Is Card Counting Applicable to Baccarat

Portrayed in multiple blockbusters, including Rain Man and The Hangover, card counting in blackjack is not as difficult as it appears in the movies. Anyone with rudimentary knowledge of arithmetic and enough patience to practice can master this craft and apply it successfully at the blackjack tables.

More importantly, this approach has been proven to reduce the house edge and tilt the advantage in favor of blackjack players. One question that commonly arises concerns the effectiveness of card counting in baccarat, another popular shoe-dealt casino game. In today’s article, we look at the applicability of card counting in baccarat and assess its effectiveness.

First Things First – What Is Card Counting?

Contrary to popular belief, card counting is neither illegal nor does it require a person to be a mathematical genius or savant. Rather than remembering each card removed from play, as some people think, the practice involves keeping track of the ratio of high to low cards that remain to be dealt.

To achieve this, most card counting systems assign value tags to the high, low, and neutral cards in the shoe. The simplest and most commonly used system is the Hi-Lo, which employs the following tags:

Aces and ten-value cards (10, King, Queen, Jack) are tagged with -1
2s through 6s are tagged with +1
7s, 8s, and 9s are tagged with 0

The player keeps a running count by adding up these values as cards are removed from play to determine the current ratio of high to low cards in the deck. For example, if an Ace, Jack, 2, and 9 leave a freshly reshuffled deck, you are looking at a negative running count of (-1) + (-1) + 1 + 0 = -1. However, most blackjack games are dealt from a shoe containing multiple decks.

The player must, therefore, divide the running count by the number of remaining decks to calculate the true count, i.e., the ratio of high to low cards in the current deck. Counters make playing decisions and size their bets based on the current true count. The edge swings in favor of players whenever the true count exceeds +1. Continue reading to see how this helps them gain a statistical advantage over the house.

1Overview

The rules, structure, and card values in blackjack make the game especially vulnerable to counting, because some cards benefit players while others significantly tilt the winning odds in the dealer’s favor.

2Aces, Tens, and Faces Help Players

Tens, face cards, and aces help the player. When these cards are plentiful, the count becomes highly positive, leading to more player blackjacks, more dealer busts on hard totals, and additional opportunities for profitable splits and double downs. Accordingly, players place larger bets during positive counts because their chances of winning are better.

3Cards 2 through 6 Help Dealers

Similarly, an abundance of low cards 2 through 6 drives the count into negative territory. These cards favor the dealer by reducing their likelihood of busting with stiff hands and enabling them to complete more winning hands.

Under these conditions, the player is more likely to experience poor splits and doubles and will receive fewer blackjacks. For this reason, counters aim to expose less money to risk during negative counts by placing smaller wagers or by not betting at all.

4Neutral Cards 7, 8, and 9 Help Neither

Cards 7 through 9 receive tags of 0 under the Hi-Lo counting system because they are neutral. Consequently, they favor neither the house nor the player, as their presence does not have a pronounced impact on the outcome of a round.

Now, let’s see whether this approach is applicable to baccarat. Excluding the Tie bet, which carries an enormous house edge of 14.36%, there are two main wagers you can place: Player (1.24%) and Banker (1.06%). Baccarat is theoretically countable but requires a system with different tags than those used in blackjack because the cards are assigned different point values.

Card Values in Baccarat

Edward Thorp’s Baccarat Counting System

A Simpler Counting System for Baccarat

Card Values in Baccarat

Edward Thorp’s Baccarat Counting System

Considering these peculiarities, mathematician and blackjack researcher Edward Thorp devised a two-level counting system applicable to the Player and Banker bets, which are the only wagers worth placing in baccarat. Thorp suggested using the following value tags when counting Banker and Player wagers.

Card Tags when Counting Player and Banker Bets in Baccarat (Thorp System)
Player Bet		Banker Bet
Card Denomination	Tag	Card Denomination	Tag
Ace	0	Ace	0
2	-1	2	1
3	-1	3	1
4	-2	4	1
5	-2	5	2
6	1	6	-1
7	2	7	-2
8	2	8	-1
9	1	9	-1
10, K, Q, J	0	10, K, Q, J	0

Thorp created this system to reduce the house advantage when betting on either outcome. Gambling experts like Eliot Jacobson have since tested it through computer simulations to measure its efficiency. One of his simulations involved 100 million shoes for each side, Player and Banker, played under the following conditions:

Based on the results, Jacobson concluded that a baccarat player needs a positive true count of at least 30 to benefit from the system devised by Thorp.

The data showed that a player will have the opportunity to back the Banker side at a count of 30 approximately once every 5,542 hands, facing a lowered casino advantage of 0.19%.

Conversely, a player can back the Player side at a count of 30 roughly once every 1,786 rounds, enjoying an advantage of 0.33%. In terms of expected value, such a player will earn about $0.15 per shoe each time they wager $1,000 at an advantage, provided they refrain from betting while at a disadvantage.

A Simpler Counting System for Baccarat

Mathematician and gambling expert Michael Shackleford devised a simpler one-level card counting system for baccarat. After studying the effect of card removal in baccarat, he discovered that a deck rich in high-value cards slightly tips the scales in favor of the Player side.

