Journal of Probability and Statistics
Volume 2010 (2010), Article ID 313148, 19 pages
doi:10.1155/2010/313148
Research Article

A Mathematical Analysis of the Card Game of Betweenies through Kelly's Criterion

Konstantinos Drakakis1,2

1UCD CASL, University College Dublin, Belfield, Dublin 4, Ireland
2School of Electronic, Electrical & Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland

Received 4 February 2010; Accepted 29 March 2010

Academic Editor: Mohammad Fraiwan Al-Saleh

Copyright © 2010 Konstantinos Drakakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the game of Betweenies, the player is dealt two cards out of a deck and bets on the probability that the third card to be dealt will have a numerical value in between the values of the first two cards. In this work, we present the exact rules of the two main versions of the game, and we study the optimal betting strategies. After discussing the shortcomings of the direct approach, we introduce an information-theoretic technique, Kelly's criterion, which basically maximizes the expected log-return of the bet: we offer an overview, discuss feasibility issues, and analyze the strategies it suggests. We also provide some gameplay simulations.