Why the slot machine return percentage you pay for isn't what you get

Payouts on slots for various results are emblazoned on the belly glasses or video screens of the machines. However, other than at video poker, the associated probabilities are normally kept under wraps. They’re assigned arbitrarily then stored in the internal computer chips. Worse, the values can’t be deduced from anything it’s feasible for the public to measure. Since the house’s edge or advantage – or its complement, the player return percentage – depends on both payouts and probabilities, this key gambling parameter is not known for the machines you choose to play.

This contrasts with the situation on most other games. At craps, for instance, the probabilities of all bets can be deduced from the one-out-of-six chance that any face from one to six will show on a die. Similarly at double-zero roulette, all probabilities can be ascertained from the one-out-of-38 likelihood the ball will settle on any number from one to 36, 0, or 00.

Mystifying matters further, it doesn’t help if players learn slot return percentages from casino advertising or reports issued by state regulatory authorities. Saying, for instance, that the dollar games in a certain joint return 95.0 percent of the gross wager is meaningless. For two reasons.

First, figures like these are averages across multiple machines. They don’t necessarily apply to every device in the indicated category on the floor. Two hundred slots, half returning 92.6 percent and the rest 97.4 percent would validate the 95.0 percent claim, and there’d be no way to determine which were which. Apparently indistinguishable units could have unique sets of probabilities – leading to different return percentages – despite the identical lists of payouts.

Second, slots typically have one or more disproportionately high-value payouts. These have such remote prospects of being hit that the majority of machine afficionados will never get any of them. The nominal statistics are calculated based on huge numbers of spins, far more than most folks will undergo. Players who don’t receive payouts at the highest levels will have effective return percentages lower than those characterizing the machines in the long term.

As an illustration, data have been published for a certain version of the popular Double Diamond slot machines approved in the province of Ontario. The game has a theoretical 92.6 percent return with the probability of a 2,500-for-3 jackpot being one out of 46,656. Assume an individual plays at a healthy clip of about 10 spins per minute. This person would get 1,800 shots in a three-hour session. With a one-out-of-46,656 probability of a jackpot on any spin, the chance of not hitting this result in the three hours is 96 percent. Even 46,656 spins, roughly 80 hours, is no guarantee of success; it has 37 percent chance of not yielding a single jackpot. Twice this many tries, 93,312 spins in something like 160 hours, still leads to 14 percent chance of missing.

Enquiring minds might want to know the effective theoretical return for the 96 percent of the solid citizens who don’t get a jackpot in an 1,800-spin session, but who hit a reasonable share of everything else. They could do better or worse, but the statistical expectation would be for a 91 percent return. Even this, however, is optimistic. The same machine pays 960-for-3 for the next highest return, with a probability of one out of 15,552. The chance of hitting neither the 2,500-for-1 or 960-for-1 payout in 1,800 spins is 86 percent, and would lead to a game having only 89 percent return. The third best level on this machine pays 480-for-3 and has prospects of success of one out of 4,666. Overall, the likelihood of not hitting any of the top three in 1,800 spins is 58 percent, and would drop the effective player return to 85 percent.

Machines with yet larger high-end returns have even lower probabilities of dispensing the dough at the elevated levels. Meaning that fewer players are apt to hit. It’s all the same to the bosses, who count the cash cascading into the casino coffers over tens or hundreds of millions of spins, where the law of large numbers virtually assures them of approaching the theoretically predicted results. Of course, games with giant jackpots are great for the rare happy campers who do hit and enjoy over-the-moon return percentages. But, the armies of aficionados who fail to luck out are pinning their hopes on risks whose return percentages they don’t know at the start, and which get worse in degrees they have no way to gauge.

Roulette, anyone? How about “the horn” at craps? The edge may be high on these bets. But at least players know what it is and how it’s affected by their wagers and the duration of their sessions. As that worldly warbler, the wagering wag Sumner A Ingmark, wrote:
Though gambling is enigma-bound,
What little data can be found,
Can make your betting choice more sound.