Jackpot Size Doesn't Reveal Much about a Slot Machine.

19 October 2005

By Alan Krigman

Many slot players use jackpot size to select from among nominally similar machines. Once they've decided on what to bet per pull and opted for a single-outcome or multi-line "matrix" game, the choices are still mind-boggling. Some solid citizens go to one machine or another because they like the theme, say a Popeye cartoon or Elvis Presley. Others stick with games on which they or their cousin Primrose have been lucky before. But, and this is admittedly anecdotal rather than based on empirical evidence, the jackpot is often the determining factor.

Ideally, players would know edge, hit rate, and other statistical parameters for each machine. They would then use the data to pick slots most apt to satisfy their personal gambling proclivities. However, even where such information is available, as in table games and video poker, bettors who consider it are rare.

Superficially, jackpot size seems like a good selection gauge. It isn't. It tells only one part of the statistical story. And a misleading part at that. For instance, you may think a relatively high jackpot will be tougher to win than a smaller amount. Or bigger returns imply less frequent payoffs for intermediate hits. Or that low jackpots simply mean the casino bosses keep more of the players' money because they give away less when patrons get lucky. None of these is necessarily true or false because no single "rest of the story" coincides with any particular jackpot.

Picture the puzzle in terms of two machines that look exactly alike except for the jackpots, $10,000 on one and $25,000 on the other. Say the chances and payouts of intermediate wins are all equal and offer theoretical returns to players of 93 percent.

Assume, arguendo, that the probability of hitting the $10,000 jackpot is one out of a million. Multiplying $10,000 times 1/1,000,000 gives 1 percent; this is the jackpot's contribution to the overall return, which becomes 93 plus 1 or 94 percent.

It's possible that the chance of hitting the $25,000 jackpot is also one out of a million. This would contribute $25,000 times 1/1,000,000 or 2.5 percent to the overall return, which would then be 93 plus 2.5 or 95.5 percent. But it's just as possible that the chance of winning 2.5 times as much, $25,000 instead of $10,000, is 2.5 times less likely. The probability would then be 1/2,500,000. Now, the jackpot contributes 1 percent and the machine would have 94 percent theoretical payback. There are any number of other alternatives. The $25,000 jackpot could have a probability of 1/5,000,000, more than proportionately worse and yielding a total return of only 93.5 percent. Or a probability of 1/500,000, easier to win and leading to a 98 percent game.

Nothing requires the intermediate paybacks to match on the two machines, either. A game with a 1/1,000,000 $10,000 jackpot might have 93 percent return at lower levels while that on a 1/1,000,000 $25,000 machine might be only 91.5 percent. In this case, the shots at the two jackpots would be the same, as would the gross return percentages.

Pretend you found a slip of paper a careless casino honcho dropped on the floor, listing the details of several machines. Would your knowledge affect your decision? And, if so, how? Were everything except the size of the jackpot to be the same on a number of otherwise identical machines, going for bigger bucks would be a no-brainer. But, what about other situations? Would you try for more money if you knew it was correspondingly harder to win, but intermediate and overall return percentages didn't change? Would you pick the game that had the best total payback albeit with a low jackpot? Would you sacrifice intermediate returns to try for the larger top prize, or conversely, realizing that the gross effect on payback percentage didn't change?

Anyone who insists you there's a right and wrong answer to these questions doesn't understand why Baskin Robbins sells 31 flavors. And obviously learned nothing from the perceptive poet, Sumner A Ingmark, who penned this paean to personal preference:

True humanity is celebration,
Of diversity in motivation.