Who Pays to Pump the Purse on Progressive Jackpot Slots?

Progressive slot jackpots often seem like manna from heaven, but they're really money from players' pockets. To understand why the bosses may sign the checks but the solid citizens pay the piper, start by imagining a simplified fixed jackpot machine.

Make believe the hypothetical device has five "win" levels with amounts returned per dollar bet and corresponding probabilities shown in the first two columns of the accompanying table. The third column is the calculated return per dollar bet. This is the contribution to theoretical payback percentage, and is obtained by multiplying the individual returns and probabilities. Add the probabilities to get the hit rate, in this case 42.11 percent. And add the individual theoretical returns to get the overall payback, in this case $0.95 on the dollar or 95 percent.

Amount returned per $1 bet	probability	Theoretical return per $1 bet
$1,000	0.01%	$0.10
100	0.10	0.10
10	1.00	0.10
5	6.00	.30
1	35.00	.35
	42.11%	$0.95

Say the bosses want to install a progressive version of the same machine. They insist on retaining 95 percent payback. But this isn't the only executive decision. Another consideration is the level at which to seed the jackpot -- that is, its initial value. A supplemental element is how rapidly and far the jackpot is to grow. There's also the extent to which the hit rate will be impacted. And a further point is whether to keep the prospects of hitting the jackpot as-is, or increase or decrease the chances.

The alternatives can be examined by adjusting the figures in the table of probabilities and returns. In essence, lower the nominal return percentage by the amount you wish to increment the jackpot per dollar bet, adding the money to the total paid when someone wins. Assuming the amounts of the non-jackpot returns stay the same, this is done by modifying one or more of the probabilities.

There's a plethora of possible permutations, and you might enjoy fiddling with a few yourself. Here's one example.

Pretend you want to increase the jackpot by $0.05 for every dollar bet. You do this by cutting the effective payback from $0.95 to $0.90 on the dollar, putting the nickel withheld from the also-rans into the purse paid at the finish line. One way would be to trim the probability of winning $5 from 6 percent to 5 percent. The corresponding contribution to the return would then be $5 x 0.05 = $0.25 rather than $5 x 0.06 = $0.30. The overall hit rate would drop from 42.11 to 41.11 percent. Assuming the probability of hitting the jackpot on this machine is kept at 0.01 percent -- one out of 10,000 -- the average number of tries between successes is 10,000. So the average payout will be the $1,000 seed money plus $0.05 x 10,000 or $500, a total of $1,500.

The options are virtually unlimited. For instance, you can raise progressive totals by reserving more on each try. Or double the seed to $2,000, halving the associated probability to 0.005 percent -- one out of 20,000. Now, keeping the escrow at $0.05 on the dollar, the average number of tries between jackpots goes up to 20,000. The statistically "expected" payout is the new seed, $2,000, plus $0.05 x 20,000 = $1,000, a total of $3,000.

There's more to mull. With a progressive set up as described, the casino still has 5 percent theoretical earnings on the machine. But what about the players? Think about the non-progressive version. Bettors are looking at 95 percent return. On the progressive machine, with the jackpot at the $1,000 seed level, it's 90 percent. It isn't until the jackpot gets to $1,500 that the game reverts to 95 percent. At $2,000, the theoretical return is 100 percent -- $0.95 on the dollar the bosses were willing to give back anyway, and $0.05 from... well, you know who it's from.

Found money? Yes, but who lost it? A philosophical riddle that recalls the rhyme of the metaphysical muse, Sumner A Ingmark:

Big jackpots paid by slots progressive,
Impose on losers costs excessive.