The Unlucky Door

TL;DR

This paper explores strategic variations of the Three-Door-Game, revealing that while Monte cannot guarantee wins with three doors, a four-door variant allows cooperative strategies enabling guaranteed victory for Conie.

Contribution

It introduces a new four-door game variant where cooperative strategies enable guaranteed wins, contrasting with the three-door game where Monte cannot ensure success.

Findings

In three-door game, Monte cannot guarantee a win.

In four-door game, Monte can reveal two useless doors to guarantee Conie's win.

Cooperative strategies in the four-door game outperform traditional approaches.

Abstract

In the famous Three-Door-Game Monte cannot help to win all the time by signaling location of the prize, using only the freedom he allowed to use. No matter which strategies played, there is always at least one door where the prize will not be found. However, already in the game with four doors cooperative Monte can reveal two useless doors in sequence (leaving two doors unrevealed), to inform Conie about location of the prize, so enabling her to beat the only-switching strategies and win all the time.