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Optimal games in Room 25 solo and coop modes

Pierre Lafourcade

TL;DR

This work analyzes optimal play in Room 25 (season 1) for solo and cooperative modes, proving that a win in a single turn is impossible under standard rules but that a two-turn win is achievable for some starting configurations. It introduces formal notation and a concrete two-turn opening, along with a modified, more aggressive opening that can yield a one-turn win under relaxed rules, and it provides probabilistic assessments of these openings (approximately $7.39\%$ and $0.36\%$ success respectively) while quantifying immediate-failure risks. The paper also explores an antagonistic context where an adversary can force defeat, showing that victory cannot be guaranteed in such setups and highlighting the role of information revealed during play. Together, these results illuminate how randomness, information, and rule variations shape the feasibility and design of optimal strategies in Room 25.

Abstract

We study the problem of optimal games for the solo and coop modes of the board game Room 25 (season 1). We show that the game cannot be won in a single turn for any starting configuration, but that it can be done in two for some configurations. We introduce an opening that wins in two turns with enough luck, while having a low probability of losing immediately. We then show that the game can be won in a single turn if the game's rules are slightly modified, although the probability of winning then becomes substantially lower than in the two-turn strategy. At last, we show that if the players are maximally unlucky, they will lose regardless of their strategy.

Optimal games in Room 25 solo and coop modes

TL;DR

This work analyzes optimal play in Room 25 (season 1) for solo and cooperative modes, proving that a win in a single turn is impossible under standard rules but that a two-turn win is achievable for some starting configurations. It introduces formal notation and a concrete two-turn opening, along with a modified, more aggressive opening that can yield a one-turn win under relaxed rules, and it provides probabilistic assessments of these openings (approximately and success respectively) while quantifying immediate-failure risks. The paper also explores an antagonistic context where an adversary can force defeat, showing that victory cannot be guaranteed in such setups and highlighting the role of information revealed during play. Together, these results illuminate how randomness, information, and rule variations shape the feasibility and design of optimal strategies in Room 25.

Abstract

We study the problem of optimal games for the solo and coop modes of the board game Room 25 (season 1). We show that the game cannot be won in a single turn for any starting configuration, but that it can be done in two for some configurations. We introduce an opening that wins in two turns with enough luck, while having a low probability of losing immediately. We then show that the game can be won in a single turn if the game's rules are slightly modified, although the probability of winning then becomes substantially lower than in the two-turn strategy. At last, we show that if the players are maximally unlucky, they will lose regardless of their strategy.
Paper Structure (18 sections, 9 theorems, 10 equations, 7 figures)

This paper contains 18 sections, 9 theorems, 10 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Notation algébrique
  3. Plateau
  4. Personnages et actions
  5. Regarder (R)
  6. Se déplacer (D)
  7. Pousser (P)
  8. Contrôler (C)
  9. Parties optimales
  10. Borne inférieure
  11. Ouverture véloce
  12. Ouverture téméraire
  13. Probabilités de succès
  14. Ouverture véloce
  15. Ouverture téméraire
  16. ...and 3 more sections

Key Result

Proposition 3.1

Quelque soit le nombre de personnages, il est impossible de remporter une partie solo ou en coopération en un seul tour.

Figures (7)

  • Figure 1: Plateau initial avec la tuile $\mathcal{D}$ face recto et les autres face verso. Les cases claires sont les positions possible de $\mathcal{S}$.
  • Figure 2: Illustration des actions $D$ et $P$. Le personnage 1 se déplace vers $[2;\!0]$ et le 2 pousse le 3 vers $[0;\!0]$.
  • Figure 3: Illustration de deux actions $C$. La première effectue un décalage cyclique, et la seconde est une fin de partie (victorieuse) parce que $\mathcal{S}$ sort du cadre en emportant tous les personnages.
  • Figure 4: Illustration de l’\ref{['ex1']}. Rappelons l’exécution du tour: $\mathbf{2:}2D[2;\!0]\mid3P1[0;\!0]\mid1D[-1;\!0]\mid\dots$
  • Figure 5: Illustration de la partie optimale: (a) configuration initiale, (b) fin du premier tour.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Proposition 3.1
  • Proposition 3.6
  • Proposition 3.9
  • Proposition 4.1
  • Proposition 4.2
  • Proposition 4.3
  • Proposition 4.4
  • Proposition 5.2
  • Proposition A.1