Discount Gambling

+EV Rapid Baccarat Dragon @ Barona Casino

Posted in +EV, baccarat, dragon-bonus by stephenhow on October 3, 2011

OMG, did you see the recent WoO post on counting the baccarat dragon bet?! That bet gets so +EV that a simple counting scheme yields an average +4% edge over 7.5% of the time. Betting $100 dragons yields an average $25 profit per shoe with the simple count.

Update: use my simple dragon tracking sheet that simulates at an $53 profit/shoe (betting $100 dragons 6.4% of the time).

I had never looked into counting for the dragon, because I assumed the 7.611% house edge was too big to overcome. However, given the 40-to-1 payout odds, a 0.25% (quarter percent) change in the dragon frequency yields a 10% change in the bet EV. And it works out that the effect-of-removal (EOR), i.e. the sensitivity, of a card to the dragon-7 EV is rather large.

So I looked into other countable dragon opportunities at my nearby Barona Casino. They have a Rapid Baccarat bank of player consoles, with the following dragon bet:

Rapid Baccarat Dragon Bet (on Player Hand)
Hand Payout Frequency Return
Non-natural winner by 9 points 30-to-1 0.003683 0.110492
Non-natural winner by 8 points 10-to-1 0.006822 0.068217
Non-natural winner by 7 points 6-to-1 0.017924 0.107543
Non-natural winner by 6 points 4-to-1 0.028257 0.113027
Non-natural winner by 5 points 2-to-1 0.033244 0.066489
Non-natural winner by 4 points 1-to-1 0.037368 0.037368
Natural winner 1-to-1 0.162589 0.162589
Natural tie push 0.017871 0.000000
All Others -1 0.692242 -0.692242
Total 1.0000 -0.026517

The sensitivity of the player dragon bet to any given card is listed in the following EOR table (8 deck shoe):

Effect-of-Removal per card for Player Dragon EV
Card EOR
Face/Ten -0.000530
Ace +0.000777
Deuce +0.001160
Trey +0.001273
Four +0.000470
Five +0.000172
Six +0.000053
Seven -0.000563
Eight -0.000619
Nine -0.000604

The result is that the player dragon bet on the Rapid Baccarat machines at Barona is countable (you can calculate when the bet is +EV). Here’s a baccarat tracking sheet that tells you when to make the dragon bet. Below are the theoretical distributions of the dragon-7 and the player dragon EVs after 7 decks are dealt.

The graph shows that the dragon-7 (banker wins with a 3 card 7) often gets very advantageous at the 7th-deck point of the shoe. This graph shows the actual EV of the bets, independent of counts. You’ll need a mobile app to track the shoe exactly to get this calculation. In the next posts, I’ll compare the return using a simple count to these ideal returns.

The graph of the Rapid Baccarat Player Dragon shows a much narrower distribution, which still yields a player advantage. The player dragon compares favorably to the dragon-7, in a few important aspects. First, you can sit around at a Rapid Baccarat terminal all day, without any floor person even noticing you. You can use your mobile device at a Rapid Baccarat terminal. Secondly, the variance of the player dragon is much, much less than the dragon-7, because you hit something 30% of the time, more than 10x as often as the dragon-7’s infrequent 2.5% hit rate. The Kelly criterion will allow you to bet much more on the player dragon than the dragon-7 for any given bankroll. (Think about it, you’re still betting on a 40-to-1 longshot on the dragon-7. On the other hand, the player dragon pays even money for a natural winner.)

Would I sit around all day at a Rapid Baccarat terminal waiting for the count to go +EV on the player dragon? While listening to my podcasts and music on my iPhone? Probably not, unless the numbers work out amazing well. I’d need the shoe to be +EV around 10% of the time. Otherwise, I’d rather play the fun -EV carnival games.

38 Responses

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  1. Gambler_guy said, on October 3, 2011 at 4:30 pm

    Wow cool article again! The 7-Dragon Bet covered at WoO (40:1 payout on Banker’s 3-card seven) is not available where I live but the other Dragon bet (with payouts ranging from 1-1 to 30-1) is available here so I will anxiously wait for your +EV strategy for that. BTW you can make this bet for either player or banker. You only covered it for Player so I guess it’s a better bet for player than banker?

    • stephenhow said, on October 4, 2011 at 6:34 pm

      The Banker Dragon started off with a -10% house edge, so I assumed it wasn’t any good, but I haven’t looked into the EORs closely. I worked out a simple set of count weights (1,2,2,1,1,0,-1,-1,-1,-1) for the Player Dragon, and I’ll make up a tracking sheet tomorrow.

  2. Russel said, on October 7, 2011 at 12:07 am

    Just out of curiosity, how many shoes/hour?

