Virtual reels and the near miss

Two crowns are sitting on the pay-line, and on the third reel the crown has come to rest one row above the pay-line. How close was that?

Both pictures show the same three reels, and only the third reel differs between the two pictures. On the left the third reel came to rest on a blank, with the crown one row above the pay-line; on the right the third reel came to rest on the crown itself. On a machine built from three teaching reels, screens of the kind on the left — crowns on the pay-line on two of the three reels, and the crown standing one row off the pay-line on the remaining reel, whichever of the three that turns out to be — turn up about 36 times as often as three crowns on the pay-line.

Leoformer dealer · rules and maths

I worked a floor for years, and after that screen people always said the same thing: “that was close”. It was not close, and it never was.

Give me a few minutes and you will be able to say why in one sentence, and count it for yourself on a reel small enough to see all of at once.

A number first, a picture second

You press the button, and before a single reel has moved the machine draws a number. Then it looks that number up and finds the symbol the number points at, one symbol for each reel. Only after that do the reels turn, and they turn until those symbols are the ones showing in the window. The order of those three things is what makes the rest of a slot machine readable: the number comes first, the picture is built to match the number, and the reels decide nothing at all while you watch them turn.

1. The drawThe machine draws a numberOne number out of the 64 on the strip behind each reel, and every one of those 64 numbers is exactly as likely to be drawn as every other.
2. The look-upThe machine looks the number upThe map says which of the 22 symbols painted round the drum that number points at. One symbol can be the answer to several numbers; the crown is the answer to 1.
3. The reelsThe reels turn, and stopThey stop with the symbols the map has already named showing in the window. Nothing at all is chosen while they are turning.

The map hands the numbers out unevenly on purpose, and each symbol's share decides how often you see that symbol.

The middle column is where the almost comes from: nothing on the drum is pointed at by fewer numbers than the crown, and nothing by more than the two blanks either side of it.

Two things about this reel are true at the same time, and they sound as though they cannot both be. Every number on the strip is exactly as likely as every other number: the draw is even, and nothing tilts it. The symbols are nowhere near equally likely: the crown comes up far less often than a blank does. Both hold at once because the map sits between the numbers and the symbols, and an even draw over 64 numbers becomes a wildly uneven draw over 22 symbols the moment one symbol is the answer to 6 numbers and another is the answer to 1. Nothing is fiddled at the moment of the spin. The unevenness was built into the map before the machine was ever switched on.

• Even, and it stays evenEvery one of the 64 numbers on the strip has exactly the same chance of being the one the machine draws. That half is written down as a requirement the machine has to meet, and it is the half people tend to doubt.
• Uneven, and it was built that wayThe 22 symbols painted round the drum do not share those numbers equally. The crown is the answer to 1 of those numbers, and each of the two blanks beside the crown is the answer to 6 of those numbers. That half is the one people tend to miss.

Why the crown keeps stopping beside the pay-line

Suppose the machine draws the one number that points at the crown: the crown comes to rest on the pay-line, and that is 1 number out of 64. Suppose instead it draws any of the numbers pointing at the two blanks beside the crown: a blank comes to rest on the pay-line, the crown is still in the window one row off it, and that is 12 numbers out of 64. The same strip, the same drum, the same even draw — and the crown stands beside the pay-line 12 times for every once it lands on the pay-line.

Without the map every symbol gets one number, so the crown lands on the pay-line on 1 position out of 22 and stands one row off it on 2. The map does not invent the almost; it multiplies it, from 2 to 12.

Three teaching reels turning together: the long bar is the ordinary shape of an evening at a machine like this, the short bar the rare one.

Ontario puts a ceiling on exactly this. The symbol of the largest award a game offers may come to rest in the window without landing on a pay-line no more than 12 times, on average, for every time it does land on one. The teaching reel is built to sit right on that ceiling: add one more number to either of the two blanks beside the crown and the reel would be over that ceiling. No rule asks a machine to go all the way up to the ceiling, though. A machine may lean anywhere from not at all up to 12 to one, and where any particular machine on any particular floor actually leans is not published by its operator, by its regulator, or by anybody else whose pages we can read.

Everything after the button

By the time the first reel begins to slow down, the spin is already over. The bet has to be committed before the machine selects the outcome, and a bet that arrives afterwards has to be voided and given back. So the crown standing a row above the pay-line is not a result that nearly went another way: it is the picture that belonged to the number the machine drew, delivered by reels with nothing left to decide. That screen is a loss with a flourish drawn on it.

1. You pressThe bet is takenIt has to be taken now. A bet that arrives after the outcome has been selected has to be voided and handed back.
2. The machine decidesThe outcome is selectedOne number for each reel, drawn from the 64 on that reel's strip. This is the step in which the spin is settled, and no reel has moved yet.
3. The showThe reels turnNothing is being chosen while they turn. The machine is holding an answer it already has and taking its time to show you.
4. The show endsThe reels stop, and the pay-line is settledEach reel stops on the symbol its own number pointed at. Only what came to rest on the pay-line is paid; the row above the pay-line is scenery.

