Discount Gambling

Player Dragon Bonus Tracking Sheet

Posted in +EV, baccarat, dragon-bonus by stephenhow on October 5, 2011

I worked out a baccarat tracking sheet for counting the player dragon bonus available at my local Barona Casino. The tracking sheet simulates at +0.112 EV/shoe, gained from an average 3.9 bets/shoe. That means the count gets good enough to bet the player dragon about 3.9 times per shoe (4.8% of the time), and you’ll profit a total of 11.2% of a fixed bet, per shoe. So, if you’re betting the max $300 per dragon, you’ll make about $33.60/shoe, on average.

That’s not bad, since you’re allowed (encouraged, actually) to use tracking sheets while sitting at the Rapid Baccarat terminals. The player dragon has payouts ranging from 30-to-1 down to 1-to-1 and pushes, so you’ll win something about 30% of the time. This is much better than waiting for a 40-to-1 payout on an infrequent $100 dragon-7 bet.

The tracking sheet below helps you maintain the running count (RC) for each hand of the shoe, and lists the required minimum RC for betting the player dragon on any given hand:

You’ll see the minimum betting RCs decrease as more hands are played. Typically, you’ll probably only be able to bet the dragon for the last 8 hands of the shoe, if at all. Welcome to the world of baccarat.


Use the following count values for each card:

Player Dragon Count Values
Card Count Value
Ace 1
Deuce 2
Trey 2
Four 1
Five 1
Six 0 (ignore)
Seven -1
Eight -1
Nine -1
Face/Ten -1

The dealer pulls the first card out of the shoe, and turns it face up. Start the running count with the count value of the card. The following unseen burn cards do not affect the RC or the bet thresholds.

Make sure you only use this sheet for betting the player dragon bet (1-1 for natural player win, push for natural player tie, else 30-1 for player win by 9 points, 10-1 for win by 8 points, 6-1 for win by 7 points, 4-1 for win by 6 points, 2-1 for win by 5 points, 1-1 for win by 4 points, lose all others).

For each hand dealt, add up the count values of each card to get the count for the hand. Notice that 2’s and 3’s are +2, then “high cards” (7,8,9,10) are -1, and “low cards” (1,4,5) are +1. Write down the count for the hand in the sub-box, and add it to the running count (RC). Write the new RC value in the box.

If the new RC is greater or equal to the number printed in the next hand’s box, then bet the dragon. That’s it.


You’re at the start of the shoe. The dealer pulls out a 7, and burns seven cards. Start the running count at -1.

The first hand dealt is player (10,9) and banker (4,5). There are no 2’s or 3’s in the hand. The two high cards cancel out the two low cards, so the count for the hand is 0. The running count remains at -1, and write it in the box.

The next hand dealt is player (1,2) and banker (8,10). The count value of the hand is 1+2-1-1 = +1. Write the new RC of 0 into the box. The RC is less than 56, so don’t bet the player dragon the next hand.

The next hand dealt is player (3,1,5) and banker (4,10,5). The count value of the hand is 2+1+1+1-1+1 = +5. Update the running count by +5, and write the new RC of 5 in the box. The RC is less than 55, so don’t bet the player dragon the next hand.

+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.