Counting Cards on the Dragon Bet in Baccarat

Counting Cards on the Dragon Side Bet in EZ Baccarat

Miscellaneous Baccarat Score Boards is straightforward. This side wager pays 40-to-1 if the dealer’s total of three cards equals 7 and beats the player's total; otherwise, the wager loses. The analysis involves systematically going through all possible hands. In Table 1, you can view the analysis for eight decks, revealing a house edge of 7.611% in the bottom right corner.

Card Counting in Baccarat

I contemplated whether the Dragon Side Bet could be affected by a card counting strategy several months ago. My intuition suggested that the bet was more likely to succeed if there were more 7s and 10-valued cards left in the deck. This is because the dealer might draw 10-10, leading to a total of 10-10-7 = 7. As I participated in various online forums, I discovered that many others shared my line of thinking. The consensus was that any potential vulnerability arose from an abundance of 7s and 10s available in the remaining cards of the shoe. Surprisingly, this is not the case. The Dragon Side Bet does allow for a card counting strategy, but the insights are unexpected.

The crux of the matter is that a player must rely on the dealer drawing a third card to succeed with the Dragon bet. This stipulation outweighs all other factors. The cards most likely to prevent the dealer from drawing that crucial third card are the 8 and 9. As these cards are removed from the shoe, the advantage quickly shifts in favor of the counter. Having more lower-valued cards is also beneficial because cards 1-7 can help bring the dealer’s total to 7 upon drawing. Identifying which of these lower cards often culminate in a total of 7 is essential.

The methodology applied in this study is quite traditional. The overall house edge for a game using eight decks is estimated to be 7.611%. By sequentially removing each card from an eight-deck shoe, we can observe its impact on the house edge. This facilitates the development of card counting systems. Once potential systems are established, computer simulations are performed to evaluate whether these systems can yield a practical advantage. Should an advantage be present, the next question is whether it is significant enough to be seen as an opportunity for the skilled player.

Table 2 illustrates the number of winning and losing hands resulting from the removal of a single card from an eight-deck shoe, alongside the subsequent house edge on removing that card.

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Using Table 2, we can analyze how the house edge for the Dragon bet changes by removing each card one at a time. The results are summarized in Table 3, where the middle column (EOR) indicates the change in house edge with the removal of the specified card. The final column (EOR x 1000) presents potential tags for card counting that can be used to create an effective system.

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Table 3 highlights the critical significance of clearing 8s and 9s from the shoe. Additionally, the 7 ranks as the most pivotal card that should remain, as expected. Other cards gradually lose relevance as their pip values decrease, likely because they have fewer applications in forming a dealer total of 7. Counterintuitively, the position of the counter improves as zero-valued cards are extracted from the deck.

By examining the values in the last column of Table 3 and making minor adjustments for balance, we arrive at card counting 'system 1' with tags (0.5, -0.9, -1.1, -2.7, -2.7, -3.3, -3.6, 5.4, 4.8, 0.9). Many readers may find system 1 challenging to implement in practice; however, it is valuable to evaluate its effectiveness concerning the baseline counting system. In an attempt to streamline this complex system, I also explored a card counting strategy featuring tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0), which I will refer to as 'system 2.' This simpler system can be easily utilized by counters of moderate skill.

To determine the efficacy of each system, I developed a computer program that simulated the use of these two strategies in real-time play. The game setup I simulated follows these shuffling and cut card rules:

• The game uses eight decks dealt from a shoe.
• Initially, a card is burned from the shoe. The number of additional cards burned equals the value of the initial burn card.
• The cut card is positioned 14 cards from the end of the shoe.
• After the cut card is dealt, one additional round is distributed before reshuffling.

Table 4 presents the outcomes of a simulation involving two hundred million (200,000,000) shoes.

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Update : 10/14/2011. Soon after the publication of this article, I recognized a significant error that resulted in an underestimation of the player's advantage. This mistake arose from utilizing single-deck estimates for the remaining cards in the shoe, rather than accurately determining the true count based on the fractional decks left. I revised my simulation program and validated the updated results with Steve How from discountgambling.net. I apologize for any inconvenience caused to readers.

The data from the last row of Table 4 makes it evident that system 2, with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0), shows exceptional performance when compared to its optimal counterpart.

A player utilizing system 2 should make the Dragon bet every time the true count reaches +4 or higher. By doing so, they can expect an average edge of 8.03% over the house with each bet placed. This counter will find the opportunity to make the Dragon bet at or above the desired true count in approximately 9.16% of their hands. Given that an average shoe consists of about 80 hands, this translates to roughly seven Dragon bets made per shoe with the edge.

In monetary terms, if the casino permits a Dragon bet cap of $100 (for instance), the counter can anticipate a gain of about $59.67 per shoe. Specifically, for every $100 wagered on the Dragon bet, the counter stands to earn around $8.03.

It's beneficial to verify that the simulated outcomes for system 2 are logically sound in combinatorial terms. One method for achieving a +4 true count is by removing eight 8s and eight 9s from the deck. This would leave 400 cards in the eight-deck shoe with a running count of +32, resulting in a true count of 4.16. In this setup, a combinatorial analysis suggests a player advantage of 1.0227%. Using a single deck, achieving a +4 true count could involve removing one 8 and one 9 from the deck, leaving 50 cards with a +4 running count, which results in a true count of 4.16. This scenario yields a player advantage of 1.3114%. Since players aim to make the Dragon bet when the true count is at +4 or higher, these calculations offer a secondary validation of the simulated results.

The placement of the cut card can vary by casino, so it's worth examining how the edge is affected depending on where the cut card is positioned. Table 5 provides statistics reflecting outcomes for all cut card placements, ranging from 14 to 52 cards, and spans half-deck increments up to four decks. Positioning the cut card at one deck instead of 14 cards significantly reduces the player's potential profit by around 50%.

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This analysis indicates that, theoretically, using card counting techniques on the Dragon Side Bet in EZ Baccarat presents an advantageous opportunity. Nonetheless, I believe due to the high variance and minimal returns, card counting does not represent a practical risk to the game.