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Reason #2 why the Wizard likes Bovada: No-hassle practice games
Most online casinos spend more effort trying to separate you from your money than they do trying to give you a good experience. They have all kinds of popup windows, they usually make you download their software, and if they do offer play-in-browser games then you have to register an account before you can play. And if you register they start sending you emails trying to get you to deposit real money.
But Bovada is different. They have no popup windows at all, and their practice games play right in your browser, with no download, and no registration required. You don't even have to give up your email address. It couldn't be simpler: just one click and you're playing the game.
I wish all online casinos showed this much respect for their players. Other casinos practically ask for your first born child to play for free. Meanwhile Bovada is patient and does not twist anybody's arm to play for real money. You can play as long as you like for free with no obligation. The real-money games are available if that's your preference, but if not, you can play the free practice games for as long as you like without hassle.
IntroductionI 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 BaccaratBy 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 dealer’s 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.
EZ Baccarat Dragon Side Bet
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 counter’s favor. An excess of smaller cards is also helpful. The cards 1-7 are each cards that can move the dealer’s 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.
House Edge by Card Removed
|Card Removed||Winning Dragon||Losing Dragon||Total||House Adv.|
Effect of Removal
|Card Removed||EOR||EOR x 1000|
Looking at the values in the last column of Table 3, and adjusting slightly to make it balanced, we get 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). 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). I’ll refer to this as “system 2.” 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:
- 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.
Table 4 gives the results of a simulation of two hundred million (200,000,000) shoes.
Simulation Results: 200M Shoes
|Item||System 1||System 2|
|Frequency of Bet||10.698%||9.163%|
|Units Won per Shoe||0.6361||0.5967|
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 8’s and eight 9’s 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%.
Card Counting Statistics by Cut Card DepthExpand
|Cut Card Depth||Trigger Count||Hands per Shoe||Expected Value||Standard Deviation||Bet Frequency||Percent of Shoes Played||Profit per Shoe (units)||Profit per Hour (60 hands)|
About the AuthorFor more information on Eliot, or to contact him, visit www.jacobsongaming.com .
Related PagesPlease also see my own card counter vulnerability study of the Panda 8 side bet in EZ Baccarat.