Figuring the Return for 8/5 Bonus Poker with Four Progressives

Note to reader: The original version of this contained an arithmetic mistake. It was pointed out to me by a man who posts under the name “New2vp”. The error, which affected one of the tables in the chart, are in the section relating to quad 5s-Ks. The corrected version follows. Thank you New2vp.

I received an email:  Sam’s Town in Las Vegas has three different banks of 8/5 Bonus. Two of those banks have progressives on the royal flush only. The third has that progressive, plus three additional ones for the quads: aces, 2s-4s, and 5s-Ks. Since the game starts out at 99.17%, sometimes these games must be pretty good. How do I figure out how to calculate the return of these games quickly if I don’t bring computer software into the casino?

I’ve received similar emails about Double Double Bonus Poker. Eventually I’ll have strategy cards published so that you can just look up these things, but today I want to describe the process of “How do you figure it out?” using Bonus Poker.

To do this you need access to computer software. I’m using WinPoker today.

The base game with a 4,000-coin royal flush returns 99.1660%. I now set the royal flush to 8,000 coins and discover the game returns 101.4376%. Subtracting the first from the second, I get 101.4376% – 99.1660% = 2.2716%.

From here I make the assumption that the change in return happens evenly. That is, for each 100 coins of progressive, the royal changes 2.2716% / 40 = 0.05544%, which I’ll round to 0.055%.

That is, at 4,100 coins, the game is worth 99.166% plus 0.055% = 99.221%. It doesn’t take much effort to create the following chart:

The value of the royal progressive is seldom exactly at one of these numbers, but you can extrapolate. That is, a royal amount of 4,234 coins is worth 99.276% + 0.34 * 0.055% = 99.294%. 

Next we look at four aces. As the progressive of four aces rises, the change in value for that progressive is largely independent of the value of the royal. So, we can just add these increments together.

With the royal at 4,000 coins and four aces at 400 coins, the game returns the same 99.166% we used before. We’ll now set the value of four aces to 500 coins and we get 99.558%. So for the 100-coin increment of aces, we get 99.558% – 99.166% = 0.392%. This means for every 10 coins of increment, the progressive rises by 0.039%. For practical purposes, I use 0.04%. It’s close enough and is much easier to work with. But using the correct amount, we get:

Obviously if there is only a progressive on the royal, we don’t make any adjustment for the aces. 

For four 2s-4s, the process is similar. The return on the game with the royal and aces at reset, but four 2s-4s at 300 (instead of 200) is 100.2205%. So for every 10-coin increment of the value of these quads we get 0.10 * (100.2205% – 99.1660%) = 0.1055%. Creating a similar chart as before we get:

Finally, for the value of four 5s-Ks, we start at 125 coins and now check 225 coins, where the return is 102.4459%. Because this progressive hits so frequently, I’m going to display the chart in increments of five coins rather than 10. That is, for every five coins in increment we add (102.446% – 99.166%) / 20 = 0.164%. Creating the same sort of chart as before, we get:

When you come across the progressives, you simply add up the value of each of the progressives. I would also add in the amount of the slot club, which is normally 0.05%, unless you’re playing on a “Young at Heart” day (for seniors at least 50 who are Sapphire level or higher) the return is 0.5%.

It’s conceivable that there is a game somewhere where there is also a progressive on the straight flush. You figure it out the same way as described above.

I do not carry around the above charts with me. I do have a note on my iPhone that says for Bonus Poker, add 0.055% for 100 coins of royal, 0.04% for 10 coins of aces, 0.10% for every 10 coins of 2s-4s, and 0.16% for every five coins of 5s-Ks. When I come across such a game, I figure it out at the time.

I have similar notes for several other games. They are not difficult to create once you know how. Knowing the return on the game doesn’t tell me when to make adjustments. That is, from Q♠ J♥ T♥ 5♣ 2♦, how high does the royal have to be to change the correct play from QJ to JT? That is an extremely important question, but one we’re going to have to leave for another day.