    • stephenhow said, on October 7, 2011 at 7:22 am

      In the “Rapid Baccarat” format, they limit the time between hands to 30 seconds, and all bets are resolved electronically. So, I’d guess it takes about 45 seconds per hand. That works out to 1 hr per shoe. This is too slow for me, and I couldn’t sit around hoping for the last few hands of the shoe to go +EV. It’s really only useful if you already sit around a baccarat table all day, and if you like small edges. That means no one is going to bother with this type of thing.

  3. sean said, on October 17, 2011 at 5:16 pm

    If the casino visibly deals 3 hands before beginning the game (rather than burn cards), how much would this swing the EV? Great information by the way. Thanks.

    • stephenhow said, on October 17, 2011 at 6:14 pm

      That would help very, very much. Is this for the dragon-7 (EZ Baccarat), or the Dragon Bonus (ShuffleMaster) of this post? I’ll run the numbers for the appropriate game.

      • sean said, on October 17, 2011 at 10:47 pm

        It’s for the Rapid Baccarat Dragon Bet (on Player hand). The bet is also available on the Banker side, though I don’t think it will be as promising since a 3 card draw is way less likely. Please email me.

      • stephenhow said, on October 18, 2011 at 9:04 am

        The improvement you get by seeing 3 hands instead of a blind burn improves the profit to a total of +14.2% of a fixed bet per shoe (i.e., $14.20 for $100 Dragon Bonus bets). That’s an improvement from the $11.20/shoe for the traditional burn procedure. You’ll make about 5.0 dragon bets per shoe.

  4. sean said, on October 18, 2011 at 11:36 am

    Wow, that’s quite an improvement. Any chance you also calculated the standard deviation?

    • stephenhow said, on October 18, 2011 at 4:05 pm

      Maybe I’ll get around to analyzing the Kelly Criterion for the bet (which might be directly related to the variance?) in the next day or so.

  5. sam said, on October 21, 2011 at 11:03 am

    I am eagerly awaiting more information on the player dragon bonus. I dont consider myself yet learned with this count. I have just learned the dragon 7 EZ bacc bonus but wagering that is quite volatile. I live in KC & the Ameristar casino has both the dragon 7 (separate of course) as well as the player 30-1 bonuses on its bacc tables. Any & all help with this player dragon bonus is much appreciated, thank you.

  6. gog said, on November 1, 2011 at 7:35 pm

    Just wonder how did you come up with EOR – I have some slightly different numbers; eg: removing a 9 leaves 415 cards in the shoe, resulting in a EV of -0.027196541 which gives a difference of about -0.000679796

    • stephenhow said, on November 2, 2011 at 12:26 am

      I use a recursive function to calculate the EV of any proposition bet for any given shoe composition. It deals out to player, banker, player, banker, possible player draw, possible banker draw, then evaluates the proposition bet for the leaf nodes.

    • James said, on November 5, 2011 at 9:02 am

      hi, gog

      Just want to know how you come up with your EOR. eg: removing a 9 leaves 415 cards, then you start simulate first round and say 4 number of cards were dealt and left 411 cards in the shoe.

      My question here is whether :-

      a) you continue to simulate the 2nd round, 3rd round….until the 80th round(or until 14 cards left in the shoe) with the same shoe with 411cards. After that only start with new shoe.

      OR

      b) you simulate the 2nd round with a totally new shoe with 415 cards(remove a 9), 3rd round with new shoe with 415 card…..means every round use a totally new shoe with 415 cards(without a 9 !).

      Please clarify

      cheers

  7. Profbac said, on November 2, 2011 at 5:05 am

    On a related note, about this time last year, casinos in Atlantic City and Connecticut that were offering the
    dragon bet “EZ Bac” games were hit hard by card counters. These casinos show the burn cards face up
    and were putting the cut card at 14 cards from the end of the shoe. They were dealing into those last 14 cards.

    Now the tables offering these bonus bets cut 1.5 to two decks off the back of the shoe.
    In Las Vegas, Wynn and Harrahs removed those tables.

  8. James said, on November 11, 2011 at 8:42 am

    The above table shown that the frequency for NATURAL TIE and ALL OTHERS is 0.0178711 and 0.692242 respectively.

    However, my simulation shown 0.03574(natural tie) and 0.66561(ALL OTHERS).

    All others figures are very close.

    Could it be my simulation mistakes ?

    • stephenhow said, on November 14, 2011 at 8:49 am

      My natural tie frequency number agrees exactly with the Wizard Of Odds, so check your simulation.

      • James said, on November 14, 2011 at 4:08 pm

        it’s my mistake, I assumed 6 vs 6(4 cards) and 7 vs 7(4cards) are natural tie ! Corrected and now my frequency for natural tie is 0.0178711.

