Atlassino Academy · Slots · Lesson 3 of 10
Hit frequency and volatility
How often a slot machine pays and what a spin on it costs are two different numbers, and an evening at the machine shows you the first and never the second.
Two slot machines stand side by side, and both return 92% of everything staked. Machine A pays something about one spin in 3. Machine B pays something about one spin in 20. You have $50 and half an hour. Which machine do you sit at?
The short answer
How often a machine pays and what a spin on it costs are two separate numbers, and the machine sets them separately. Machine A and machine B return the same 92%, so a spin costs the same on machine A as on machine B, however often each of them pays. What you choose between is not the price but the evening: on machine A the money lasts longer and the night ends close to where it started; on machine B the money goes faster, and the night can end far above where it started or far below it.
Machine Apays often
Machine Bpays rarely
Leoformer dealer · rules and maths
People pick a machine by how it feels, and the feeling is about how often it pays, not about what it costs. So I built two machines whose whole pay table you can see, gave them the same return, and looked at what is actually different between them.
How often it pays and what it returns are two numbers
Machine A and machine B are teaching machines, so their pay tables show both what each combination pays and how often it lands. A machine on a casino floor keeps the second column to itself.
| Machine | Pays | How often it lands |
|---|---|---|
| Machine Apays often | 6× the stake | 8% of spins |
| 2× the stake | 22% of spins | |
| nothing | 70% of spins | |
| Machine Bpays rarely | 320× the stake | 0.1% of spins |
| 12× the stake | 5% of spins | |
| nothing | 94.9% of spins |
Multiply what each line pays by how often that line lands, add the lines up, and you have what the machine returns. Machine A and machine B come out at the same figure, and the two bars below are the same length because of it.
Machine A, pays often: $0.92 of every $1 staked comes back
the 6× line brings back $0.48the 2× line brings back $0.44the machine keeps $0.08
Machine B, pays rarely: $0.92 of every $1 staked comes back
the 320× line brings back $0.32the 12× line brings back $0.60the machine keeps $0.08
| Machine Apays often | Machine Bpays rarely | |
|---|---|---|
| What it returns | 92% | 92% |
| Pays something on | 30% of spins | 5.1% of spins |
| So a paying spin comes about every | 3.3 spins | 19.6 spins |
| And when it pays, it hands back about | 3.1× the stake | 18× the stake |
Machine B pays on fewer spins, so each payment it makes has to be bigger. What it returns is untouched by it.
The share of spins that pay has a name in the trade, hit frequency, and you will not find that name written anywhere in a casino. Volatility is the trade’s word for both halves at once: how big the payments are, and how many spins apart they come. One provincial operator puts it in a single sentence:
The size and frequency of payouts are determined by a game’s volatility. Some games have small, frequent payouts while others pay out big wins at much less regular intervals.
Another operator describes the same thing without using the word:
Did you know that not all slot machines and VLTs are the same? Some pay smaller prizes more often and have more bonus games, while others pay out more in the middle or top prize categories.
Four real machines at a casino in Ontario paid on 4.9% to 16.7% of spins. Here are the two ends of that band beside machine A and machine B:
| Pays something on | Average payment needed to return 92% | |
|---|---|---|
| The least frequent of four real machines | 4.9% of spins | 18.8× the stake |
| Machine Bpays rarely | 5.1% of spins | 18× the stake |
| The most frequent of the four real machines | 16.7% of spins | 5.5× the stake |
| Machine Apays often | 30% of spins | 3.1× the stake |
The more often a machine pays, the smaller each payment has to be. Machine B sits inside the band; machine A pays far more often. Real machines get into the band partly by counting a payment smaller than the bet as a payment, and machine A and machine B never pay less than the bet. That is lesson 5 of this track.
Now the half you can check for yourself at a real machine. What a combination pays is on the machine before you put money in:
All paytable awards, Game rules, feature information, and automatic selection behaviour rules must be available to the player prior to the player committing a Bet.
- Printed on the machine before you betwhat every combination pays — the pay tablethe rules of the gamewhat each feature does
- Not printed anywhere you can reachhow often each combination landswhat the machine returns over its lifetime (lesson 2)
The same price per spin, a different evening
Sit down at machine A with $50, at $1 a spin, for an hour, and then do the same at machine B. The hour costs the same on average on both:
The price of the hour is the bet, times the spins in the hour, times the share the machine keeps; how often the machine pays is not in that multiplication. The hour around that average does not look the same at all.
Where eight hours in ten end, at $1 a spin. The upright mark is level with the $50 you sat down with: to its right the hour ended with more than you brought, to its left with less.
Machine A keeps the evening inside a corridor $108 wide. Machine B throws the evening across $652, and most of that width comes from one line of its pay table: whether the payment of 320 times the stake landed during the hour or did not.
