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Hot and Cold Machines
Video Poker for Fun and Profit
by Dan Paymar

A reader writes, “I am struggling with the statement that a video poker machine does not have a memory; i.e., that each spin is an independent, random event, unaffected by the results of any previous plays. You say that full pay Deuces Wild has a payoff of 100.75% of what is bet. If such a machine has not paid off for a long period of time then the law of averages would have to kick in, and it would start paying more. But how can one determine when that will happen? Is it one royal cycle (40,000 plays) without hitting a royal? Is it related to how much it is behind the 100.75%?”

Sorry, but that rated payback, (not payoff which is a single event), is only a statistical projection derived from the game’s payoff table and your playing strategy. The machine doesn’t know that it’s supposed to pay back 100.75%. The law of averages is the most misunderstood concept in gambling. There is no such law! This fallacy comes from misunderstanding the statisticians prediction that, the more you play, the closer your results can be expected to approach the game’s projected payback, but that is on a relative basis only.

Depending upon your criteria (i.e., what probability of being within what percent of expected payback do you want?), the long run could be months, years, or many lifetimes of full time play. Also, the term royal cycle is only the statistician’s way of stating the expected average number of plays per royal flush. In other words, it is simply the reciprocal of the probability of hitting a royal on any one play.

Let’s look at a much simpler situation. Take a pair of casino dice, or better yet just one die. The die is thrown against the knobby end of the table, so the result is random, with each side having one chance in six of coming up. Suppose you roll the die five times, and the numbers 1 through 5 each occur exactly once. Would the law of averages compel the next roll to be a 6? Of course not! The probability of any specific number on the next roll is still one in six.

Similarly, each play on a video poker machine is an independent event.

The virtual deck of cards is shuffled randomly, and the top cards off the deck are dealt. The machine doesn’t even look at the cards or check to see if you have a payoff until after the deal. It doesn’t matter whether you just hit a royal or it’s been a million plays since it hit one; you have the same approximately 1 in 40,000 chance of a royal on the next play regardless of what has happened before.

The reader also asked if it made sense to play only one coin for a while after any big payoff. Again, he’s assuming that the law of averages will result in fewer payoffs for a while, but the only effect of playing fewer than five coins is a 1.5% reduction in expected payback because you don’t qualify for full payoff on a royal flush. You’re making a smaller bet, which will make your bankroll last longer, but playing at less than 100% expected payback makes risk of ruin certain (more on that in my next article).

Game selection and playing strategies may be found in my 199-page book, Video Poker—Optimum Play. It gives the easy Precision Play rules for several potentially profitable games, and lots of related advice.

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