Mental Poker

Abstract

Can two potentially dishonest palyers play a fair game of poker without using any cards—for example, over the phone? This paper provides the following answers: 1. No. (Rigorous mathematical proof supplied.) 2. Yes. (Correct and complete protocol given.) Once there were two "mental chess" experts who had become tired of their pastime. "Let's play 'Mental Poker,' for variety" suggested one. "Sure" said the other. "Just let me deal!" Our anecdote suggests the following question (proposed by Robert W. Floyd): "Is it possible to play a fair game of 'Mental Poker'?" We will give a complete (but paradoxical) answer to this question. First we will prove that the problem is intrinsically insoluble, and then describe a fair method of playing "Mental Poker".