Playing It Smart: How does jackpot size affect slot machine performance?

You're cruising the aisles of your favorite den of iniquity. You see that some slots have huge jackpots while others have rather moderate high-end returns. Many solid citizens figure only suckers don't go for the gold. A jackpot is a longshot, anyway. And, OK, the chance may get more remote as the amount increases. But a score is just one spin away whichever game is chosen. So, all else being equal, why not aim as high as you can?

The trouble is that all else isn't equal. You usually can't tell whether two nominally similar machines have the same or different theoretical payback percentages. So the best assumption is that they do. Then, if they have similar lists of payouts except for the jackpot, other characteristics of the game are adjusted to bring the designated return percentage to the desired level.

Lower jackpots generally do have greater chances of being won. But, two other factors may be more important to the majority of slot aficionados, even though few consciously think about them.

* Hit rate: how often the machine returns anything. Low hit rates are discouraging, creating the impression of a "cold" game and causing players to flee. Conversely, high hit rates reinforce the perception of building toward victory.

* Probability of survival: the likelihood of a player with a certain budget still being in action, ahead or behind, after a given period. Everybody wants to win. What of those who are losing or aren't sufficiently far ahead to be happy? They want their money's worth of gambling time. For the entertainment merit as well as enough runs at the prize.

A simplified hypothetical example illustrates how internal changes made to maintain a specified payback percentage, for alternate jackpot sizes, affect hit rate and chance of survival. The same basic principles hold for real, more complex, devices.

Picture a group of machines. Each has three windows, in which there are two possible symbols a happy face (H) and a sad face (S). Three H's is the jackpot, the size of which can be arbitrarily specified by the bosses on any machine. The other combinations are uniform: any two H's and an S returns 10-for-1, one H and two S's returns 1-for-1, and three S's loses. More, suppose the return to players is 90 percent on all of the machines. Given a jackpot size and the desired return percentage, the math mavens can figure what probability to assign to H. Everything else is a consequence of this value.

The data confirm that the chance of a jackpot is small, under 1 percent in any case, but rises as the amount falls. Players will be more aware of hit rate; here, it increases from a discouraging 22.2 percent (roughly 2 out of 9) with jackpot at $1,000 to a relatively encouraging 36.7 percent (about 3 out of 8) when it's $25. Chances of a $250 bankroll lasting for at least 1,500 spins are especially striking. They're only 18.7 percent with the jackpot at $1,000, compared with a 79.0 percent when it's $25.

Somewhere along the line there's a machine you should think represents a good trade-off for yourself. Maybe it's the biggie, despite the low hit rate and prospects for being in action very long. Perhaps it's at the other end of the scale. More likely, given what you now know about the compromises, you'd choose something in between. For, as the poet, Sumner A Ingmark, wrote:

Unwise are they who for greed's sake,
Do not allow for give and take.