Last week I discussed the importance of playing max-coin in order to maximize the payback of video poker. I mentioned the Royal Flush pays 250 for 1 instead of 800 for 1 when you play less than max-coin. Further, the Royal Flush accounts for 2% of the payback when using the 800 for 1 figure.
The calculation is really not a complex one. We take the probability of each hand and multiply it by the payout of that hand to get the contribution rate of that hand. A Royal Flush occurs roughly 1 in 40,000 (or 0.025%) hands. We multiply that by 800 to get 2.0%.
If we use a payout of only 250, we get 0.625%. Thus, we see the payback of the game is almost 1.4% less with less than max-coin. This same calculation comes into play to help us figure out the payback of almost any paytable. Of course, you need to know the probability of each hand in order to calculate this.
The good news is the three most common hands that have their payouts changed have very easy to remember frequencies – 1%. This is only an approximation, but good enough for getting an idea of the payback of the machine you are thinking about playing.
It might sound strange, but Full Houses, Flushes and Straights all occur at about that same frequency. So, a one unit reduction in payout means a 1% reduction in payback. When you play an 8-5 machine as opposed to a 9-6 machine, you are reducing your payback by a total of 2%, one percentage each for the Full House and Flush.
You think playing a 6-5 game isn’t so bad? Well that will take about 4% off the payback, reducing it all the way down to a 95.5% game!
As I said earlier, this is just an estimate of the impact to use as a guide. Once you choose to play a game, the actual payback is far less important than playing the proper strategy for that paytable. Also, as the paytable changes, the strategy can change a bit, which in turn changes the frequency of the hands, which in turn changes the contribution of that hand and thus the impact. So, knowing the exact payback of the game to the nearest 0.1% is far less important than knowing how to play each hand.
The other hand that has its payback change most often is the Four of a Kind. Four of a Kinds, while paying 25 contribute about 6% to our payback. So, a payout of 20 will reduce the payback by about 1.2%. Adding to the complexity here is that many games nowadays pay different amounts for different Quads; and adding more complexity yet, pay even higher if those Quads have certain kickers. These probabilities are all known, but a bit harder to remember and/or calculate on the fly.
But, I’ll try to give you a few guides for the more common games. Quads occur about once in 423 hands. Each Quad occurs with similar frequency. So, any particular Quad occurs about 1 in 5,500. This is just under 0.02%.
So for each 25 unit bump up PER rank, the payback goes up almost 0.5%. So, when 2’s to 4’s pay 40, this is a roughly 0.75% bump up in the payback. Pay 80 for Aces and this adds about a full 1%. These are the payouts for Bonus Poker. So, the added payouts for Quads adds about 1.75% to the payback compared to full-pay jacks or better.
Bonus Poker reduces the Full House and Flush to 8 and 5, respectively, reducing the payback by 2%. So, the net should be a 0.25% reduction compared to jacks or better. Lo and behold, we find the payback of Bonus Poker is 99.2% or about 1.3% below jacks or better. This 0.05% is attributed to the fact these are all rough estimates and the payout changes cause strategy changes that can increase the payback just a smidge.
The most important part here is to know Bonus Poker pays 99.2% (or 99.25% based on our rough estimate) and full-pay jacks or better pays 99.5%. So, if you have a choice of which one to play, you know which one you should be playing based on payback. Using what you have learned today, you should be able to approximate the paybacks of most games you’ll see on the floor. This should help you immensely with the first leg of Expert Strategy – know which games to play.