How Long Does It Take to Get a Jackpot?

24 August 2005

By Alan Krigman

Frustrating, isn't it? Maybe even aggravating. You've been playing the slots for years and have come close but never won a jackpot. Your braggadocios brother-in-law got dragged into a casino, kicking and screaming, once in his smug life, and bagged big bucks on the first (and last) machine he ever tried. Grrrr.

So, how long do you have to play before you can expect to line up those three, four, or five Bozo-the-Clowns? The answer depends on the machine, since games may be programmed with different jackpot probabilities. And, in most cases, you can't find out what those probabilities are. Video poker is an exception, since the chances of the top hand are on the order of one out of 40,000 if you follow anything close to expert strategy. About the only thing you can figure on any of the other slots is that the more the prize money, the lower the likelihood you'll get in on any spin.

The math mavens could tell you that when a jackpot has a probability of one out of 40,000 or one out of 20 million, on the average it'll hit once per 40,000 or 20 million pulls, respectively. But averages are just convenient fictions. They help describe the net effect of huge numbers of tries but aren't much good for predicting how any particular event will unfold.

For instance, say that two solid citizens test their luck at video poker. One gets a royal on the first round and the other on the 79,999th try. The average will be once in 40,000 hands but this value gives no clue about what actually happened.

The casinos could conceivably record how many rounds one or another patron or machine went before hitting a jackpot. They don't, and wouldn't be apt to blab if they did. However, computer simulations offer an illuminating way to peer into this phenomenon.

For this purpose, pretend that over some period, 10,000 hopefuls play slot machines having jackpots with chances of one out of a million. Assume they're all facile with their fingers and get 500 spins per hour. On the average, it'll take a million tries to hit the jackpot. That's 2,000 hours. About 10 years visiting a casino once a week and indulging their fantasies four hours each time.

But, the simulation offers more of the desired details about how many stalwarts hit after how long. Data from one such computer run are shown in the accompanying table. Of the 10,000 aspirants, seven won within an hour. An additional 17 heard those bells and whistles before finishing their first four-hour forays. The rest? Well, everyone in the simulation hit eventually, but it took 29 of the 10,000 gamblers between 50 and 60 years, one disappointing weekly trip after another, before fate finally delivered.

How long it took 10,000 virtual players to hit a slot jackpot
having a probability of one out of a million

Duration	How many did it
within an hour	7
within a session but over an hour	17
within a month but more a session	48
within a year but over a month	900
within two years but over one year	884
within five years but over two years	2126
within 10 years but over five years	2399
within 20 years but over 10 years	2317
within 30 years but over 20 years	886
within 40 years but over 30 years	263
within 50 years but over 40 years	124
within 60 years but over 50 years	29

Be a bit careful with these figures. They tell how a specific 10,000 virtual players fared, not how every such assemblage will do. Other groups of 10,000 real or imaginary bettors should be roughly but not precisely comparable. The figures also don't say that if you live long enough and keep playing, you're sure to hit. Rather, that everyone in this group did.

For inquiring minds who want to know, the chance of never hitting a one-in-a-million jackpot, playing 2,000 spins a week, 50 weeks a year for 60 years is a quarter of one percent. Maybe you think that's so small you can neglect it. But, look over there, in the corner of the Vita-Glas solarium at your friendly neighborhood retirement villa (formerly, the old folks' home). See that sullen couple? Guess what. They never did hit. Nor, apparently, did they learn this lilting lyric by the beloved bard, Sumner A Ingmark:

If failure whomps you in the eye,
Be wary of another try.