Frequencies of video poker winning hands can vary
November 01, 2011 3:00 AM
by Elliot Frome
A couple of weeks ago, I described in detail the math behind progressives. I mentioned how video poker progressives works just a little different.
There are still two paybacks to be concerned with – the long term theoretical that the casino is concerned with and the specific payback at any point in time that should be the attention of the player.
The majority of the calculation is still the same in that we multiply the payout by the frequency of the winning hands and sum up these values. What is different about video poker is that the frequencies of the winning hands can vary as the amount on the meter changes.
To video poker players, this should be no surprise. For years, I’ve been saying that a single unit change in the payout of a hand not only changes the payback but can alter the strategy. Each time the strategy differs you potentially increase the frequency of some hands at the expense of others.
As a very simple example of this, imagine how the strategy changes as we go from a standard full-pay Jacks or Better machine to a Double Double Bonus machine. Because the payout for four aces is so high, we actually find that the player should discard two pair in favor of a single pair of aces.
This will obviously reduce greatly the frequency of two pairs and full houses and increase the frequency for three and four of a kind hands.
So, it should be no surprise that as the jackpot for a royal flush increases above 800 that the strategy will begin to shift. Hands with the potential to be a royal will have their expected values increase.
This will lead to more straights, flushes and of course royals and the expense of pairs, trips and quads. Of course, we will also throw away a variety of partial straights or flushes to go for the royal, so this will work against the straights and flushes and might increase the number of high pairs.
Pinpointing the exact frequencies can be a bit tricky. Fortunately, the far easier of the paybacks to determine is the one at any point in time. This is because at any point in time, we can know the exact amount of the Progressive jackpot and use this number to determine the exact strategy and in turn the exact frequency of each hand.
The most common video poker progressive is an 8-5 machine, meaning it pays about 97.3% when the jackpot is reset to 800 (per unit wagered). At this level, the frequency of the royal is about 1 in 40,200 hands. If the jackpot were to climb to 1,600 (per unit wagered) then the payback of the game will go up to about 99.5% and the frequency of the royal rises to 1 in 32,700 hands.
Of course it is rather unlikely that you’re going to see a progressive for a royal get this high. With only 1% of the amount wagered (at most) going to the meter, the average total that will be added to the progressive jackpot is somewhere between $327 and $402 (1% of the previously mentioned frequencies).
Of course, something that can occur 1 in 40,000 hands can easily occur every 10,000 or 80,000. So, it is not impossible to see the progressive meter go to 1,600. It would have to reach about 1,800 for the game to become positive (payback over 100%). This is not impossible, but not very likely.
As the payback goes up, the strategy changes and the frequency of the royal increases, making it increasingly harder for the jackpot to keep rising as the likelihood that it gets hit goes up. Because of this, it is a bit harder to calculate easily the long term theoretical payback.
It is reasonable, however, to approximate it using the same process used for regular progressives. In this case, I would take the frequency of each hand using the reset value of the jackpot and multiply each by the payout of the hand and sum these up.
Lastly we would add the percent of each wager going to the jackpot. This means that the long term theoretical payback of a royal paying 8-5 with an 800 unit reset amount is about 98.3%.
I have to admit, if I were designing a pay table for a video poker progressive, I would probably make the likelihood of the game going over 100% a bit more common. I think it would be a lot of fun to the frenzy that would/should occur each time the payback at any point in time goes over 100%.