Machine A, pays often
43 minutes of machine time from the $50, on average
Machine B, pays rarely
18 minutes of machine time from the $50, on average
Machine A keeps handing small amounts back, so the $50 goes down in steps; machine B pays on fewer spins, so between payments the $50 goes down in a straight line. One operator says the second half of that plainly:
Machines with bigger jackpots tend to have less frequent payoffs and will deplete your bankroll faster
A machine that empties the $50 sooner is not a machine that costs more. Over the hour machine B takes less money from you on average than machine A does, and only because the $50 is gone sooner on machine B, so less of it ever goes through the machine. Per spin actually played, machine A and machine B take the same 8% of everything staked.
Machine A, pays often
12.2% of hours end with more money than you brought
Machine B, pays rarely
41.5% of hours end with more money than you brought
Leoformer dealer · rules and maths
Here is the part people refuse to believe: machine B ends more hours ahead than machine A and still costs exactly the same per spin. So “the machine that swings harder is the worse machine” is simply false. What you choose with machine B is how far the hour can land from where it started, in both directions.
What the last ten games can tell you
Every machine can show you its last ten games:
All Gaming Devices must have the capacity to display a complete Play history for the most recent Game played and nine Games prior to the most recent Game.
The last ten games on the machine: game paid nothing, game paid 2 times the stake, game paid nothing, game paid nothing, game paid 6 times the stake, game paid nothing, game paid 2 times the stake, game paid nothing, game paid nothing, game paid nothing.
Three of ten games paid, and all three payments were small: machine A, the one that pays often, in its ordinary rhythm.
The last ten games on the machine: game paid nothing, game paid nothing, game paid nothing, game paid nothing, game paid nothing, game paid nothing, game paid nothing, game paid nothing, game paid nothing, game paid nothing.
Ten games with nothing at all. Ten blank games in a row happen 2.8% of the time on machine A and 59.2% of the time on machine B.
Ten games are enough to tell machine A from machine B, because they are far apart on how often they pay.
What the machine returns hides much better than how often it pays. Sit at either machine for a full hour, 600 spins, and count what happens:
| After 600 spins you know | Machine Apays often | Machine Bpays rarely |
|---|---|---|
| How often it pays | 30% of spins, give or take 3.7 points | 5.1% of spins, give or take 1.8 points |
| What it returns | anywhere from 83% to 101% | anywhere from 50% to 158.7% |
The last ten games are honest about how often the machine pays and silent about what it returns.
What differs online in Ontario
Volatility lives in the pay table, so a game on a screen swings the way a machine in a room does. Neither of Ontario’s two sets of standards puts a floor or a ceiling on it, and neither makes anyone state it. What differs between a room and a screen is what has to be written down:
| A machine in a room | A game on a screen | |
|---|---|---|
| What each combination pays | On the machine, before you bet | Before you bet, one of three things: the odds of a prize, the payout odds, or the return to players |
| How often each combination lands | Not required anywhere | Written into the game’s specification, as the odds of each prize — and a return figure before the bet satisfies the rule without ever showing it to you |
| How long the odds on a single payout may be | No longer than a stated ceiling, unless those odds are disclosed to you | No ceiling |
| A volatility rating for the game | Nobody publishes one | Nobody publishes one |
The internet gaming standard says the two things in its own words. First, what the game must have on paper:
Odds of winning for each prize available to players
Then, what the player must be told before a bet:
contain comprehensive, accurate and understandable information on the odds of winning, payout odds, or returns to players
That “or” is why a site can meet the rule with a single return figure and never show you the odds of each prize. And neither a room nor a site hands you a volatility rating for a single game, because nobody publishes one.
Practice: same price, different ride
A slot machine gives you nothing to decide once the button is down: the outcome is drawn before the reels move. Everything you actually choose happens before that — which machine to sit at, how big a bet to make, and what to make of the last ten games on the screen in front of you. Those three choices are the practice. There is no balance, no spin button and no reels: the lesson is one run, every square on the strip is one moment of it, and when a level’s squares are full the next level begins by itself.
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Level 1 · Which machine
Machine A and machine B both return 92%. You have $50 and half an hour.
Machine Apays often
Returns 92%, paying on 30% of spins.
Machine Bpays rarely
Returns 92%, paying on 5.1% of spins.
You would rather still be playing when the half hour is up. Which machine do you sit at?
The answer: Machine A.
- Machine A Machine A pays small amounts often, so the money keeps coming back a little at a time while the machine takes it, and the $50 walks down in steps. On machine A the $50 is still there at the end of 71.9% of half hours; on machine B, 13.9% of half hours.
