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Best of Alan Krigman

Gaming Guru

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Jackpots Are Tougher to Get on Machines that Let You Play Longer

9 September 2003

Slot machines are rated according to "return percentage." This is the fraction of the gross wager paid out to players. Most slots are in the 90 percent range. A figure like 96 percent means that if players bet a total of $100,000 over enough trials that the law of averages applies reasonably well, $96,000 will accumulate on the "win" meter and $4,000 ends up in the bosses' pockets.

Sophisticated solid citizens know that the $100,000 doesn't necessarily represent moolah gamblers bring into the casino, nor the $96,000 money they carry home. But the $4,000 is what the casino actually stuffs into its mattress at the end of the day.

Here's how it works. Pretend that 100 hopefuls arrive with $100 each. That's $10,000. They all bet $1 a shot. Almost nobody quits with what's on the credit meter or in the tray after one pass through their bankrolls, here, 100 spins. Most pump intermediate returns back through the game. If the 100 players average 1,000 rounds apiece, the gross wager or "handle" will be $100,000. The casino expects to keep $4,000; the punters, in principle should finish with $4,000 less than their $10,000 stakes, or $6,000. These are theoretical averages since any particular 100 players may wind up with anything from zero to zillions of dollars.

Frequent slot players don't have (or want) to be told how often they go belly-up. Conversely, hardly anybody has good intuition about the chances of a sizeable score and various trade-offs involving the amount, the chance of winning, and the rate at which contenders who go for broke can anticipate doing so.

To put the figures into perspective, assume a hypothetical machine with only two payout levels. A winning $1 bet returns $2 or the jackpot. Further assume that the game has a 100 percent return. It turns out that adding payout levels and giving the casinos a few percentage points won't change the results much.

What does prove to be important is the size of the jackpot and, surprisingly to most folks, the "hit rate" on the machine. The hit rate, a figure that's rarely discussed, is the chance of getting any return whatsoever on a round.

People like high hit rates. Getting something, anything, back boosts their levels of interest and anticipation and contributes to the enjoyment of a longer session for the same bankroll. They also like big jackpots -- why go to the casino for a crummy $10,000 when $1 million or even $10 million seem like the same "one pull" away? Unfortunately, they can't have it both ways.

The maximum possible hit rate on the hypothetical two-level 100 percent payback machine is 50 percent. At this rate, players would get 2-for-1 on the average of half the time, leaving no margin for any jackpot whatsoever.

Were the hit rate 40 percent, four out of 10 pulls, the chance of a $1 million jackpot would be one out of just under 5 million. Raise the prize to $10 million and the overall return stays at 100 percent when the probability is one out of 50 million.

What if the hit rate were cut in half, from four to two out of 10 pulls on the average? Players would go bust faster. But chances of a $1 million jackpot would improve to about one out of 1.6 million and of a $10 million score to one out of 16.7 million. Halve the hit rate again, to 10 percent (a level at which players would drop like flies and swear they'll never come to that casino again) and the chances of $1 and $10 million jackpots are one out of 1.25 million and one out of 12.5 million, respectively. Still longshots, as you would anticipate, but a lot less so.

Is there a happy medium? Probably. And the casinos are still trying to find it. In the meantime, they tend to err on the side of higher hit rates and lower jackpots because this keeps players in their seats thinking they had a good run for their money. And the jackpots are few and far between, anyway. It's the philosophy the poet, Sumner A Ingmark, obviously had in mind when he wrote:

Keep it secret, why alert 'em?
What they do not know won't hurt 'em.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.