Optimal policies for playing variable wager HI-LO

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.