- Machine B Machine B can hand back 320 times the stake, and when that payment lands the evening starts over. It lands on 0.1% of spins, and the question was whether the $50 survives half an hour.
- Either — they return the same Machine A and machine B do return the same, and a spin costs the same on both. How long the $50 lasts is a different question, and machine A and machine B answer it differently.
What a machine returns and how often it pays are set separately. Machine A pays something about every 3.3 spins and machine B about every 19.6 spins, and how often the machine pays is what decides how long the $50 lasts.
Level 2 · How big a bet
Machine B, $50 in the machine, $1 a spin.
Machine Bpays rarely
Returns 92%, paying on 5.1% of spins.
You double the bet to $2. What happens to the share of hours that end with more than you brought?
The answer: Nothing: it stays 41.5%.
- Nothing: it stays 41.5% Every share in this lesson — how often machine B pays, how often an hour on it ends with more than you brought — comes from the pay table, and doubling the bet does not touch the pay table.
- It doubles Then a big enough bet would put every hour in front. What doubles is the dollars, not the shares.
- It halves Nothing about the odds moved. The same spins come up in the same proportions.
The bet multiplies the dollars. It leaves every share exactly where it was.
Level 3 · Read the screen
The last ten games on a machine you have just walked up to.
Ten games, nothing paid.
Which of the two machines is more likely to be sitting in front of you?
The answer: Machine B.
- Machine B Ten blank games happen 59.2% of the time on machine B and 2.8% of the time on machine A. Ten blank games are not proof, but they are a strong lean towards machine B.
- Machine A Machine A pays on 30% of spins; ten blanks in a row is a 2.8% event on machine A. Possible, and much the rarer of the two.
- Equally likely Only if machine A and machine B paid at the same rate. Machine A pays about six times as often as machine B, and ten blank games is exactly where that difference shows.
The last ten games are honest about how often a machine pays, and they say nothing about what it returns.
How the practice table works
One strip, no rounds. Every square is one moment, and all the squares are there from the start. A square keeps your first answer on that moment: right first time, or a mistake. When a level’s squares are full the next level begins with no button in between, and the level buttons above are all live if you would rather jump.
Practice. Each mistake goes on a list. Practising deals those moments again; answering a moment right takes it off the list and turns its cross into “fixed in practice”. Only your first answer counts towards the score.
What the machines are. Machine A and machine B are teaching machines, and both pay tables are on the page in full. Every figure in the practice comes from the same two pay tables and the same engine that runs our How long will it last? tool. Level 1: eight moments in front of two pay tables. Level 2: five moments on one machine at two bet sizes. Level 3: seven moments with the last ten games.
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.
And the question at the start
All three answers had something right in them, which is why the question was worth asking. “Either machine, they return the same” is right about the price: a spin costs the same on machine A as on machine B, and no amount of waiting changes that. It is wrong that the choice makes no difference: the same $50 lasts about 43 minutes on machine A and about 18 minutes on machine B, and the hour lands somewhere inside $108 on machine A and somewhere inside $652 on machine B. “Machine A, the money will last” and “Machine B, that is where the big payments are” are each half of that, stated as if it were the whole.
Before you sit down
Mayaformer floor supervisor · manners, money and breaks
A machine that pays often feels cheaper than a machine that pays rarely. It is not, and the feeling is usually what decides how long you stay.
So decide the minutes and the money before you sit down, not at the machine — Game plan walks you through it. And if a bad stretch starts to feel like something the machine owes you back, that is the moment to stand up and call one of the lines below. Day or night, they answer.
If it stops being fun
If gambling stops being entertainment, help is available. 19+ in most of Canada; 18+ in Alberta, Manitoba and Quebec. More on responsible gaming.
Where this leads
19+ (18+ in AB, MB, QC) · Play responsibly · the helplines for every province are above
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.
- PAR sheets, probabilities, and slot machine play · Harrigan & Dixon, PAR sheets, probabilities, and slot machine play, 23:81–110 (2009)The four machines whose pay tables were read out of the manufacturers’ sheets, and where the 4.9% to 16.7% band comes from.
How it’s worked out
The machines, the numbers and the hosts
Where this sits. Lesson 3 of the slots track takes as read what a spin costs and what return to player means, which are lessons 1 and 2, and asks what is left to choose between two machines that return exactly the same.
The machines. Machine A and machine B are teaching machines of ours, declared in full on this page and nowhere else. Their returns are asserted in the code rather than typed into the text: if a pay table were edited so that it no longer came to 92%, this page would refuse to build rather than print a different figure. Real machines are not like this in one respect that matters here: their reel weightings are not published, and researchers get theirs through freedom-of-information requests, which is why our own How long will it last? offers no slot machine at all.
