Hit Rate and the Popularity of Multi-Line Slot Machines

Multi-line slot machines have captured the fancy of the gambling public. In most cases, they offer solid citizens essentially the same chance of fulfilling their fantasies or going down the tubes as do traditional slots with comparable payout structures when bet at equivalent levels. So, why the popularity?

The low denominations in which these machines are offered pennies and nickels, even in hoity-toity joints are a come-on. But folks with $25 or $50 in their fanny packs won't be fooled by this for long when they notice how fast their credit meters decrement if they bet 10 pennies on each of 20 lines.

Heightened excitement is also a factor. This results from much happening at the same time with multiple lines played at once.

"Hit rate" is yet more significant. This is the fraction of rounds after which the machine tells players they're winners and adds credits back into the meters. Whether or not the amount credited equals or surpasses that debited when the round began.

Although most pronouncements by punting pundits about slots focus on payback percentage, this turns out to be of minor consequence to individual bettors in sessions of reasonable duration. Hit rate, however, noticeably impacts each person as a game evolves. If you've ever told yourself that a machine was hot or cold, this is most likely what lead you to that conclusion. High hit rate is what the psychologists call "positive reinforcement."

Within bounds, the two elements can be specified independently. For instance, payback percentages of 95 and 97 percent could both be achieved with 40 percent hit rates. Conversely, 97 percent payback could be implemented with hit rates of 30 or 40 percent.

There's no great secret to how this works. If a machine has a certain payback percentage, hit rate can be raised by paying out lower amounts more often. Or lowered with fewer bigger returns.

What everyone wants, of course, is high frequency of big hits. This is a mathematical impossibility on traditional slots. Akin to having your cake and eating it, too. But it's where multi-line machines show their mettle. And, here's what's behind it.

Picture a single-line machine with a 40 percent hit rate. This will have lots of rounds which the machine calls wins but are really only "pushes" players get back their bets. It's also apt to be heavy in 2-for-1 returns and light in anything greater. The frequencies of these teasers are high enough to keep bettors at the machine, believing it's either hot or warming up.

Were a single-line machine with the same payback percentage to have only a 25 percent hit rate, it would be averaging higher returns on the winning rounds. But bettors would get discouraged losing on an average of three out of every four spins.

Now, imagine a game with 10 lines, each of which has a measly 25 percent hit rate. With all 10 lines bet, the overall hit rate the proportion of rounds yielding at least one win would be a spectacular 94 percent. Hits on half or more of the lines would be rare, about 8 percent. However, one hit could be expected in 19 percent of all rounds, two simultaneously in 28 percent, three in 25 percent, and four in over 14 percent; taken together, that's an 86 percent success ratio. And, since hits on individual lines aren't that common, the gross gains flashed at players on those that do score tend to be high. Obfuscating the fact that, for example, three attractive paybacks may not look quite so good when netted against the seven concurrent losses.

To be sure, casinos could tighten the return percentages and use the high overall hit rates of multi-line slots to delude their patrons into thinking the games were loose. Some may. But this would be attributing a level of sophistication to the bosses that few are justly accused of demonstrating. Still, as the immortal muse of the machines, Sumner A Ingmark, meaningfully muttered:

For many a gambler it's close to a heresy,
To say when they lose that it's not a conspiracy.