Recent studies on the Dice Race Problem and its connections

Abstract

The following type of dice games has been mentioned and/or studied in the literature. Players take turns in rolling a fair die successively, each player accumulating his or her scores as long as the outcome 1 does not occur. If the result 1 turns up, the accumulated score is wiped out, and the turn ends, that is the player gives the die to the next player. At any stage after a roll, the player (she, say) can choose to end her turn and bank her accumulated score. The winner is the first player to reach some fixed target n ∈ N. We present some new results on optimal strategies and winning probability in a one or two players game. For just one player there is no competition of course, and in this case we suppose that the player simply wants to minimize her total expected number of tosses over all possible banking strategies.

A non-iterative algorithm for generalized pig games

“…The first solution for the competitive Pig game was obtained by Neller and Presser [16], with the help of a value iteration algorithm. Tijms [20] considers also the competitive pig game and a simultaneous-decision-taking variant, named Hog (see also [21]), and Louchard [12] examines some optimal strategies for the solitaire and competitive variants of the game. In these papers, no complexity analysis of the proposed algorithms is presented.…”