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Sunday, January 29, 2023

Expected Return

When a casino orders a slot machine from the manufacturer, they specify the payback return they want for that machine, which generally ranges from 90-98%. If a machine is set to pay back 95%, then that means in the long term (millions of spins) it would pay out 95% of the money put into it.

That may seem like a good deal, but it’s not. If you’re getting back 95% of your money, that means the casino is keeping 5%. If you play a dollar machine, two coins at a time, 800 spins an hour, for one hour, you’re putting \$1600 into the machine. The casino’s 5% take means you lose \$80/hr. on average. Ouch.

This is one reason that casinos don’t cheat on slot machines: They don’t have to. The odds are so overwhelmingly bad, all they have to do is put the machine on the floor and rake in the money.

Understand that your expected loss is based on how much money you play, not how much money you take with you. For example, you might think, “Okay, I’m bringing \$500, and the slots take an average of 5%, so I should lose about \$25.” Wrong. Because you’ll go through that \$500 in less than an hour on a \$1, two-coin slot, and lose an average of \$25 on that. But then when you play the \$475 or so that you got out of the machine, you’ll expect to lose 5% of THAT, etc. Losing a bit every time you replay your bankroll is called the grind. The casino grinds you down. To figure your expected loss, figure how much you’re playing total. Here’s our primer on figuring expected loss.

The return on a machine is figured by the manufacturer, by taking all possible combinations and adding how much would be won on those combinations. For example, if a machine is picking a number from 1 to 64 on each of three reels, then there are 643 = 262,144 combinations. Let’s say they have a computer play out all these combinations at the two-coin per spin maximum, which would represent 524,288 coins wagered, and they find that 498,074 would have been won. So 498,074 / 524,288 = 95%. Ta-da.

Of course, this doesn’t mean that you’ll get back exactly 95% every time you play. Anything can happen in the short term. Obviously if you put a 168bet dollar coin into a machine you’re either going to lose that whole dollar or win some random number of coins, but in no event will the machine spit back exactly 95 cents at you. But if you sat there and played for years, your wins would equal about 95% of what you put into the machine.

In general, the higher denomination the machine, the higher the return. For example, the average return between Vegas Strip & Downtown casinos is 95% for dollars but only 94% for quarters and only 92% for nickels. But even though the odds are better on the higher-stakes machines, you’ll still lose more money playing them, because you’re wagering more money. If you want to limit your losses, play the lowest stakes machines you’re comfortable with.

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