Is the Banker a Myth?

Mike Cox

doi:10.6339/jds.201104_09(2).0005

Abstract

The actions of the anonymous banker in the highstake television gambling programme Deal or No Deal is examined. If a model can successfully predict his behaviour it might suggest that an automatic process is employed to reach his decisions. Potential strategies associated with a number of games are investigated and a model developed for the offers the anonymous banker makes to buy out the player. This approach is developed into a selection strategy of the optimum stage at which a player should accept the money offered. This is reduced to a simple table, by knowing their current position players can rapidly arrive at an appropriate decision strategy with associated probabilities. These probabilities give a guide as to the confidence to be placed in the choice adopted.

Highlights

This paper addresses the operation of a risk-based game show where prizes range from very high to very low in monetary value; no skill but limited judgement is involved
While Deck et al (2008) estimated the degree of risk aversion of players appearing in the Mexican version (52 shows, some of which provided different prizes)
There have been some reservations voiced about the box allocation being truly random and affecting the Players behaviour, it is believed that this is not a problem here since the model will attempt to predict a strategy given the current state of the game (Bankers offer, Players average and boxes available), no information being retained on which boxes contained which sums

Summary

Introduction

This paper addresses the operation of a risk-based game show where prizes range from very high to very low in monetary value; no skill but limited judgement is involved. While Deck et al (2008) estimated the degree of risk aversion of players appearing in the Mexican version (52 shows, some of which provided different prizes) They considered both dynamic players, who fully backward induct and myopic players that only look forward one period. Blavatskyy and Pogrebna (2008) having described the Italian (114 shows) and United Kingdom (256 shows) versions of the game, proceeded to consider a natural experiment in which two groups were studied They had been told that the chances of their boxes containing a large prize were 20% and 80% respectively. They calculated risk-aversion bounds for each player, revealing considerable heterogeneity They estimated a structural stochastic choice model that captured the dynamic decision problem faced by players. The previously proposed models are briefly discussed and conclusions drawn

The Data

Modelling the Bankers Offer

When to Deal?

Summary

Findings

Conclusion