Something's Gotta Fall when Slot Machine Hit Rate Rises

What most people enjoy best about the slots is the chance to get rich quick. This, and the notion that their bankrolls buy them as good a shot as the same moola merits an Einstein or Rockefeller. Make no mistake... as a gambler, I relish these things, too. But, as a numero-noodnik, I also like the way the math buried within the boxes can be tweaked, crafting the characteristics of the games without adjusting the advantage the house holds so holy.

The changes can be made using lots of means, along any or all of several dimensions. As an example, I'll show how it's possible to modify hit rate -- the chance of getting something back on any spin -- keeping payback schedule and return percentage constant.

Say a machine shows payouts for relevant winning combinations of 1, 2, 5, 10, 25, 100, 500, and 2,500 coins. The game is set for 90 percent return; that is, players collectively recoup 90 percent of their wagers and the casino gets the other 10 percent.

Without affecting payouts for winning combinations or overall percent return, the slot machine maker can specify hit rate over a fairly wide range. For instance, this device could be made to hit on the average of 40, 50, or 60 percent of the time. An unlimited variety of paths might lead to these frequencies. I'll pick a viable avenue and examine some vital implications.

One obvious effect is motivational reinforcement. The higher the hit rate, the more often there's a reward, and the more strongly players are inspired to proceed. Even solid citizens who should know better, succumb to equating recurrent hits with hot cycles.

Less evident but more tangible is the impact of hit rate on the duration of play expected on a particular bankroll. As a point of reference, assume an individual starts with $100 and bets $1 per spin. With one approach, 40 percent hit rate on the machine in question yields 18 percent chance of still being in action after 1,000 rounds. A 50 percent hit rate can be effected which raises the likelihood of lasting 1,000 rounds to 19 percent. And, a 60 percent rate can be utilized which offers a 21 percent prospect that the $100 bankroll will survive 1,000 rounds. If your primary goal is time at a machine -- along with the credits you thereby earn for meals, cashback, and whatnot -- go for high hit rate.

But, few issues are as simple as they at first seem, especially in the wondrous world of wagering. Slot machine hit rate is no exception. It turns out that a high rate, with its consequent benefit in stretching bankrolls, carries detriments as well. Er, you didn't think that gambling's gaudy glitzatoria are really philanthropic trusts, did you? Or that they indulge insiders who discover secrets the casino bosses don't want the great unwashed masses to know?

To raise hit rate without affecting overall return percentage, machines normally emphasize more but lower winning spins. This turns out to trim the chance that players will reach any particular earnings level before depleting their stakes. To illustrate, on the configuration considered, a player with a $100 bankroll and a $500 win goal has over 9 percent chance of success when hit rate is 40 percent, 8 percent chance with a 50 percent hit rate, and 6 percent probability with a 60 percent hit rate.

Odds of winning a jackpot are a third significant factor that may drop as hit rate rises. Here are the figures for the prototype device with the selected hit rate implementations. At the 40 percent level, odds against winning the $2,500 jackpot are 79,967-to-1. When hits rise to 50 percent, odds against the big score jump to 99,595-to-1. And, at the 60 percent rate, odds against catching the gold ring further worsen to 133,279-to-1.

Since bettors generally don't know either the return percentage or the hit rate on a machine, how do these insights help in the casino? To answer, I bow to the balladry of Sumner A Ingmark: