The Dragon Bonus (DB) baccarat side bet is by far the most popular baccarat side bet in the domestic market. Internationally, I have not seen it that much in my travels, but maybe I just haven't been to the right places. I considered card counting DB in this post, where I concluded that counting was useless. Recently a reader posted a comment asking about the edge he could get against DB if he knew one of the cards in the Player hand before deciding whether to make the DB wager. "Phil" wrote:
I understand that counting the dragon bonus is useless and I completely agree, however, what if I have the knowledge of a hole-card for Player or Banker, will it give me an advantage worth exploiting?
This question reminded me of a conversation I had with an AP in about 2003 regarding the Lucky Ladies (LL) blackjack side bet. LL pays whenever the first two cards dealt to the player total 20. While this wager has a huge house edge (nearly 25%), it is easily countable (see this post). However, the conversation was not about counting. The AP dismissed counting LL as mostly worthless. Our conversation was about the edge that could be gained against LL with additional information, for example knowing in advance that a ten-valued card would be dealt to you in the next round.
At the time, I did not fully appreciate the power of what the AP was suggesting. I thought he was referencing shuffle tracking. Now I know that the AP was talking about the situation when he was either first-carding, card steering, edge sorting or using some other method that gave him sufficient information to determine he would get a ten-valued card.
In Exhibit CAA, James Grosjean devoted nine pages to an analysis of Lucky Ladies. In the subsection titled "The Bet Card," Grosjean stated:
Counting performs fairly well, but the edges would be even higher with stronger information. If you happen to know your first card, the "bet card," prior to placing the Lucky Ladies bet, then ...
Grosjean went on to state that in a two-deck game, knowing that you will get a ten-valued card gives you a 94.17% edge, and knowing that you will get the Queen of Hearts gives you a 236.67% edge.
The question addressed in this post is to determine the edge possible against DB if the player knows the first card the Player hand will be dealt.
As a reminder, here are the rules for DB. To play DB, a wager is made on the side bet on either the Player or Banker side, or both. The DB wager wins if the side wagered on wins by a natural, or else wins by 4 or more points. The most commonly used pay table is the following:
- Natural win (two card 8 or 9) pays 1-to-1.
- Natural tie (two card 8/8 or 9/9) is a push.
- Win by 9 pays 30-to-1.
- Win by 8 pays 10-to-1.
- Win by 7 pays 6-to-1.
- Win by 6 pays 4-to-1.
- Win by 5 pays 2-to-1.
- Win by 4 pays 1-to-1.
- All other results lose.
The combinatorial analysis for DB is given in this post. In particular note that the house edge for the Player side of the DB wager is 2.652%, but the house edge for the Banker side of the DB wager is a much larger 9.373%.
The following table gives the edge on the Player DB wager and the Banker DB wager if the AP knows the first card to be dealt in advance of making a wager:
Notice that if the first card is a 7, 8 or 9 then the AP will get an edge by making a Player DB wager. If the first card is 0-valued (T, J, Q, K), then the AP will get an edge by making a Banker DB wager. In all other cases, the AP cannot get an edge over the casino.
The following table summarizes the profitable situations and computes the overall advantage the AP can gain:
We see that if the AP knows in advance that the first card to be dealt (which goes to the Player hand) is 7, 8, 9, T, J, Q or K, then his average edge over the casino is 9.8534%. Since the AP can get an edge on 7 out of the 13 possible first-cards, he gets an edge over the casino 7/13 = 53.846% of the time.
The following table summarizes these statistics:
One way to gain first card knowledge in baccarat is by edge sorting. For example, if the cards are edge sorted into the groups,
- Low = {0, 1, 2, 3, 4, 5, 6} and
- High = {7, 8, 9},
then the AP can use ordinary edge sorting to play against baccarat. For the main game, the AP makes a Banker wager whenever a low card will be dealt, and a Player wager whenever a high card will be dealt. Using this sort, the AP gets a 6.4782% edge. (Note, this is not the optimal sort, which gives an edge of 6.765%. See this post).
Although the sort above is not quite optimal for ordinary baccarat, it does give perfect information for making Player DB wagers. Whenever a high card is due to be dealt as the first card, the AP makes a Player DB wager. Otherwise he makes no DB wager. As the following table shows, the AP has an average edge over the house of 13.8610% on his Player DB wagers using this strategy:
The player gets an average edge of 13.861% on 23.077% of the hands, for a win rate of 3.1987 units per 100 hands.
First carding baccarat is one of the most sought after opportunities in high-level baccarat advantage play. It turns out that this knowledge can also help the AP crush DB as well. Card counting is not the only advantage play method to worry about with your side bets.