        Thanks for your comments !

  9. James said, on November 14, 2011 at 4:32 pm

    Hi, Stephenhow,

    I need your comments on this statement(from other analysist) :-

    “…….The first step in developing a card counting system for any game is to calculate the effect the removal of one card of each rank has on the payout percentage of the game. The analysis will focus on the DRAGON BONUS PLAYER bet. Table 4 presents the results. The first column displays the new payout percentage of the game with all the cards of a particular rank removed. The second column displays the change in payout percentage relative to the base payout. Finally the last column displays the effect removing just one card of a particular rank from an eight deck shoe has on the overall payout percentage………….”

    Normally we just remove one card of a particular rank and calculate the EOR base on 415 cards.

    Instead of doing that, he removed all the cards of a particular rank( 8 deck, removed 32 cards !) and then simulate the remaining cards(384 cards) to get the EOR, then divide it by 32 to get EOR for one card !

    Do you think that his method is correct ?

    Cheers

    • stephenhow said, on November 14, 2011 at 6:16 pm

      I prefer to calculate the sensitivity of the EV to a single card vs. all cards of the same rank. The latter is basically a calculation of the EV sensitivity for a single-deck shoe. But overall, it’s not a big deal, since we all end up simulating the effectiveness of a given count scheme. So, don’t worry about it, because it doesn’t affect the end result.

  10. John said, on December 10, 2011 at 3:13 pm

    Hi Stephen –

    For somebody w/ a limited bankroll $200 per month is the player dragon a good bet since it has a payout 30% of the time compared to the dragon 7? I could easily lose my $200 bankroll quickly betting the dragon 7 plus it’s so slow & betting $1 just isn’t much fun. I typically only stay @ a casino 3, 4 hrs max.

    Do you have any statistics on the estimated deviation? Say I bet $40 on the player dragon when the count is good what are the odds I’ll lose my $200 for the night?

    Do you recommend another +EV game w/ a limited bankroll $200? The 3x attach B.J. game looks good but $200 probably wouldn’t be enough. MS Studs looks like it needs a big bankroll too.

    Also is it me or is Barona very generous w/ comps? Many times I’ll gamble and lose @ max $25 or $50 and I’ll get two free buffets to help me breakeven for the night. Plus some nights I’ll walk away a winner. Pala is VERY tight and I don’t go there anymore.

    Great site. Glad to see somebody helping out the players. Maybe you can get some ad space on here – you deserve it.

  11. stephenhow said, on December 11, 2011 at 11:33 am

    John,

    Personally, I think the best advantage game out there is Mississippi Stud. Yes, the session swings can easily reach +/- $500, but if you have a big enough bankroll, you’re playing with a reasonable edge at a full table. I was at Barona last night, and counted the dragon until I gave up from boredom. I played MS Stud when the game filled up at 5:30pm, and quickly won $420. I figured I won enough, and I left early. I was lucky and won $400 on Friday too. Of course, I’ve had similar losing sessions, but overall, it’s a lot of fun to play the game when you get to see 12 cards before the hand starts.

    Any time you see me playing, you’re welcome to form a corporate bank with me (e.g., 20% your money, 80% my money) on my spot. You can join and quit at will (i.e., divide up the bankroll). Since we both play the same way (same decisions), there’s no conflict. It’s not as fun as sitting down and playing your own hands, but its better than standing around and counting the dragon 🙂

    Barona is really good with the food comps. I’ve heard that it’s really easy to earn a buffet comp. They’re not as good as Viejas with the daily cash player rewards, but I’d still rather play at Barona with their liberal Mississippi Stud rules.

    Steve

  12. James said, on January 29, 2012 at 5:42 pm

    Hi, stephenhow

    I need your comments on the new game call POWER BACCARAT 98 which found at local casino here.

    you can download the game rules from : http://app.cra.gov.sg/public/www/download.ashx?id=308

    IS IT BEATABLE(especially for the side bet !) ?

    cheers

    James

    • stephenhow said, on January 30, 2012 at 3:50 pm

      OMG!! I just analyzed one of the side bets. I’ll email you, you might want to keep this to yourself.

      • James said, on January 30, 2012 at 5:24 pm

        I just simulate the whole game(all side bets , Tie, banker and player) and found that the house edge for side bets varies from 4% – 10%.

        The house edge for Tie, player and banker are 13.6%, 1.0% and 1.01% respectively(all slightly lower than the conventional baccarat)

        May be we can compare the house edge for side bets as well ?

