Monopoly Deal: A Benchmark Environment for Bounded One-Sided Response Games
Will Wolf
2025-11-03
Summary
This paper explores a specific type of game structure, called Bounded One-Sided Response Games (BORGs), which haven't been studied as much as other game types, and tests how well existing computer algorithms can play them.
What's the problem?
Many games used to study strategy involve players taking turns, or having predictable outcomes, or constantly reacting to each other. This paper focuses on a less common structure where one player's action temporarily gives the opponent a limited task they *must* complete before play returns to the first player. The challenge is understanding how best to play in these situations and whether standard computer strategies are good enough.
What's the solution?
The researchers created a version of the card game Monopoly Deal that perfectly demonstrates this 'bounded one-sided response' dynamic. They then used a well-known computer algorithm, Counterfactual Regret Minimization (CFR), to train an AI to play this modified Monopoly Deal. Surprisingly, the algorithm worked well without needing any changes, and they built a platform where people can play against the AI. They also made the AI and the code publicly available.
Why it matters?
Understanding these types of game structures is important because they show up in real-world situations like negotiations, financial markets, and even cybersecurity. If we can create AI that can master these games, it could lead to better strategies and decision-making in these complex real-world scenarios.
Abstract
Card games are widely used to study sequential decision-making under uncertainty, with real-world analogues in negotiation, finance, and cybersecurity. These games typically fall into three categories based on the flow of control: strictly sequential (players alternate single actions), deterministic response (some actions trigger a fixed outcome), and unbounded reciprocal response (alternating counterplays are permitted). A less-explored but strategically rich structure is the bounded one-sided response, where a player's action briefly transfers control to the opponent, who must satisfy a fixed condition through one or more moves before the turn resolves. We term games featuring this mechanism Bounded One-Sided Response Games (BORGs). We introduce a modified version of Monopoly Deal as a benchmark environment that isolates this dynamic, where a Rent action forces the opponent to choose payment assets. The gold-standard algorithm, Counterfactual Regret Minimization (CFR), converges on effective strategies without novel algorithmic extensions. A lightweight full-stack research platform unifies the environment, a parallelized CFR runtime, and a human-playable web interface. The trained CFR agent and source code are available at https://monopolydeal.ai.