Data Analysis and Related Applications 3

4Blackjack and the Kelly Bet: A Simulation Assessment of Selected Playing Strategies

In this chapter, we explore the efficacy of rival strategies/bet size options for playing Blackjack using Monte Carlo simulation. Strategies selected for the modeling are “Blind gambler”, “Never bust” and “Imitating the dealer”. Corresponding bet size choices include the Kelly bet and a number of non-Kelly alternatives.

The resulting analysis yields a wealth of insights – not least the potentially perilous nature of adopting a “pure” Kelly approach to playing the game.

4.1. Introduction

Blackjack is an enduringly popular casino game and has been for the last century (Grant and Kim 2001). Though its exact roots remain something of a mystery, it is believed to have Roman/Spanish/French origins (The World of Playing Cards 2023).

Because of the skill element involved in playing Blackjack (Chantal and Vallerand 1996), the game offers tantalizing opportunities for gamblers to gain an advantage over the casino (Fogel 2004). Indeed, according to Bond (1974), Blackjack is the only game that has the possibility of a positive expected return at the casino.

Over the years, a range of strategies has evolved for playing Blackjack, for example, the “basic” strategy (GamblingSites 2023), the 1-3-2-6 system (Betway n.d.), the counting card strategy (Autodesk Instructables n.d.; Pinnacle 2018), etc.

Alongside these, a number of bet size options have emerged, including, for example, the Kelly bet, fractional ...