risk
• stochastic
• Markov processes