A game-theoretic analysis of baccara chemin de fer

TL;DR

This paper provides a comprehensive game-theoretic analysis of baccara chemin de fer, extending previous solutions to scenarios with multiple decks and different information structures for players and bankers.

Contribution

It introduces a solution for baccara as a large matrix game with multiple decks and various information assumptions, generalizing prior work.

Findings

Solved for all positive integers d with full information on hands.

Extended previous models to include multiple decks and partial information.

Provided explicit solutions for complex game matrices.

Abstract

Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 x 2^88 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his own two-card hand while Player sees only his own total, baccara is a 2 x 2^484 matrix game, which was solved by Downton and Lockwood in 1975 for d=1,2,...,8. Assuming that cards are dealt without replacement from a d-deck shoe and that each of Player and Banker sees the composition of his own two-card hand, baccara is a 2^5 x 2^484 matrix game, which is solved herein for every positive integer d.