# The Game of Poker Chips, Dominoes and Survival

## TL;DR

This paper analyzes a simple cooperative game involving poker chips and dominoes, providing insights into strategies for group survival, game solvability conditions, and educational applications in game theory and discrete mathematics.

## Contribution

It offers a formal analysis of the game's rules, solvability conditions, and complexity, linking game theory, number theory, and algorithmic analysis.

## Key findings

- Game is solvable if initial chips meet specific conditions.
- Optimal strategies minimize time for group survival.
- Analysis informs game design and educational use.

## Abstract

The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to make exchanges with the game coordinator according to two rules, and must secure a domino before time is called in order to `survive'. Though the rules are simple, it is not evident by their form that the survival of the entire group requires that they cooperate at a high level. From the point of view of the game coordinator, the difficulty of the game for the group can be controlled not only by the time limit, but also by the initial distribution of chips, in a way we make precise by a time complexity type argument. That analysis also provides insight into good strategies for group survival, those taking the least amount of time. In addition, coordinators may also want to be aware of when the game is `solvable', that is, when their initial distribution of chips permits the survival of all group members if given sufficient time to make exchanges. It turns out that the game is solvable if and only if the initial distribution contains seven chips that have one of two particular color distributions. In addition to being a lively game to play in management training or classroom settings, the analysis of the game after play can make for an engaging exercise in any basic discrete mathematics course to give a basic introduction to elements of game theory, logical reasoning, number theory and the computation of algorithmic complexities.