Taro Kuriyama

Game of Risk

These slides provide an overview of the Game of Risk and the solver logic to find exact win probabilities given arbitrary starting game configurations. The Wolfram Alpha blog has a post describing a materialy similar approach to the problem.

The below Elm visualization shows a given game's probability tree from the attacking player's perspective. The first tree below yields reasonable visual semantics, in the sense that: But the proportion of green typically overrepresents the actual probability of winning, due to: As an alternative version, the second tree focuses on visualizing the probability space more intuitively. In this version, every row represents the complete game probability space at a given iteration. For example, the second row reprents the outcome of all possible second-round battles.

As the game progresses, more and more outcomes are determined, filling in the rows with either green or red. The bottom row of the tree represents the final probability, where the proportion of green reflects the probability of the attacker winning the game.

Github repo | Built with Elm