The numbers. Everything about the machines themselves — the return, the share of spins that pay, the average payment, the money each line of the pay table brings back — is worked out by going through the whole pay table, every line of it. Everything about the evening is worked out by the engine behind that tool: every possible hour-long total counted exactly rather than simulated, and the bankroll run with a spin starting only when a whole bet is left. The band on an hour is the middle eight tenths of that distribution, taken from the distribution itself and not from a standard deviation: on machine B the whole shape of the night is one question, and a symmetrical interval would misdescribe it. “One spin in three” and “one spin in twenty” are the exact figures in the tables rounded to whole spins.
The band of real machines. Four machines at a casino in Ontario, measured and published in a research journal. It is four machines, not a figure for the country: no operator we could read publishes a hit frequency at all, for any game. The average payment printed beside each edge of that band is not a measured figure; it is what a machine paying that often would have to hand back each time to return 92%.
Hosts. Leo and Maya are illustrated characters. Their backstories, a former dealer and a former floor supervisor, are written for the course: neither is a real person, and neither speaks for any casino. The rules and numbers on this page come from the sources it cites, not from their experience.
No promise. Slot machines are played against the house, and machine A and machine B both keep 8% of everything staked. Nothing here makes a machine cheap, and nothing here tells you how an evening will end.
What a machine must show before a bet
All paytable awards, Game rules, feature information, and automatic selection behaviour rules must be available to the player prior to the player committing a Bet.
Section 11.1 Rules of Play and Information Display
AGCO · Minimum Technical Standards for Gaming — 11. Game Behaviour · read
What a machine in a room must show before a bet
All paytable awards, Game rules, feature information, and automatic selection behaviour rules must be available to the player prior to the player committing a Bet.
Section 11.1 Rules of Play and Information Display
AGCO · Minimum Technical Standards for Gaming — 11. Game Behaviour · read
What an internet game must tell the player
contain comprehensive, accurate and understandable information on the odds of winning, payout odds, or returns to players
Section 4.06
AGCO · Registrar's Standards for Internet Gaming — Game Integrity · read
What an internet game specification must document
Odds of winning for each prize available to players
Section 4.05
AGCO · Registrar's Standards for Internet Gaming — Game Integrity · read
The ceiling on undisclosed odds in a room
The Top Award displayed on the Gaming Device must not have odds exceeding 17 million : 1, unless the odds of winning the award are disclosed to the player.
All other awards displayed on the Gaming Device must not have odds exceeding 34 million : 1, unless the odds of winning the award are disclosed to the player.
Section 11.10 Award Odds
AGCO · Minimum Technical Standards for Gaming — 11. Game Behaviour · read
What a machine must show before a bet
All paytable awards, Game rules, feature information, and automatic selection behaviour rules must be available to the player prior to the player committing a Bet.
Section 11.1 Rules of Play and Information Display
AGCO · Minimum Technical Standards for Gaming — 11. Game Behaviour · read
Volatility, in an operator’s own words
The size and frequency of payouts are determined by a game’s volatility. Some games have small, frequent payouts while others pay out big wins at much less regular intervals.
Loto-Québec · Wise Play — Understanding chance: Slot machines · read
Two machines are not the same machine
Did you know that not all slot machines and VLTs are the same? Some pay smaller prizes more often and have more bonus games, while others pay out more in the middle or top prize categories.
Manitoba Liquor & Lotteries · Informed Gambling — Slots and VLTs (brochure, February 2023) · read
Four real machines in Ontario
Worked out: the two teaching machines are enumerated in full; the return, the hit frequency and the average payment are taken from their pay tables, and the average payment at each edge of the band is the return divided by the hit frequency.
hit frequencies of the four games ranged from 4.9% to 16.7%
What a machine must show before a bet
All paytable awards, Game rules, feature information, and automatic selection behaviour rules must be available to the player prior to the player committing a Bet.
Section 11.1 Rules of Play and Information Display
AGCO · Minimum Technical Standards for Gaming — 11. Game Behaviour · read
Bigger jackpots, fewer payments
Machines with bigger jackpots tend to have less frequent payoffs and will deplete your bankroll faster
OLG PlaySmart · Slots — strategies: Make the most of your play · read
The last ten games
All Gaming Devices must have the capacity to display a complete Play history for the most recent Game played and nine Games prior to the most recent Game.
Section 11.12 Game History
AGCO · Minimum Technical Standards for Gaming — 11. Game Behaviour · read
What an internet game specification must document
Odds of winning for each prize available to players
Section 4.05
AGCO · Registrar's Standards for Internet Gaming — Game Integrity · read
What an internet game must tell the player
contain comprehensive, accurate and understandable information on the odds of winning, payout odds, or returns to players
Section 4.06
AGCO · Registrar's Standards for Internet Gaming — Game Integrity · read
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