How to Play Dundee
Kevin Liwack, Oleg Pikhurko, Suporn Pongnumkul

TL;DR
This paper analyzes the game of Dundee, determining optimal strategies for different variants, including adaptive and pre-planned bidding, and provides solutions for specific deck configurations and game lengths.
Contribution
It offers the first comprehensive analysis of optimal strategies in Dundee, solving both adaptive and fixed-sequence variants for certain deck structures.
Findings
Optimal strategies are characterized for adaptive bidding.
Explicit solutions are provided for fixed-sequence bidding when deck sizes are equal.
The problem is solved for arbitrary game lengths with equal deck sizes.
Abstract
We consider the following one-player game called Dundee. We are given a deck consisting of s_i cards of Value i, where i=1,...,v, and an integer m\le s_1+...+s_v. There are m rounds. In each round, the player names a number between 1 and v and draws a random card from the deck. The player loses if the named number coincides with the drawn value in at least one round. The famous Problem of Thirteen, proposed by Monmort in 1708, asks for the probability of winning in the case when v=13, s_1=...=s_{13}=4, m=13, and the player names the sequence 1,...,13. This problem and its various generalizations were studied by numerous mathematicians, including J. and N. Bernoulli, De Moivre, Euler, Catalan, and others. However, it seems that nobody has considered which strategies of the player maximize the probability of winning. We study two variants of this problem. In the first variant, the…
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Taxonomy
TopicsCultural Industries and Urban Development · Theatre and Performance Studies · Scottish History and National Identity
