Math geeks and advantage players: They seem to go hand in hand.
But unlike love and marriage, theirs is a match made in gambler’s ruin heaven.
One of the most common mistakes made by gambling analysts is that they apply principles of higher mathematics — probability theory, differential equations, laws of permutations and other heady stuff — to games of chance, notably slot and video poker machines.
The notion of a poker machine paying over 100% to the player is an attractive concept, but it must be viewed through jaundiced eyes. Unlike slot machine "par values," which are conditions built into the computer program that determine the amount of money the machine will spit back, video poker payback percentages are based on the games’ pay tables.
Let’s state that again so everyone understands: the game’s payback percentage is based solely on the paytable. Thus, if you adjust the paytable, you adjust the payback percentage.
Assuming the poker game is dealt from a 52-card deck (53 cards in joker poker), the laws of chance will determine the frequency of the various hands, but the paytable will determine the payback.
Also keep in mind that the poker game’s return is based on the life of the machine and quite possibly millions and millions of poker hands.
Thus, any gaming machine manufacturer will tell you that the results a player can expect in the short term can and will vary significantly from the long-term payback percentage.
Once you understand this concept then it becomes easier to see that trying to apply an hourly win rate to playing a video poker machine is, quite frankly, ludicrous.
To recommend planting oneself in front of a machine and fire off Benjie after Benjie in hopes of raking in a few Georges is patently absurd. And anyone who further suggests that payback percentage can be translated into an hourly win or loss rate has never played video poker.
It’s more likely that a video poker player will insert a fixed amount of money and lose it over a specified period of time — even if the game is on a 100% or higher machine.
During the course of that period of time, it’s also likely that there will be swings in which the player will experience a short-term profit then subsequent losses or vice versa.
Another significant concept that the probability experts fail to understand is that in order to get the full payback percentage — 100.76% in the case of full-pay deuces wild — the player has to hit every jackpot, including the natural royal flush!
This will be easier to understand if you examine the payback table of FPDW, which is reproduced on this page.
Note that the "probability" of a hand is expressed as a decimal rather than the more familiar odds. So a royal flush has a probability of .000022, which is equivalent to odds of about 44,000-to-1 (one divided by .000022).
In addition, the "return" gives the amount that that hand contributes to the overall payback percentage. In the case of the royal flush, it contributes 1.76% to the payback percentage.
In other words, you have to hit the royal to get the 100.76% If you don’t hit the royal, you only get 99%, assuming you hit everything else — the four deuces, 5-of-a-kind, etc.
Now, according to the mathematician’s argument, a drop from 100.76% to 99% is like the death penalty for the player. How can you win with a negative expectation?
Of course, the real world of video poker play — that is, the definite time in which a player will actually play — won’t exactly mirror the paytables.
In the real world, the player most likely won’t hit one royal flush for every 44,000 hands, just like he likely won’t hit the four deuces for every 4,900 hands, a "dirty royal" for every 556 hands, a straight flush for every 242 hands or a 4-of-a-kind for every 15 hands ”¦ well, you get the picture.
It’s possible to hit several royals over the course of a session, like it’s possible to never hit a single dirty royal after thousands of hands.
That’s the nature of "chance," and those who try to apply a long-term percentage return — such as the amount earned from a mutual fund — are asking for trouble. At best they’ll be disappointed in the outcome; at worst they’ll go broke.