Set-Based Retrograde Analysis: Precomputing the Solution to 24-card Bridge Double Dummy Deals

TL;DR

This paper introduces setrograde analysis, a novel approach that operates on sets of game states to efficiently solve complex bridge deals, significantly reducing computational effort and enabling deeper retrograde searches.

Contribution

The paper presents setrograde analysis, a new algorithm that computes exact solutions for bridge double dummy deals more efficiently than traditional methods.

Findings

Performs 1000 times fewer search operations

Produces a database with 10,000 times fewer entries

Enables unprecedented search depths in applicable domains

Abstract

Retrograde analysis is used in game-playing programs to solve states at the end of a game, working backwards toward the start of the game. The algorithm iterates through and computes the perfect-play value for as many states as resources allow. We introduce setrograde analysis which achieves the same results by operating on sets of states that have the same game value. The algorithm is demonstrated by computing exact solutions for Bridge double dummy card-play. For deals with 24 cards remaining to be played ($10^{27}$ states, which can be reduced to $10^{15}$ states using preexisting techniques), we strongly solve all deals. The setrograde algorithm performs a factor of $10^3$ fewer search operations than a standard retrograde algorithm, producing a database with a factor of $10^4$ fewer entries. For applicable domains, this allows retrograde searching to reach unprecedented search depths.