Is Card Counting Applicable to Baccarat

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

More importantly this approach provenly reduces the house edge and tilts the advantage in favor of blackjack players. One question that commonly arises concerns the efficiency of card counting in baccarat, another popular shoe-dealt casino game. In today’s article, we are looking at the applicability of card counting in baccarat and address its effectiveness.

First Things First – What Is Card Counting?

Contrary to popular belief, card counting is neither illegal nor does it require one to be a mathematical genius or a 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 uses the following tags:

Aces and ten-value cards (10, King, Queen, Jack) are tagged -1
2s through 6s are tagged +1
7s, 8s, and 9s are tagged 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 A, J, 2, and 9 leave a freshly reshuffled deck, you are looking at a negative running count of (-1) + (-1) + 1 + 0 = -1. Most blackjack games are dealt out of a shoe containing multiple decks, however.

The player must, respectively, 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 gets higher than +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 render it highly vulnerable to counting. This is because certain cards work to the advantage of players whereas others heavily tilt the winning odds in the dealer’s favor.

2Aces, Tens, and Faces Help Players

Tens, faces, and aces help the player. Their preponderance means high positive counts, which results in more player blackjacks, more dealer busts on hard totals, and more opportunities for successful splits and double downs. Players make larger bets during positive counts since they stand better chances of winning.

3Cards 2 through 6 Help Dealers

Likewise, the abundance of low cards 2 through 6 leads to negative counts. These are advantageous for the dealer because they decrease their probability of busting with stiffs and help them make more winning hands.

In such circumstances, the player is more likely to suffer lousy splits and doubles and will get fewer blackjacks. Counters are logically seeking to expose less money to risk during negative counts by placing smaller wagers or not betting at all.

4Neutral Cards 7, 8, and 9 Help Neither

Cards 7 through 8 receive tags of 0 under the Hi-Lo counting system because they are neutral. As such, they favor neither the house nor the player because 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 (14.36%), there are two main wagers you can make here – on 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, 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 invented this system for the purpose of decreasing the house advantage when betting on either outcome. Gambling experts like Eliot Jacobson have since tested it through computer simulations to determine its efficiency in this regard. One of his simulations involved 100 million shoes for each side, Player and Banker, played under the following playing conditions:

Looking at the results of this simulation, Jacobson established that the baccarat player needs a positive true count of at least 30 to benefit from using the system devised by Thorp.

The results showed that a player will have the opportunity to back the Banker side at a count of 30 approximately once per every 5,542 hands, in which case he or she will be up against a lower casino advantage of 0.19%.

Respectively, a person will be able to back the Player side at a count of 30 roughly once every 1,786 rounds at an advantage of 0.33%. Where expected value is concerned, one such player will generate profits of around $0.15 per shoe each time they wagered $1,000 at an advantage without making any bets when at 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 established that a deck rich in high-value cards slightly tips the scales in favor of the Player side.

And vice versa, the winning odds swing in favor of the Banker bet whenever low-value cards preponderate in the deck. Resting 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 bet 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 increases from 1.06% to 1.15%. The table below shows the discrepancy between the house edges of the two main bets is the smallest at -4 RC. The difference gradually grows the further away the count moves 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 greater the negative count gets, the further the house edge for the Player drops.

At -23 RC, for example, the casino holds an advantage of 0.76% on the Player wager. And vice versa, high positive running counts produce bigger house edges for the Player bet, reaching 1.76% at +25 RC. The opposite is true for Banker wagers whose house edges get lower during positive counts and increase during negative counts.

Under this strategy, counters will wager on the Player side approximately 28% of the time at a lower house edge. Respectively, the Banker will be the better bet in the remaining 72% of the time when 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. This applies on condition the player bets during all rounds without skipping hands during disadvantageous counts.

Further, albeit even more negligible, reductions are possible when the player refrains from betting during unfavorable counts. For instance, if the player skips hands at counts -9 through +1, they will play approximately 47% of all rounds and the hands they do play will yield an average house advantage of 0.93%.

Is Card Counting Effective in Baccarat?

Card counting is applicable to baccarat and can potentially reduce the house edge for the two main wagers by a fraction of a percent. However, you need very liberal shuffle points and deep enough penetration for this to happen.

Thorp’s system, for example, produced negligible results during the above-mentioned simulation where the dealer inserted the cut card 14 cards from the shoe’s end. 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 puts it, baccarat generally is not a favorable game from the perspective of the player. Advantageous situations arise once in a blue moon, not to mention players face enormous variance as they must risk huge amounts to compensate for this rarity of occurrence. At the same time, risk exposure is massively disproportionate to one’s expected value which amounts to meager cents at best.

2Player and Banker Are a Coin Toss

Furthermore, baccarat is a game of almost perfect symmetry where the winning chances of the Player and Banker are concerned. The two main wagers are pretty much a coin toss, with the Banker side having a negligible edge over the Player. No cards benefit either side massively as is the case of blackjack.

3Counters Must Overcome Higher Initial House Edges

Baccarat players must overcome greater initial house edges which further adds to the impracticality, ineffectiveness, and futility of counting this game. The Player and Banker 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. The low edge percentage combined with the greater effect 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 destroys the efficiency of counting cards in this game. There is almost no decision-making here since players must only determine which side to back and how much to bet.