Conversely, the winning odds shift toward the Banker bet whenever low-value cards predominate in the deck. Based on these findings, he developed an uncomplicated counting system with the following tags:

9s and cards worth zero points (10, K, Q, J) count as 0.
Aces, 2s, 3s, and 4s count as +1.
Cards 5 through 8 are tagged -1.

Gamblers place wagers on Player or Banker in line with the current running count (RC). According to Shackleford, the Player side becomes the better bet when the running count reaches -4 or less.

At this point (-4 RC), the house advantage drops from 1.24% to 1.14% for the Player, while that for the Banker rises from 1.06% to 1.15%. The table below shows that the gap between the house edges is smallest at -4 RC. The difference grows the further the count moves away from -4.

House Edge (HE) Differences Based on Running Count
Running Count	Banker Bet HE	Player Bet HE
-10	1.28%	1.01%
-9	1.26%	1.03%
-8	1.23%	1.05%
-7	1.22%	1.07%
-6	1.20%	1.09%
-5	1.17%	1.12%
-4	1.15%	1.14%
-3	1.13%	1.17%
-2	1.10%	1.19%
-1	1.08%	1.21%
0	1.06%	1.24%
1	1.03%	1.26%
2	1.01%	1.29%
3	0.98%	1.32%
4	0.97%	1.33%
5	0.94%	1.36%
6	0.92%	1.38%
7	0.90%	1.39%
8	0.88%	1.41%
9	0.88%	1.42%
10	0.86%	1.44%

A counter using this straightforward system will wager on the Player side at running counts of -4 or less and back the Banker proposition in all other cases. The more negative the count, the further the house edge for the Player drops.

At -23 RC, for instance, the casino holds an advantage of 0.76% on the Player wager. Conversely, high positive running counts produce larger house edges for the Player bet, reaching 1.76% at +25 RC. The opposite is true for Banker wagers, whose house edges fall during positive counts and rise during negative counts.

Under this strategy, counters will wager on the Player side roughly 28% of the time at a reduced house edge. In the remaining 72%, the Banker will be the better bet, and its combined house edge will decrease from 1.06% to 0.99%.

The aggregate house edge of both wagers drops from 1.15% to 1.01% with this counting strategy, provided the player bets during all rounds without skipping disadvantageous hands.

Even further, though negligible, reductions are possible when the player refrains from betting during unfavorable counts. For example, if the player skips hands at counts -9 through +1, they will play about 47% of all rounds, and the hands they do play will carry an average house advantage of 0.93%.

Is Card Counting Effective in Baccarat?

Card counting can be applied in baccarat and can potentially reduce the house edge on the two main wagers by a fraction of a percent. However, very liberal shuffle points and sufficiently deep penetration are required for this to occur.

Thorp’s system, for example, produced negligible results during the simulation mentioned above, in which the dealer inserted the cut card 14 cards from the end of the shoe. The chances of this happening in the real world are zilch, as baccarat dealers are generally instructed to place the cut card at least one deck from either end of the shoe.

While gaining a minuscule advantage over the house through counting is theoretically possible, baccarat players will almost never witness the counts that can yield it. Counting cards in this game is impractical, laborious, and largely ineffective, as multiple experts (Shackleford and Jacobson included) have confirmed.

Edward Thorp himself echoes these sentiments, stating that “Despite the resemblances between baccarat and blackjack, the favorable situations detected by perfect card counting […] are not sufficient to make the game favorable. Thus, baccarat is not in general a favorable game.”

MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (2011). Kelly Capital Growth Investment Criterion, Theory and Practice. World Scientific Publishing Co. Pte. Ltd. 63

1Rare Yet Negligible Edges Combine with Crushing Variance

As Thorp bluntly states, baccarat is generally not a favorable game for the player. Advantageous situations are rare, and players face enormous variance because they must risk huge amounts to compensate for how infrequently these situations occur. At the same time, the risk is greatly disproportionate to the expected value, which amounts to mere cents at best.

2Player and Banker Are a Coin Toss

Furthermore, baccarat is a game of almost perfect symmetry when it comes to the winning chances of the Player and Banker. The two main wagers are essentially a coin toss, with the Banker holding only a negligible edge over the Player. No cards massively benefit either side, unlike in blackjack.

3Counters Must Overcome Higher Initial House Edges

Baccarat players must overcome higher initial house edges, which further highlights the impracticality and futility of counting this game. The Player and Banker wagers give the casino advantages of 1.24% and 1.06%, respectively, for a combined house edge of 1.15%.

By contrast, blackjack games with liberal playing conditions can produce house edges of less than half a percent. This low edge percentage, combined with the greater impact of card removal, makes it easier to profit from card counting in blackjack.

4Baccarat Plays by Fixed Rules

The house rules for drawing cards to the Player and Banker hands are fixed, which further undermines the efficiency of card counting in this game. There is virtually no decision-making, as players need only choose which side to back and how much to wager.