by Dan Paymar
In this article we will look at how to use a video poker software training program to determine possible strategy changes when playing a game with a large progressive jackpot.
The most common type of video poker machine with a progressive jackpot will only offer a single meter on the royal flush and it is typically shared among a bank of machines with the same game. Here we will be discussing such a situation.
The two most important questions about video poker progressive jackpots are:
1. How high does the meter have to be to make it attractive to you?
2. What is the best strategy to use?
All of the mathematical calculations that follow were created using Optimum Video Poker (OpVP) software. This is a video poker training program that teaches you how to play your hands correctly for any video poker game. It also has many extra features such as printing out strategy charts, ability to analyze any hand to determine the best play, and when it comes to bankroll considerations a special feature it offers is to calculate the cost of a royal for progressive jackpot evaluations.
When using the software, the “Cost of a Royal” calculation in Optimum Video Poker assumes perfect play for the payoff schedule currently shown in the game window.
That is, if you play every hand for the highest possible Expected Value (EV), the Cost of a Royal (CoR) is the expected average loss per royal cycle. (Note: The term “cycle,” which is typically shown in a game analysis as “One in _ Hands,” is simply a statistician’s term for the reciprocal of the probability of a royal in any one play. A machine is never “due” to hit a royal no matter how many hands have been played. The probability of a royal on the next play is always as shown in the game analysis.)
The game most frequently played for a progressive royal flush is five-coin $1 8/5 Jacks or Better, so we’ll use that game as an example.
With only a $4,000 royal, the Cost of a Royal computes to $9,456, suggesting that we should not play the game until the royal meter exceeds that amount. That calculation, however, assumes that we are following the strategy for the current game; that is, with a $4,000 royal.
But wouldn’t it make sense to adjust our strategy for the higher royal? Of course it would, but if we enter $9,456 as the royal payoff and analyze the game, the Cost of a Royal then computes to $8,669 (rounding to the nearest dollar).
If you now change the royal payoff to $8,669, a game analysis shows 99.9996% expected return (ER). Repeat that one more time, and we find that a royal payoff of $8,670 yields an ER of 100.002%.
What I have just described is an iterative procedure to calculate something that can’t be calculated directly. In this case, it took only three iterations, but some situations require more. The important thing to remember is that the software performs these calculations for you!
We have now found the break-even point for this game, so we know how high the meter must be to make the game at least marginally attractive, but there is an even more important aspect to this.
It may seem unintuitive, but it turns out that a strategy developed for the break-even royal payoff will yield the lowest cost of a royal regardless of the actual royal payoff. A few serious players always play the break-even strategy no matter how high the meter eventually gets.
But do you want to just break even? Most of us want to play for a profit, so let’s see how we can calculate an optimum play number.
Suppose we decide we won’t play until the progressive meter rises enough to give us a two percent advantage.
To make this adjustment, all you have to do is select the basic 8/5 Jacks or Better game, then select “Progressive Royal” from the Analysis menu, and click the Start button. If the game has already been analyzed for break-even, the meter breaks will be shown immediately; otherwise, it will go through the iterative procedure described above. In this example it will show a royal payoff of $11,905 for 102.01429% payback.
Now all that is needed is an accurate strategy for this game with a royal meter at that payoff, and of course Optimum Video Poker will do that, too.
Select “Strategy” in the Special menu, click the “Generate Strategy” button, and in less than one minute it will generate a basic (no penalties) strategy chart.
Evaluating that chart shows that it is within about 0.04% of the Expected Return for perfect play. Select “Improve Basic Strategy”, and the chart is improved to 0.01758% off of perfect. At 800 hands per hour that’s a deficiency of only 70 cents on $4,000 in action.
If that is not good enough for you, you can click “Penalty Consideration” and select which penalties you wish to consider, but even applying all five possible penalties improves this by only 0.00026%.
Most players will be giving a higher advantage to the casinos through reduced speed and occasional playing errors by using these additional penalty considerations, which is why I rarely bother with them.
Dan Paymar was a video poker expert with a background in computer programming who passed away on July 17, 2020. He had written several books on video poker, including Video Poker – Optimum Play. For 14 years he edited and published his own newsletter, the Video Poker Times. Dan was also the developer of “Optimum Video Poker”, an analysis and training program for Macintosh and Windows computers.
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