By the Time Progressives Hit, They’re Usually Paid for!

December 26, 2000 12:03 PM
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The progressive jackpots at some machines and table games are among the gaming innovations that catapulted casinos to the top of the leisure and entertainment heap in America. They satisfy the public’s lottery-fed fantasy of being within reach of riches. Yet their workings remain mysteries to most solid citizens.

Here’s the skinny. The casinos "seed" starting values for the payouts. The seed might be just about any amount. It’s usually enough to be enticing from the outset, but not so much that the bosses wince when someone wins before it’s covered by previous players’ losses. A share of every bet is then diverted from the routine put-and-take of the game, and added to the progressive total.

In situations where the jackpot is the highest payout on a regular bet, as is normally true on the slots, the set-aside is small — a penny or less per dollar. Alternately, the jackpot may involve a side bet whose only purpose is to go for the gold, as is common on table games. The fraction can then be substantial. For example, it’s $0.70 per dollar at Caribbean Stud.

When there’s only one way to win the accrued funds, the prize keeps growing until it’s hit. When some outcomes pay portions of the jackpot, the grand total is reduced by the amount of every partial withdrawal in from most slot progressives. Still, examining this jackpot offers insights into what’s behind progressives in general.

First, from the jackpot size, you can estimate how many tries have been made in the current progression cycle. If you’re handy with a calculator or computer, or good with arithmetic, you can use the exact theoretical formula. With R standing for number of rounds and JP the amount of the jackpot, the relationship is:

R = 1,443,866x(10,000-JP)/(JP-490, 914)

Happily, there’s an easier, back-of-the-napkin method. And it’s as reliable, in practice, because the "exact" calculation has a margin of error anyway. This results from its being based on chances rather than tallies of partial payouts for flushes, full houses, and non-royal straight flushes. The simpler formula is:

R = 6xJP - 200,000

The second thing you can deduce from the jackpot is how much the bosses have pocketed at any point. Now, with P standing for the casino’s profit and JP the jackpot, the exact formula is:

P = 433,160x[(JP-10, 000)/(490,915-JP)] - 10,000

The simplified approximation is:

P = 1.8xJP - 70,000

Here’s how to use these formulas:

Say a Caribbean Stud jackpot is $220,000. The exact equations give 1,167,185 rounds and $325,764 casino profit. With the approximations, first multiply 220,000 times six to get 1,320,000, then subtract 200,000 for 1,120,000 rounds; and finally multiply 220,000 times 1.8 to get 396,000 and subtract 70,000 for $326,000 casino profit.

Run the jackpots you see on the floor to ascertain how many players have bet and lost, and to compare how much the casino earns with what the winner takes home. If you know your algebra, you can even find the crossover where the casino makes more than the winning player. The results help show why gambling halls are rarely confused with charitable trusts. Or why, as the poet, Sumner A Ingmark, wryly rhymed:

Those who think a game’s a gift,

Pay the laws of chance short shrift.