That Slot Machine Mystique
Bigfoot? Stonehenge? Poe? How about the slots?
Mystique is a quality that’s diﬃcult to pin down because of its very nature. There’s an aura about a person, place or thing that we’re drawn to. We’re drawn to it, perhaps even a little in awe of it, without fully understanding how or why.
There’s a mystique about Bigfoot, the Abominable Snowman and the Loch Ness monster; a mystique about Stonehenge and Machu Pichu; a mystique about the life and times of Edgar Allen Poe; or the losing ways of the Chicago Cubs and their strange hold on fans.
For a woman who once phoned and asked for a luncheon appointment, there certainly was a mystique about slot machines, and she wanted background for a book she was planning. In mind’s eye, she practically ﬂoated into the room like Sybill Trelawney, the divination professor in the Harry Potter novels, creating her own mysterious atmosphere. But then, that’s looking back a few years.
“Slot machines have this aura, this mystery,” she said. “I want to capture the mystique of slot machines.”
She didn’t really get the answers she wanted. Slot machines, I told her, are mathematics and electronics. The mystique of slot machines really comes from players not understanding how the games work, or even how some of the peripherals around the games work.
The book never appeared, but slots haven’t ceased to be machines of mystery. Questions roll in every week about aspects of the games and the math surrounding them that many players don’t understand. Let’s stroll through a few players’ questions, and unveil some of the mystique.
When you read about somebody betting millions of dollars on the slots, do they have to have millions of dollars in their hands? How do they do it?
The short answer is multiple long sessions and lots of $100 bills, but that’s not really what was meant by the question. Variations on this theme ﬂooded my email box a few years ago when it was reported that politicians had made millions of dollars in wagers. Everyone wondered where they got the millions, and questions of embezzlement were raised.
But making a million dollars worth of wagers doesn’t mean putting a million dollars at risk. Most of the wagers are made with recycled winnings. That’s a concept most of us are familiar with at a low level. We might start with a $20 bill in a video poker game, but we draw some high pairs, a few two- pair and three-of-a-kind hands, the odd straight, ﬂush or full house. If we’re lucky, we might draw four of a kind and have a shot at a winning session. If we’re super lucky, a royal ﬂush makes us a big winner.
Most of the credits added by those high pairs through full houses, and even from four of a kind, goes right back into the machine. Players rewager their small winnings. Your $20 investment might bring several hundred dollars worth of wagers before it either drains you or you cash out.
How much would you actually have to risk to wager $1 million? It depends on the game. If you’re playing 9-6 Jacks or Better video poker at expert level and getting a 99.5 percent return, $1 million in wagers represents an average of $5,000 in losses. If you’re playing a $5 slot machine, returning about 96 percent, $1 million in wagers represents about $40,000 in losses. And if you’re playing a penny slot with an 87 percent return, $1 million in wagers leads to an average loss of $130,000—an awful lot of coppers.
That’s a good deal of money to put at risk, but it’s not millions of dollars.
I’ve read that slot machines are random, and I’ve read that they have programmed percentages. They can’t be both, can they?
Let’s start oﬀ by pretending we’re ﬂipping a coin. Results are random, right? In the long run, about half are going to be heads, and about half are going to be tails, but you can have winning streaks and losing streaks on either side.
Now let’s say you’re betting 50 cents on each ﬂip. Each time you lose, I take your 50 cents. Each time you win, you keep your 50 cents, and I pay you 45 cents in winnings.
On the average, 20 ﬂips will bring you 10 heads and 10 tails. You’ll risk $10, and you’ll have $9.50 left. The average expected payback is 95 percent. So now you have a game in which results are random, but which also has a “programmed” payback percentage.
That’s analogous to the way it works on the slots. The programmer sets the possibilities, and they will appear in a random fashion. In the long run, each possible combination will come close to the expected average number of appearances. And just as in our coin ﬂip example, the payouts will be something less than would yield an even game.
Table games supposedly have lower house edges than slots. But I saw a gaming commission report online that listed table game hold percentages three or four times higher than on the slots.
Hold percentages are calculated diﬀerently on slots and table games, creating a statistical illusion. The unwary often are fooled. A nationally televised special report got it wrong a few years ago, and so did a nationally syndicated general interest columnist. A casino marketer got it wrong in a letter he sent to me many years ago.
The confusion comes because slot machines track every wager, and table games don’t. Hold percentages on slots are the percentage of all wagers kept by the house, while table hold percentages are the percentage of all buy-ins kept by the house.
When I slide $100 into the bill validator on a slot machine, I win on some spins, lose on more, and continue to play. Let’s say I’ve had about average luck on a dollar machine, and before I lose my $100, I’ve had enough winning spins to make $2,000 in wagers. In the end, I lose 100/2,000ths, or ﬁve percent, of my total wagers. That ﬁve percent is the slot hold percentage for my play.
Now let’s say I sit down at a blackjack table, and push $100 across the layout to the dealer, who then gives me $100 in casino chips. I bet $5 a hand, and I win some and lose a little more. A couple of my $5 chips bring smaller denomination tokens when I win 3-2 payoﬀs on blackjacks. I stick around to replay my winnings until I’ve made $2,000 worth of bets, and ﬁnd I’ve lost $14. So I go to the cage to cash in $86 worth of chips.
What is the casino’s hold on my table action? It’s $14 of my $100 buy-in, or 14 percent.
Look at that carefully. I’ve wagered the same amount of money at table and slot, and walked away from the table with most of my money while losing it all on the slot. Yet the hold percentage is higher at the table.
That’s one of the basics of casino math. Slot hold percentages and table hold percentages measure diﬀerent things and cannot be used to compare one to the other. Some gaming commissions have taken to listing slots’ “win percentages” instead of hold percentages, to distinguish it from non- comparable table statistics.
How can you tell when a slot machine is ready to pay out?
Ah, the ultimate, most-asked question in the pursuit of slot mystique.
Much has changed in the last couple of decades. Video slots have taken over large chunks of slot ﬂoors and raised their own mysteries. The combination of video, multiple paylines and ticket payouts have brought penny slots back from extinction. Coins, tokens, coin buckets and change carts have all but disappeared.
One thing hasn’t changed. Results on slot machines are still determined by random number generators, and there is no way for the player to know what’s coming. Machines don’t give any signal that they’re going to pay out—they don’t know that themselves.
It’s almost a shame to look too deeply into the question of how to tell when the payoﬀs are coming, but the answer is simple. You can’t.