# Discount Gambling

## Counting The Royal Match Sidebet @ Barona Casino

Posted in +EV, blackjack sidebets by stephenhow on December 20, 2011

My local Barona Casino offers the Royal Match blackjack side bet which pays 75-to-1 when you’re dealt a suited K-Q on your first two cards, and 2-1 for any other suited hand. Normally, the house edge is 4.06% for this side bet, but as readers of this blog know by now, sucker bets are often countable. Using a simple true K-Q count, the bet yields an average 5.4% player edge.

I always play this bet for \$1, and get really excited when I hit it for \$75. The last time I hit it, I decided to analyze it’s countability.

I first looked at the bet’s distributions of EVs at the last hand of the shoe. This would show me if there was any potential for a counting scheme. I’d see how often and how strongly the bet went +EV. Here’s what it looks like with one deck remaining:

I could tell from the graph that the bet was exploitable. So I calculated the average profit per shoe, assuming heads-up play with the dealer. This theoretical limit comes out to a profit of +0.504 bets/shoe. That’s a really good profit rate (compare to the Dragon-7 profit rate of 0.54 bets/shoe). That means a player betting a fixed amount on the Royal Match will net an average profit equal to half his bet per shoe, when heads up with the dealer. On a per bet basis, the average Royal Match bet EV is +5.9%, assuming perfect knowledge of the dealt cards.

I then looked for a simple (practical) counting scheme that would capture most of the theoretical edge. As it worked out, the second idea that came to mind happened to be very effective. A simple true count of excess Kings and Queens yields about +0.43/shoe (85% of the theoretical edge):

```trueCount = (8*decksDealt - countedKingsAndQueens)/decksRemaining
```

where decksDealt and decksRemaining are floating-point numbers.

The relationship between the true KQ-count and the Royal Match side bet EV is shown in the following graph:

Note that you should bet the Royal Match when the true count is >= 0.8.

In heads-up play, you’ll get an average of 8.0 bets/shoe, with an average bet EV of +5.4%. The scheme is very comparable with the highly profitable Dragon-7 counting scheme (EV +0.54/shoe), but it’s much faster, and has much lower variance.

So if you don’t find me at the full-exposure Mississippi Stud game, look for me in the i-Table pit counting the Royal Match.

### 7 Responses

1. interestingstuff said, on January 2, 2012 at 4:26 am

Do you have to be heads up with the dealer in order for the count to work or can there be other players and if there can be, which base do you take for optimal results?

• stephenhow said, on January 2, 2012 at 12:13 pm

The count is independent of the number of players at the table. The statistics like bets per shoe, profit per shoe will vary with the number of players, but it’s not important. The percentage of hands the Royal Match is +EV is probably the same, regardless of players. Personally, I prefer a full table, because you get through the shoe faster, and the best opportunities come at the end of the shoe. It all evens itself out (faster shoe, but less opportunities, etc.), so it’s probably just a matter of taste. But the per hand numbers are all the same, regardless of players.

2. Steve Edwin said, on January 4, 2012 at 8:21 pm

Sorry but you don’t credible data here to prove this is worthwhile. I’ve done my own analysis and yes I agree that favorable situations arise. However, they don’t occur often enough and the player edge does not become significant enough to make it worth the effort to do this. You need to provide more data because what you have posted so far is not convincing at all. I am open if you have more, otherwise this is just hollow words. Sorry.

• stephenhow said, on January 5, 2012 at 3:33 am

I’ll present simulation results in a follow-up post.

3. John D. said, on January 13, 2012 at 12:00 pm

Nice work! I get very similar results, the difference probably due to using a different penetration level. Do you know what the max bet for the side bet is? And does it have to be <= your main bet?

• stephenhow said, on January 13, 2012 at 3:42 pm

At Barona, the max bet is \$15, because they don’t want to pay off much more than \$1000 on any bet. Thanks for the corroboration of my numbers. My simulations use a 6-deck shoe, with one shoe placed behind the cut card. I think Barona allows a Royal Match bet of \$15, even for a \$5 main blackjack bet.

4. JC said, on November 3, 2012 at 2:25 pm

This is interesting data. A casino near me offers royal match but the suited king and queen only pays 25 to 1 instead of 75 to 1. The other payouts are 5 to 1 and 2.5 to 1. What would the player edge be in that case? Does that make the game unbeatable? How effective would hi-lo be at counting this side bet?