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Best of Alan Krigman
What if They Let you Choose Your Own Slot Jackpot?29 August 2000
Crazy idea? It wouldn't work? The casinos would go broke? Solid citizens would get too greedy? Not really! In fact, with the computer chips that the manufacturers already use in all contemporary slots, such a feature would be eminently practical.
I'll explain how it would work on a hypothetical machine. The bells and whistles of a real device wouldn't change the concept.
Make believe you're on a three-reeler with only five winning combinations. It's a $0.50 machine. You play the two-coin maximum -- $1 per spin. The belly glass shows these symbols and payouts:
You have complete freedom to specify the jackpot. As little or as much as you and your 1-900-PSYCHIC advisor crave. When you pick, the computer inside the machine automatically adjusts the odds of winning to keep the overall payback percentage, and therefore the house edge, at whatever level the casino bosses decree.
In practice, the adjustment might involve changing the chances associated with all the returns. This would accommodate features such as more frequent small hits for players who were satisfied shooting for modest jackpots. In principle, however, if hit rate is ignored and the sole goal is to maintain payback percentage, only the probability of hitting the jackpot has to be varied.
Assume that the probabilities of non-jackpot wins are: mice -- 250/1,000, stooges -- 100/1,000, maids -- 40/1,000, and pigs -- 1/1,000. Get payback percentage by multiplying each probability times its return and adding the products. Without the jackpot, this is 950/1,000 or 95 percent. Get hit rate, the likelihood of any winning spin, by adding the probabilities. In this case, again without the musketeers, it's 391/1,000 or 39.1 percent.
Say that, in total, the machine is set to return 96 percent. For
simplicity, ignore hit rate implications and keep the original odds for
mice, stooges, maids, and pigs. Non-jackpot wins then still account for
95 percent payback. The musketeers must return the other 1 percent with
only jackpot parameters to be varied.
Maybe you prefer a $10,000 jackpot. Now, your shot is one in a million because 10,000/1,000,000 equals the required 1 percent. The hit rate is 39.1001 percent. Likewise, the overall 96 percent return is maintained if jackpots of $100,000 and $1 million are chosen and probabilities are set to one in 10 million and one in 100 million respectively. Corresponding hit rates are 39.10001 and 39.100001 percent.
The bottom line is that you can select the jackpot arbitrarily as long as the computer can adjust the associated probability to maintain the ordained payback percentage. And the pattern should be clear. In cases when other payouts and returns are constant, raising the jackpot by some factor lowers the chance it'll occur in the same proportion. That is, if you try for 100 or 1,000 times as much, you're 100 or 1,000 times less apt to succeed.
The poet, Sumner A Ingmark, summarized such situations like this:
As prizes become more effusive,
Best of Alan Krigman