Further Look at Changing Strategy

A few weeks ago, I discussed a long-gone game where getting all 13 quads yielded a 500-coin bonus. In the article, a lady, “Joyce,” asked me about a situation where you just needed four kings to complete the cycle and you were dealt KK443 in 9/6 Bonus Poker Deluxe.

I said you should hold two pair — and Joyce said that whatever I said she was just going to hold the kings because it made more sense to her.

One of my readers, John, wanted a better clarification because holding the kings made sense to him as well.

Another reader, Mike, suggested he read the Wizard of Odds discussion of Power Quads — which describes a very similar situation. In that discussion, Michael Shackleford analyzed the game under a “use a constant strategy for the entire cycle” strategy — but suggested at the end that the return might be higher with strategy deviations — but the reader would have to figure out those adjustments for himself. If you’re going to be making adjustments, presumably, at the minimum, you’d hold the kings from KK443 if kings were the last quad you needed to get your bonus.

With a great deal of nervousness, I suggest Shackleford is wrong! I believe a constant strategy is best. 

By the time you see this, you can be sure that Shackleford has been forwarded the original article and my statement that I think his line in the Power Quads article is incorrect — and if he chooses to respond, I will publish here what he says. 

Shackleford is an extremely proficient mathematician, specializing in analyzing games, and my skills in this area pale in comparison. Comparatively speaking, I might be a smart high school student and he would be an award-winning college professor. Not in the same league at all!

I did reach out to Shackleford. He said he stands by what he wrote in his original article, and from the hand in question, he would just hold the kings. He went over the math of the value of holding the kings — for this one hand only — and the value of holding two pair — and holding the kings was clearly superior.

I’m not disputing that. But I’m looking at maximizing the value of getting all 13 quads, again and again, not getting kings once. I didn’t continue the discussion with Shackleford. He’s largely retired now from analyzing games and living in the state of Washington.

There was another promotion years ago that leads me to my belief that a single strategy might be best.

Perhaps 25-30 years ago, the Orleans casino in Las Vegas had a promotion where connecting on two royal flushes in the same denomination within a certain time period (perhaps it was one week — perhaps it was one month — I don’t remember) would lead to the second royal being paid double.

They had a dozen or so dollar Triple Play machines with a number of games on them including both 9/6 Jacks or Better (99.54% — royal cycle 40,391) and 10/7 Double Bonus Poker (100.17% — royal cycle 48,048). (Those were the days!)

At the time, Triple Play was relatively new and they didn’t have any version with more lines than three. Still, if you’re playing a promotion where you get paid double on the second royal within a given time period, playing the same pay schedule on Triple Play rather than single line is a no-brainer you had sufficient bankroll. Royals come about much more frequently on Triple Play than they do on single line games. I think I decided to play JoB because the royal cycle was shorter.

The question then became: What strategy should I use? Although there are many possible strategies, I decided to look at two.

1. For the first royal, use regular 4,000-coin royal strategy. After I got that one, if I still had time to play, use an 8,000-coin royal strategy until I hit the second one.

2. Use a 6,000-coin royal strategy and keep going until I hit two royals. 

I’m not going to reproduce my analysis here, but I remember it came out using the single 6,000-coin strategy until I hit two royals was more profitable than using the 4,000-coin strategy until I hit the first one and then use the 8,000-coin strategy. 

The differences between the two promotions are numerous. Still, I’m guessing (hoping, really) that the one strategy rule applies in both cases.

I still believe that the one strategy approach is better — even though Shackleford seems to believe otherwise. I have a ton of respect for him. But this time I think my approach is better.