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Best of Alan Krigman

Gaming Guru

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Bankroll Helps at High-Jackpot Slots…But Doesn't Help Much

18 August 2000

To certain solid citizens, the whole idea of a casino is a shot at a giant slot jackpot. They jump on machines with set-for-life top lines. They rarely stop with mere respectable earnings, or when a few good spins lift them from loss to profit. They keep pumping until they either hit it big or run out of time or money.

Some scorn this strategy. But there's no disputing personal preference. And it's a valid way to gamble, especially when players know that goals get tougher to reach as they get loftier. But folks who focus on fantastic fortunes often fail to fathom the chance of any earnings at all, let alone a big score. And few have a clue as to how bankroll affects likely session results.

No single set of figures applies to all machines, even those in a particular class. Slots may look alike and show the same payouts on their belly glasses, yet differ markedly. Machines with equal payback percentages aren't necessarily identical, either. For instance, one apparatus may yield lots of small wins. Another may hit less often but attain payback equanimity by returning more when it does. Sessions on the two will have distinctive profiles. And, anyway, casinos generally keep specifications of individual units under wraps so there's no way to know the details.

Still, by considering a representative device, it's possible to get a perspective on the kind of performance you can expect in sessions at high-jackpot machines. For this purpose, imagine a dollar slot with the payout parameters shown in the accompanying table. This prototype has a 97.5 percent payback, to which the million dollar jackpot contributes 6.7 percent. And players experience hits on an average of 426 out of every thousand spins.

Payout schedule for prototype
high-jackpot $1 slot machine
for three-coin play
 
return
average wins per five
($)
million spins
5
2,000,000
10
70,000
25
30,000
50
17,500
100
12,500
1,000
50
1,000,000
1

Say 10,000 players try this machine, each with $250 stakes. They hope to gamble for four hours, maybe 2,000 spins, to get multiple shots at the biggie and to rack up rating points. Computer simulation predicts the following: average survival is less than 1.5 hours per bettor; over 9,300 players will tap out in under four hours; roughly 400 will finish with money in the tray, but showing a loss; almost 300 will go the distance and emerge with profits from $1 to $1,000; one or two will hit jackpots.

Here's what's projected if 10,000 players start with $500 each: an average of about 3 hours per person; nearly 7,000 players will bite the dust early; about 2,600 will finish with money left, but be in the hole; nearly 400 will show complete their four hours with profits from $1 to $2,500; three will be new millionaires.

These are the prospects for 10,000 players with $1,000 bankrolls: an average of about 3.5 hours per bettor; only about 700 players will wash out early; roughly 8,800 will weather the four hours but finish in the hole; just under 500 will end with profits from $1 to $5,000; three or four will hit the jackpot.

The figures confirm that going all out for big bucks yields a small chance at success, offset by a likely partial or total loss, with little in between. More, they highlight the effect of bankroll size on longevity and its consequent impact on prospects for the jackpot. On the prototype machine, the probability of a jackpot on any spin is one out of 5 million. A $250 bankroll gives 10,000 players a total of about 8 million spins, so chances of a jackpot are 1.6 out of 10,000. Doubling the bankroll to $500 provides 10,000 players with almost 15 million spins, so chances of a jackpot increase to 3 out of 10,000. Doubling the stake again, to $1,000, yields about 17 million spins, so chances of a jackpot grow to 3.4 out of 10,000. The improvements, as well as the limitations imposed by the law of diminishing returns, are evident. Is this mode of play for you? The poet, Sumner A Ingmark, surveyed the sorrows of some who supposed so:

Most gamblers more than once have said:
I should have quit. I was ahead.
But I played on, and lost instead.

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.