I don't like to accept articles by other writers. Few writers out there freelance at the kinds of standards I expect of myself for this site. Until now, I believe the only outside page I have accepted is the one on Flip It, by Michael Bluejay.
However, when Eliot Jacobson mentioned he had found the Dragon Bet in EZ Baccarat easily countable I was eager to cover it. As far as I know this topic has never been covered before. So I was quite happy when Eliot agreed to share the results of his analysis with my readers. Enjoy! — Wizard
Card Counting the Dragon Side Bet in EZ Baccarat
By Eliot Jacobson Ph.D., © 2011
The Dragon Side Bet for EZ Baccarat is simple to describe. This side bet pays 40-to-1 if the dealerís three-card total of 7 beats the player, otherwise the bet loses. Analysis of the wager consists of a straight forward cycle through all possible hands. Table 1 gives the analysis for eight decks, with the house edge of 7.611% appearing in the lower right cell.
I first considered if the Dragon Side Bet was susceptible to a card counting methodology several months back. Intuitively, it seemed as though the wager was more probable to hit if there was an excess of 7 and 10 valued cards in the deck. In this case, the dealer would be more likely to draw 10-10 and hit to a 10-10-7 = 7. Later, as I read several Internet discussion boards, it became clear that others thought as I did. The conclusions were that if there was any vulnerability at all, it would come when 7ís and 10ís were in excess in the remainder of the shoe. It turns out this is not the case. The Dragon Side Bet is vulnerable to a card counting methodology, but the answer is surprising.
The key is that in order for the player to win the Dragon bet, the dealer has to draw a third card. This requirement trumps everything else. The cards that keep the dealer from drawing that third card most often are the 8 and the 9. As these cards are removed from the shoe, the edge moves quickly towards the counterís favor. An excess of smaller cards is also helpful. The cards 1-7 are each cards that can move the dealerís final total to 7 if he draws. Determining which of these low cards result in a final total of 7 most often is the key.
The methodology used in this study is familiar. The overall house edge for the game dealt from eight decks is 7.611%. By removing each card in turn from an eight-deck shoe, its effect on the house edge can be determined. This allows card counting systems to be developed. After arriving at candidate systems, computer simulations are run to see if these systems can generate an edge in practice. If there is an edge, the question then becomes if this is significant enough to become an opportunity for the advantage player.
Table 2 shows the number of winning and losing hands that result from removing one card from an eight-deck shoe, along with the house edge after removing that card.
Table 2 allows us to compute the effect on the house edge for the Dragon bet by removing each card. Table 3 gives these results. The middle column (EOR) shows the change in house edge when the indicated card is removed. The final column (EOR x 1000) indicates potential card-counting tags to use in an optimal system.
Table 3 indicates the extreme importance of ridding the shoe of 8ís and 9ís. Also, the 7 is the most important card, as expected, to remain in the shoe. The other cards diminish in value as their pips go down, presumably because they are used in fewer and fewer situations to draw to a dealer total of 7. Working against intuition, the counterís situation improves as zero-valued cards are removed from the deck.
Looking at the values in the last column of Table 3, and adjusting slightly to make it balanced, we get card counting ďsystem 1Ē with tags (0.5, -0.9, -1.1, -2.7, -2.7, -3.3, -3.6, 5.4, 4.8, 0.9). The reader will most likely consider it daunting to use system 1 in practice. However, as a baseline counting system, it is worthwhile to see how it performs. In an effort to simplify this unwieldy system as much as possible, I also considered the card counting system with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0). Iíll refer to this as ďsystem 2.Ē This latter system is easily implemented by a counter of average skill level.
To gauge the effectiveness of each, I wrote a computer program to simulate using these two systems in live play. The game I simulated has the following shuffling and cut card rules:
Table 4 gives the results of a simulation of two hundred million (200,000,000) shoes.
It is clear from the last row of Table 4 that system 2, with tags (0, 0, 0, -1, -1, -1, -1, 2, 2, 0), performs remarkably well in comparison to its optimal cousin.
The person who uses system 2 should make the Dragon bet whenever the true count is +4 or higher. If he does so, then on average he will have an 8.03% edge over the house each time he makes the bet. This counter will have the opportunity to make the Dragon bet at or above the target true count on 9.16% of his hands. Given that the average shoe yields about 80 hands, the counter should be able to make, on average, about seven Dragon bets per shoe with the edge.
In dollar terms, if the house allows a Dragon bet up to $100 (say), then on a per-shoe basis the counter will average about $59.67 profit. The counter will earn about $8.03 per $100 wagered on the Dragon bet.
It is worthwhile to check that the simulated results for system 2 make sense combinatorially. One way to get a +4 true count off the top is to remove eight 8ís and eight 9ís from the deck. This will leave 400 cards remaining in the eight-deck shoe, with a running count of +32, for a true count of 4.16. In this case, combinatorial analysis gives a player edge of 1.0227%. Using a single deck, one way to get a +4 true count is to remove one 8 and one 9 from the deck. This leaves 50 cards with a +4 running count, giving a true count of 4.16. In this case, combinatorial analysis gives a player edge of 1.3114%. Because the player is making the Dragon bet at a true count of +4 and above, not just at +4, these computations represent a secondary confirmation of the simulated results.
Cut card placement varies by casino, so it is worthwhile to investigate how the edge changes with the placement of the cut card. Table 5 gives statistics for all cut card placements from 14 cards to 52 cards, and then by half-deck increments up to four decks. A cut card placement at one deck, instead of at 14 cards, decreases the potential profit to the player by about 50%.
About the Author
For more information on Eliot, or to contact him, visit www.jacobsongaming.com .
Please also see my own card counter vulnerability study of the Panda 8 side bet in EZ Baccarat.
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