How Do You Figure?

A reader posed the following question, which I lightly edited: I came across a quarter pay table I have a question about. It’s a three-coin game, with progressives on the royal flush, straight flush, and four aces. It’s 9/6 Double Bonus, and the royal is currently at $1,122. I think it’s probably pretty positive, but how do I figure that out for sure?

I’ve never seen a three-coin quarter game, but I have played three-coin games for higher denominations. I invite my readers to try to figure it out before I explain how I would do this.

Before any of us get started, there are a couple of things to specify. Saying the game is 9/6 Double Bonus doesn’t tell us how much you get for the straight. One can find both 9/6/5 games (where the straight returns five-for-one) as well as 9/6/4 games (where the straight returns four-for-one). I’ll figure it out for both pay tables.

Second, the question said there were three progressives, but only provided the level for one of them. Presumably, this means that ethe other two progressives were currently close to their reset values, but surely that won’t always be the case. While the latter two progressives aren’t part of today’s problem set, I’ll outline at the end how you can include them in your calculations.

Once you have figured this out for both the 9/6/5 and the 9/6/4 games, then you can read the rest of this blog. As I frequently say when I ask you to figure something out yourself before reading on: Take as long as you like. I don’t mind waiting for you.

Here’s how I would attack this problem.

Video poker software is generally set up for five-coin games. The adjustment for three coins isn’t very difficult, but it’s not obvious to all players. Once you figure out, or are told, what the “trick” is, it’s pretty simple.

A three-coin quarter game costs 75¢ to play per hand. This makes it equivalent to a 15¢ game, played five coins at a time, which comes out to the same 75¢. While there are no actual 15¢ coins in the real-world United States, we can imagine such coins if that’s what it takes to figure this out. To calculate out how many of these 15¢ “coins” would be necessary to total the royal flush amount of $1,122, we simply divide $1,122 by $0.15. When we do this, we get that the royal flush is equivalent to 7,480 coins. This is almost a “double royal,” as royals typically return 4,000 coins.

So now we plug this into any video poker software. Doing so, I get 99.78% for the 9/6/5 pay table and 98.38% for the 9/6/4 pay table. Reset on the straight flush (250 x 15¢) is $37.50 and reset for four aces (800 x 15¢) is $120. If the existing progressive numbers are higher than these, simply divide the numbers by 15¢ and plug those values into the same computer software.

I suspect the game is more likely to be 9/6/4 than 9/6/5. Four-for-one is far more common for straights, and the original poster possibly would have noticed the “unusual” five-for-one had it been there. This leaves the game with a 98.38% return, which is nowhere near “pretty positive,” although in many casinos this would be the loosest game available for quarters or less.

So, those of you who were able to figure this out before I gave you my answer, congratulations!