The reason some sources differ on the house edge in baccarat has mostly to do with how the house edge is defined. I prefer to define the house edge as the ratio of the expected casino win to the initial wager. Other gambling writers define it as the ratio of the expected casino win to bet resolved. The difference is in whether or not ties are considered as a possible outcome. In an eight-deck game the following are the probabilities in baccarat: Banker wins: 45.8597% Player wins: 44.6274% Tie wins: 9.5156% Here is how I calculate the expected return on each bet by counting ties. Banker: 0.458597*0.95 + 0.446274*-1 + 0.095156*0 = -0.010579 Player: 0.458597*-1 + 0.446274*1 + 0.095156*0 = -0.012351 Tie: 0.458597*-1 + 0.446274*-1 + 0.095156*8 = -0.143596 So I get a house edge of 1.24% on the player, 1.06% on the banker, and 14.36% on the tie. Other gambling writers prefer to think of ties as a non-event, in other words leaving the bet up until it is resolved. The probability of a banker or player win is 45.8597% + 44.6274% = 90.4844%. The probability the next bet resolved will be a player win is 44.6274%/90.4844% = 49.3175%. The probability the next bet resolved will be a banker win is 45.8597%/90.4844% = 50.6825%. The way the other camp would calculate the expected return on the player bet is 49.3175%*1 + 50.6825%*-1 = -1.3650%. The expected return on the banker bet, ignoring ties, is 49.3175%*-1 + 50.6825%*0.95 = -1.1692%. Thus the house edge ignoring ties is 1.36% on the player and 1.17% on the banker. One reason I think counting ties is appropriate is that it gives the player an accurate measure of expected losses over time. For example if a player bet $100 a hand on the banker in baccarat for 4 hours, and the casino’s average rate of play was 80 hands per hour, then the expected player loss is $100*4*80*0.0106=$339.20. No need to worry about the probability of a tie in the calculation. If a casino used the 1.17% house edge for the banker it would be overestimating expected loss, and perhaps over-comp the player as a result. Another reason I count ties is all the major blackjack and video poker experts count ties in the analysis of those games. For example if you ignored ties in 9/6 Jacks or better, when getting a pair of jacks to aces, then the return would be 99.4193%. Never once have I seen such a figure quoted for 9/6 jacks; it is firmly held that it is 99.5439% with optimal strategy. Finally, here is a table of some gambling books and the figures used for baccarat.
House Edge in Baccarat
BookAuthorCopyrightPlayerBanker Casino Operations ManagementJim Kilby & Jim Fox19981.24%1.06% The Casino Gambler’s GuideAllan N. Wilson1965, 19701.23%1.06% Smart Casino GamblingOlaf Vancura, Ph.D.19961.24%1.06% The American Mensa Guide to Casino GamblingAndrew Brisman19991.24%1.06% Casino Gambling for DummiesKevin Blackwood20061.24%1.06% Scarne’s New Complete Guide to GamblingJohn Scarne1961, 19741.34%1.19% The New American Guide to Gambling and GamesEdwin Silberstang1972, 1979, 19871.36%1.17% Casino Gambling: Play Like a Pro in 10 Minutes or LessFrank Scoblete20031.36%1.17% Beating the Casinos at Their Own GamePeter Svorboda20011.36%1.17% The Complete Idiot’s Guide to Gambling Like a ProStanford Wong & Susan Spector19961.36%1.17%
Casino Math by Robert C. Hannum and Anthony N. Cabot lists the house edge both ways.