Royal Match Analysis

I'm new here but I've been playing blackjack for a number of years now. I just wanted to drop by and let those who are interested know about a quick analysis I did on the Royal Match side bet a few days ago. They have RM out at the casinos I used to frequent so I wrote a quick program to find the EV at different points in the deck. I may add some more to this in the future, such as integrating a counting strategy. I put the code in the article in case anyone is interested. Any feedback is welcome, I hope this helpful for some folks here. Check it out at:

(Dead link: http://www.l1ghtm4n.com/?q=node/8) _Royal Match: Probabilities and Payouts_

So the red-black count will produce PosiEV for RM in 20%+ of hands dealt when dealt to 50% level? zg

No, the red/black count was some experimental code that I didn't use as generation of the graph data. The graph should be read "at 50% penetration, 20% of all decks have a positive EV for RM bet". That is just raw statistics with perfect knowledge of cards dealt. A count is used to recognize when these decks appear, which of course won't be perfect, so you can only expect a betting opportunity <20% of the time at 50% deck penetration. Hope that's clear. The numbers are a little easier for side bet's than the normal bet since there's no strategy involved, just a bet/no bet choice.

The Soaring Eagle Casino only pays 2 to 1 for a match, but 50 to 1 for a Royal Match. I assume this works more to the house advantage, yet betting small amounts such as $1-$2.50 seems to work well sometimes (not much risk w/ potentially bigger rewards). The matches seem to be quite streaky too. I'll usually try to guess when a matched suit is coming and play it until I lose a hand, as 3 matches in a row is not at all uncommon. If I'm doing well and seem to have a good spot I may bet more on the sidebet and keep betting it every hand until it starts to turn sour, but I wouldn't recommend playing it every hand all the time. Any thoughts on this?

What basis do you use for your guess? Not seeing a given denomination for a long period?

I don't know why the RM would be streaky. If it truly is then a positive progression would work well IF you had some way of determining when the streakiness is going to be in your favor. I'm guessing if the wins of the RM bet are streaky, then the disappearence of the match is going to be streaky also. Assuming that what you mean by streaky is long stretches of no matches followed by 3 or more matches in a row or 3 or more matches in several hands?

What kind of shuffle is used at the places where you play this? Perhaps the shuffle could explain the streakiness.

Jimbob: "If [RM] truly is [streaky] then a positive progression would work well IF you had some way of determining when the streakiness is going to be in your favor."

I'm not sure what you mean by "streakiness is going to be in your favor." Even though I'm not a statistician by trade, I'd like an explanation in more precise (perhaps mathematical) terms. For instance, perhaps you mean to say that we need to determine when a hand(s) has positive expectation. If so, then a positive progression would indeed work, but guess what would work even better ...

You want a hint? OK, your hint is ... flatbet.

You got it--the answer is to flatbet the max on the RM on any positive-expectation hand. Despite the "streakiness"--which might be a layman's term meaning, "You can lose lots of hands in a row and get crushed"--are we really worried, when the table max on RM is usually a paltry $25 (and never more than $100)?

jimbob: "What kind of shuffle is used at the places where you play this? Perhaps the shuffle could explain the streakiness."

Scapegoating the shuffle is second only to scapegoating the RNG as an explanation (always a bad one) for any and all phenomena that are not understood by the baffled rookies (who are usually losing). The shuffle has nothing to do with this. Do you know the probability of winning a Royal Match bet? Whenever the win probability of an event is low, it feels "streaky" to the layman. That is, they lose LOTS of hands in a row. Then "suddenly" they hit two or three winners. Wow, it's "streaky"! Indeed.

I strongly advise anyone who has the capability of doing Royal Match analysis to not waste their time. The Royal Match bet has no practical value, and there are other side bets out there that are worth much more, and easier to count. Arnold Snyder has already done an analysis of Royal Match in his "The Big Book of Blackjack."