Maximizing the Score in "Ticket to Ride"

TL;DR

This paper develops graph-theoretic models and a mixed-integer programming approach to determine the maximum possible score in 'Ticket to Ride,' providing insights into game balancing and optimal strategies.

Contribution

It introduces novel graph models and an optimization framework to compute maximum scores and analyze game balance in 'Ticket to Ride.'

Findings

Optimal score with 45 train cars is 285 points.

Identified most frequently chosen tickets and routes.

Suggested adjustments to point values for better game balance.

Abstract

We give two graph-theoretic models and a mixed-integer program to calculate the maximum achievable score in the popular board game "Ticket to Ride." In Ticket to Ride, players compete to claim railway routes on a map, with points awarded based on the length of each route and the successful completion of destination tickets connecting specific city pairs. Each player has 45 train cars available, and each route can be chosen by only one player. Using the mixed-integer programming model, we examine the optimal solution with the 45 allocatable train cars, leading to an optimal score of 285 points. We also calculate the optimal solutions for up to 50 train cars. We determine the most frequently chosen tickets and routes over these 50 instances, giving insight into how optimization might be used to balance games. In particular, we identify several instances in which the point values can be adjusted to better balance the game.