# Card Counting in Baccarat

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From time to time the question of card counting in baccarat comes up. Because baccarat is dealt from a shoe, it follows that the odds for the banker/player/tie bets change as cards are dealt. As more and more cards are dealt, a counter will get an ever more precise estimation of the composition of the cards that remain. If conditions are just right, the counter may get an opportunity towards the end of the shoe to make a wager with an advantage. All of this is absolutely true. It is possible to make a wager in baccarat with an edge over the house, using a card counting system. Each of the player, banker and tie bets are vulnerable

Now for a dose of reality. Imagine a blackjack card counter faced with a situation of trying to count a six-deck shoe game where two rounds are dealt between shuffles. He gathers all the information he can by watching the first round without making a bet. If things are just right, he makes a maximum table wager of \$1000 on the second round. Then by house policy the cards are shuffled and the situation repeats. Hopefully you do not fear this card counter. Nevertheless this blackjack counter’s earning potential exceeds by an order of magnitude the potential earnings of a baccarat card counter.

Card counting works so well for blackjack because certain cards heavily favor the player and certain cards heavily favor the dealer. Faces and aces favor the player: with an abundance of high cards the player makes more blackjacks, his double downs get better cards and the dealer busts stiffs more often. Likewise, 2-6 favor the dealer: with an abundance of low cards the player gets fewer blackjacks, the player’s double downs get lousy cards, and the dealer makes more hands with his stiff totals. I assume you are familiar with the high-low system for blackjack, using the tags {-1, +1, +1, +1, +1, +1, 0, 0, 0, -1}. These tags are in the order A, 2, 3, 4, 5, 6, 7, 8, 9, T. The cards that the player is happy to see leave the deck have a +1 tag. The cards the player doesn’t want to see leave the deck get a -1 tag. Using these tags, the player has an edge whenever the true count exceeds +1.

Now let’s try and apply a heuristic to baccarat. Which cards favor the banker? Which favor the player? What is a good drawing card for the player that doesn’t favor the banker if he draws the same card? A “nine” is going to make a natural for the player and dealer equally as often. There is no intuition here that will lead to a correct solution. The complex interplay between the cards inhibits intuition and handcuffs heuristics.

Dr. Ed Thorp  stated that: “Despite the resemblances between baccarat and blackjack, the favorable situations detected by perfect card counting methods are not sufficient to make the game favorable.” He also stated that: “… no practical winning strategy is possible for the Nevada game, even with a computing machine playing a perfect game.” .

James Grosjean  stated that: “baccarat counting is weak for several reasons: (1) The game is symmetric so that there are no cards that massively favor one bet or the other … (2) The initial advantage to overcome is greater in baccarat than in blackjack; (3) Baccarat is usually dealt from an 8 deck shoe, so the volatility of the edge is low; (4) A baccarat count cannot be used to increase playing efficiency, because the drawing rules are fixed.”

Peter A. Grffin, discussing the futility of using a card counting system to beat baccarat, begins his discussion stating: “Before you start wondering why I’m offering these marvelous gambling aids to you at such a ridiculously low price (along with the ginzu knife and the wok) instead of trying to peddle them to some well healed sucker …”

Michael Shackleford  stated that: “For all practical purposes, baccarat is not a countable game.”

There are card counting systems that can work to “beat" baccarat. Both Griffin and Shackleford gave tags for card counting in baccarat. These card counting systems are impractical, to say the least, involving adding decimals to the hundredth place and perfect conversions to true counts. Griffin  stated that: “… assuming you’ll wager \$1000 whenever you get the go-ahead, this translates into an expected earnings of 70 cents per shoe. In an eight hour day you might make three bets.” Shackleford says that the player can earn about 15 cents per wager: “… assuming the player is able to keep a perfect count and the casino is not going to mind the player making a bet once every 475 hands ...” .

Ed Thorp developed a simple card counting system that he suggested to use to make the decision to make a “player” bet in baccarat. The “player-system” has tags {0, -1, -1, -2, -2, +1, +2, +2, +1, 0}. Thorp did not claim his count would give the card counter a way to beat the house; rather, he intended it as a method for reducing the disadvantage betting on the “player” side. There is a similar card counting system to use if one wants to make wagers on the “banker” side. This “banker-system” has tags {0, +1, +1, +1, +2, -1, -2, -1, -1, 0}. If a card counter was going to use any system in practice, it would be one of these two systems.

To investigate these card counting systems, I wrote a computer program to simulate a card counter using them in a game with the following common dealing rules:

• The game is dealt from a shoe with 8 decks.
• At the start of each shoe, a card is burned. Based on the value of the burn card, an additional number of cards are burned, equal to the value of the card.
• The cut card is placed 14 cards from the end of the shoe.
• After the cut card is dealt, one more round is dealt before shuffling.

I then ran a simulation of one hundred million (100,000,000) shoes, using each of these card counting systems. The following table gives a summary of the results from this simulation.

For example, a card counter who makes the banker wager whenever the true count is 30 or higher will make the wager about once every 5542 hands, and will be playing against a house edge of about 0.185%. A card counter who makes the player wager whenever the true count is 30 or higher will make the wager about once every 1786 hands, and will be playing with a player edge of about 0.329%.  A true count of 30 is the lowest true count that yields an edge over the casino.

Yes, that’s right; a card counter can get an edge over the casino using Thorp’s system! But don’t freak out about it. If a card counter were to wager \$1,000 every time he had the edge and make no other wagers, then on average this counter would make just over 15 cents per shoe in profit using the Thorp count. This profit amounts to theoretically winning about the cost of a cup of coffee per day. At that rate, in about two centuries the card counter can retire.

Finally, about the Tie bet, Thorp stated : “the advantages which occur with complete knowledge of the used cards are limited to the extreme end of the pack and are generally not large. Practical card counting strategies are at best marginal and at worst precarious.”

Well known baccarat author John May developed a card counting system for the Tie bet that targets remainders consisting of all even-valued cards (0,2,4,6,8). Using his system, he claims the player can get up to a 62% edge over the house. Unfortunately, as May states, this player advantage occurs “roughly once every 10,000 hands.” At 80 hands dealt per hour, playing 40 hours per week, that would mean the player could make one Tie bet wager every three weeks with an edge.

Any time multiple rounds are dealt from a deck or shoe, card counting becomes a potential issue. Therefore, in baccarat, it is reasonable to wonder if card counting can be used to beat the game. However, there is widespread agreement among the experts, dating back over 40 years, that card counting does not work at the baccarat tables. My research is consistent with those who have come before. There are no professional baccarat card counters. There are no baccarat card counting teams. Just because it’s possible does not mean it’s probable.

With baccarat there are much bigger problems; the spectrum of tools used to beat baccarat is enormous. From card marking, to card location techniques, to false shuffles, to edge sorting, to outright cheating, there are fortunes that are made over the baccarat tables.  But these fortunes are not being made by card counting. Keeping ahead of the baccarat curve means knowing when to leave old baggage behind. Ordinary card counting at baccarat is old baggage.

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1. Peter A. Grffin, The Theory of Blackjack, Fifth Edition, Huntington Press, 1996. pp. 221-223
2. James Grosjean, Beyond Counting Exhibit CAA, South Side Advantage Press, LLC, 2009, pp. 493
3. John May, Card-counting at Baccarat, Casino City Times website, September 9, 1999
4. Michael Shackleford
5. Ed Thorp, The Mathematics of Gambling, Lyle Stuart, 1985, pp. 36-39.
6. Ed Thorp, Optimal Gambling Systems for Favorable Games, Review of the International Statistical Institute, Volute 37:3, 1969