  13. c_ming said, on April 3, 2012 at 12:40 pm

    Hi Stephen,

    I have no doubt with your method for Dragon 7, however, I cannot acheive postive outcome with my own Bac program written by excel. My program use random function in excel to acheive different order of 416 cards and calculate the result from there. I have carefully check that all the formula is written correctly. Do you think excel is not suitable for large amount of data acquiring? What program would you suggest for testing Bacarrat tactics?

    Thank you very much

    • stephenhow said, on April 15, 2012 at 2:58 pm

      I haven’t done any programming in Excel, but if was capable of shuffling the shoe, and you have a function for calculating the dragon EV for the first hand of a subset of the shoe, then you’d see it gets +EV often towards the end of the shoe. I like programming in Java for quick results. Check out Eclipse or NetBeans as a Java IDE.

      • c_ming said, on April 16, 2012 at 12:44 am

        Thank you for your reply, Stephen. As I said, my program do shuffle 8 decks of cards and generate about 70 hands per shoe. By following your sheet, I do found betting opportunities usually at the end of the shoe. However, the losing are getting bigger and bigger as more results are generated (after 500+ shoes). I really don’t understand where did I went wrong?

        I would like to try this strategy more serious at my local casino, however, I hope I can try it out on computer first before using real money. Can I email you my program? Can you give me more advises, please?

        Thank you very much.

      • stephenhow said, on April 18, 2012 at 7:12 pm

        Sounds like you’re on the right track. Of course, you can easily still be losing after 500 shoes. The chances are your program is right, and you’re just on a (typically) bad streak 🙂 Or, you might have a simple bug somewhere in your program. I don’t use spreadsheets beyond simple formulas, so I can’t help you. You’ll get your program working, and you’ll come up with the same results as me.

  14. sidinsd said, on April 27, 2012 at 7:38 pm

    Hello

  15. sidinsd said, on April 27, 2012 at 7:47 pm

    I just got back from Barona where I played the Rapid Baccarat game using Steven’s count and tracking sheet for the Player Dragon Bet. The problem with playing this game, as Steven mentioned, is that it is so boring that you have to have almost a saintly patience to play it. I played just two shoes and did fairly well, but I attribute that mostly to pure dumb luck, nothing more. The opportunity to play the Dragon Bet came up only 3 times in those two shoes, all in the first shoe. I played the game by betting the minimum of $5 on the banker on egvery hand except the ones that the tracking sheet told me I should play the dragon bet. On those hands I bet $5 on the player and $25 on the Player Dragon. I won two out of three of the Dragon bets, one for even money (a natural 9) and one for a 2:1 payout (player win by 5 points). I lost the third one, making a total profit on the Player Dragon Bets alone of $50. I walked away from the tables up $115, but I attribute that to pure dumb luck. I like to play poker and often times you jave to wait 1/2 hour or more for a poker table, so I intend to use this game as a timekiller for me while I am waiting for poker tables. I do not see it as much more than that.

  16. Herman Munster said, on May 2, 2012 at 2:09 pm

    Thank you for the wonderful work and website!

    Can you redo your Flash games with and older version of Flash? Many who use Linux (or who merely have older systems) cannot get your games to run.

    Thanks!

  17. Royal_Hunter said, on May 14, 2012 at 9:09 pm

    Does your 53 hourly win rate factor in the losses of betting the banker/player even money bets? In a different post you mention maintaining a win rate of $5.30 per shoe betting 10 dollars on dragon, but that included making 10 dollar player/banker bets. Should we assume that winning 53 dollars an hour includes making 100 dollar banker bets 100% of the time? Thanks. Your site is extraordinarily insightful.

    • Royal_Hunter said, on May 14, 2012 at 9:17 pm

      Sorry, I misread it. 5.30 BEFORE the banker/player bets. Feel free to delete both of my posts.

  18. Princess said, on November 6, 2012 at 10:53 am

    Would patron have a large advantage if they were allowed to play only the dragon bonus wagers (player and/or banker) for up to two spots? Essentially, you can sneak by the maximum wager limit and get up to a 60 to 2 payout for 9 points. I have witness it happen and it was allowed.

    • stephenhow said, on November 6, 2012 at 1:25 pm

      I was doing that last weekend, seems to be the norm. (In fact, the house allowed all the free hands I wanted.)

      • Princess said, on November 7, 2012 at 6:30 am

        Usually the rules say you can’t place a dragon bonus wager without a traditional mini-bacc wager. I’ve seen a lot of players win big from just playing the bonuses. Free hands are allowed but I never noticed it on the bonuses until recently

  19. richard lofink said, on September 29, 2015 at 4:40 am

    I am just interested in a program that will simulate the dragon game as played in vegas I need to be able to edit it to do my own research not interested in what others have concluded. Do you have a program and how much?


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