You watch the reels turn and the reels stop. Every decision had already been taken when the bet was taken and the outcome selected, which is why a reel that is still turning cannot be willed, talked or leaned into landing on the crown.

That flourish costs nothing on its own. It costs nothing when it happens, it costs nothing three times in an hour, and the next spin knows nothing about any of it. It begins to cost at the moment it talks somebody into putting more money on the next press than that person meant to put on it — and talking people into exactly that is the one thing an almost is genuinely good at.

• What that screen changedHow the next bet feels to the person looking at it. That is the entire list, and it is the only part of a slot machine that lives in your head instead of inside the cabinet.
• What that screen did not changeThe map behind the reels. The number the next spin is going to draw. And what the machine owes you, which is nothing at all, because a machine never owes anybody anything. The map cannot read a screen, the next number cannot read a screen, and neither of the two keeps any record of the spin that has just finished.

Loto-Québec owns slot machines and publishes its own plain-language guide to how they work, and it says the same thing about its own machines without softening it: a row of symbols one short of a payout makes a player feel they almost did it and entices them to try again, when in reality they were never close, because the chance on the next spin is exactly the chance they have just had.

Mayaformer floor supervisor · manners, money and breaks

If you take one habit away from this, take this one: decide what tonight costs while you are still at home, and give the screen no vote in it (Game plan does that in a couple of minutes). An almost is the machine's way of saying no. It is not a debt the machine has run up with you, it is not a hint about the next spin, and it is not a reason to put more money through.

And if the money on the machine starts to feel like money you need, or you are sitting there to get away from something, stop at that point and ring one of the lines at the end of this page. That is what those lines are for, and the people answering them have heard this evening before.

The same rule in two books

A machine standing in a room and a game running on a screen answer to two separate books of rules, and the same office writes both books: the Alcohol and Gaming Commission of Ontario. Both books open on the same sentence — a game must be clear and must not mislead the person playing it. Both then forbid, word for word, the same thing: once the outcome of a game has been selected, the game may not substitute a particular kind of loss to show you. Both name the near miss in brackets, as the example of what that means.

Read the first two rows across and they are the same sentence twice, once in each book. Read the last three rows across and the two books part company, and they part in both directions. The book for rooms describes a reel strip down to the count of numbers standing behind each symbol, and the pages for screens never mention a reel strip at all. The pages for screens ask that no amount and no symbol be shown that cannot be reached, and the book for rooms asks that only of the symbols painted on a drum.

That rule forbids choosing a losing picture after the outcome is selected. It does not touch the reel strip: a map that puts the crown beside the pay-line 12 times for every once on it substitutes nothing, because the picture was settled the moment the number was drawn.

Practice: where will it stop?

Once the button is pressed a slot machine offers no decisions at all, so there is no spinning to do here. The decisions in the practice run are the ones you really do make: which reel you are reading, what a screen is telling you, and what you do next. Three levels of those decisions, and the strip below is the whole lesson — every square is one moment, and all of the squares are there from the start. Only your first answer on each square counts, and when the squares of one level are full the next level begins by itself.

Check yourself

Mayaformer floor supervisor · manners, money and breaks

Five quick ones. Pick an answer, then check it. No timer, no points: just whether it stuck.

Back to the question we opened with. Two crowns on the pay-line and the third crown one row above it. On a machine built from three teaching reels, screens of that kind — crowns on the pay-line on two of the three reels and the crown one row off the pay-line on the remaining reel — turn up about 36 times as often as three crowns on the pay-line. It was not close. It is the picture a machine of that shape is built to show you most of the time.

Where this is written down

Further reading

• Minimum Technical Standards for Gaming, 11: Game Behaviour · Alcohol and Gaming Commission of OntarioWhat a slot machine in a room is allowed to do, clause by clause: the payout floor, the reel strip, the odds on the largest prize and the ten games of history every machine can show you.
• How to play slots · Ontario Lottery and Gaming Corporation (PlaySmart)An operator walking through the arithmetic of one spin, with its own worked example: nine lines on a nickel machine, and what one press of it takes.
• How to play slots · British Columbia Lottery Corporation (Casinos BC)Reels, lines and the province’s average return, in the words of the corporation that runs the rooms.
• Understanding chance: slot machines · Loto-Québec (Wise Play)The near miss, volatility and the illusion of control, named and explained by a provincial operator rather than by us.
• Informed Gambling: slots and VLTs · Manitoba Liquor & LotteriesA short brochure on what a payout percentage is and is not, and why two machines with the same one can empty a wallet at different speeds.
• Registrar's Standards for Internet Gaming: game design and features · Alcohol and Gaming Commission of OntarioThe same machine on a screen: what a regulated site in Ontario may not do with the picture after the outcome has been drawn.

How it’s worked out