Conservative moralist William Bennett says he’s “come out pretty close to even” gambling over the past decade, contradicting a report that pegs his losses at around $8 million. Given Bennett’s stated preference for high-stakes slot machines and video poker, does his claim hold mathematical water?
As a few lucky Powerball winners can attest, nothing’s impossible when it comes to fighting astronomical odds. But it’s highly improbable—bordering on absurd—that Bennett has broken even through the years. The primary factor working against the former White House drug czar is his choice of games. Professional gamblers and mathematicians alike eschew slot machines as suckers’ bets; since no skill is involved, they’re fixed to favor the house, and the rapid action translates into rapid losses. The notion of any machine being “hot” or “cold” on a given evening is pure myth since they’re powered by computer chips that function as random number generators. The belief among slot pullers that past losses mean soon-to-be-realized jackpots—the “I’m due” mentality—is referred to as the “gambler’s fallacy.” One bet has absolutely nothing to do with the next.
Slots are fixed to pay out a certain percentage of the money wagered in each machine. In Atlantic City, for example, where Bennett has done much of his gambling, state law sets a minimum payout of 83 percent. However, because of market competition—everyone wants the “Loosest Slots in Town!” title—the actual average is much higher, usually estimated in the range of 90 percent to 95 percent. (Predictably, casinos are rather cagey about their gaming statistics.) The remaining 5 percent to 10 percent is referred to as the casino’s hold, or take. The high-stakes machines, which Bennett favors, have higher payout percentages, sometimes hitting 98 percent.
Over the long run, of course, the house always wins, thanks to a mathematical principle known as the Law of Large Numbers. Simply put, the larger the number of plays, the more likely that the fixed probability will catch up with the player. Bennett may have had a lucky night here or there, but after untold thousands of spins, the fixed nature of the slots likely caught up with him: Bennett almost certainly lost between 2 percent and 10 percent of the millions he bet.
Bennett might have helped his case by following intelligent slots protocol, such as carefully reading the payout rules on each machine (identical-looking slots may feature different maximum payouts, a classic casino trick) and always betting the maximum allowable (which increases the probability of hitting the top jackpot). Over a decade’s worth of gaming, however, that’s not enough to beat the Law.
The wild card (pun intended) in Bennett’s hobby is his taste for video poker, which requires a bit of skill rather than just lever-pulling. (Gaming experts always recommend video poker over slots.) There are even video poker machines with theoretical long-term payouts exceeding 100 percent—assuming that the player executes a perfect strategy on each and every hand. Since that’s not likely, a competent player can expect an average payout ranging from 90 percent to 98 percent, depending on his skill and the type of machine. Which means he or she is still going to lose in the long run.
Explainer thanks “Ian B. Williams,” the pseudonymous author of Slot Machines: Fun Machines or Tax Machines?