Atlassino Academy · Slots · Lesson 3
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 units 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 units of every 1 unit staked comes back
the 6× line brings back 0.48 unitsthe 2× line brings back 0.44 unitsthe machine keeps 0.08 units
Machine B, pays rarely: 0.92 units of every 1 unit staked comes back
the 320× line brings back 0.32 unitsthe 12× line brings back 0.60 unitsthe machine keeps 0.08 units
| 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 gambling regulator puts it in a single sentence:
Most commonly the standard deviation of the game is used to represent the game’s volatility.
A highly volatile game will have a larger tolerance and might be comprised of prizes falling into the ‘very large but rare’ category.
A low volatility game will be much more predictable and mostly comprised of prizes falling into the ‘small and often’ category.
Four real machines at a casino, in the study behind these figures, 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.
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:
Los jugadores pueden aprender a jugar y conocer los premios que se pueden obtener con las jugadas a través de las instrucciones disponibles en la misma máquina de juego. Estas instrucciones deben estar siempre en idioma castellano.Free translation: Players can learn how to play and find out the prizes that can be obtained from the plays through the instructions available on the gaming machine itself. These instructions must always be in Spanish.
Tenga presente que las máquinas exigen una apuesta mínima, que puede ser mayor o igual al valor de la moneda.Free translation: Please note that the machines require a minimum bet, which may be greater than or equal to the value of the coin.
- 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 units, at 1 unit 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 unit a spin. The upright mark is level with the 50 units 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 units wide. Machine B throws the evening across 652 units, 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 units, on average
Machine B, pays rarely
18 minutes of machine time from the 50 units, on average
Machine A keeps handing small amounts back, so the 50 units goes down in steps; machine B pays on fewer spins, so between payments the 50 units goes down in a straight line. The same regulator says the second half of that plainly:
A highly volatile game will have a larger tolerance and might be comprised of prizes falling into the ‘very large but rare’ category.
A machine that empties the 50 units 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 units 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.
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. Those two 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 units 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 units walks down in steps. On machine A the 50 units 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 units 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 units 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 units lasts.
Level 2 · How big a bet
Machine B, 50 units in the machine, 1 unit a spin.
Machine Bpays rarely
Returns 92%, paying on 5.1% of spins.
You double the bet to 2 units. 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 units, not the shares.
- It halves Nothing about the odds moved. The same spins come up in the same proportions.
The bet multiplies the units. It leaves every share exactly where it was.
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. Level 1: eight moments in front of two pay tables. Level 2: five moments on one machine at two bet sizes.
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 units lasts about 43 minutes on machine A and about 18 minutes on machine B, and the hour lands somewhere inside 108 units on machine A and somewhere inside 652 units 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. And if a bad stretch starts to feel like something the machine owes you back, that is the moment to stand up and read the box below: it says where self-exclusion and the regulator are reached.
If it stops being fun
If gambling stops being fun, the SCJ self-exclusion applies in every casino in the country. Minimum entry age: 18 (age of majority under Law 19.221; Law 19.995 bars minors from gaming rooms). The casino may ask for an official ID. More on responsible gaming.
Show all regions
Where this leads
18+ across Chile · Play responsibly · self-exclusion and the regulator are above
Further reading
- Estándares para Máquinas de Azar · Superintendencia de Casinos de JuegoThe regulator’s technical standard for slot machines: the 85% minimum return, the random number generator and the ban on faking a near miss.
- Funcionamiento de los juegos: Máquinas de azar · Superintendencia de Casinos de JuegoThe regulator’s plain-language page on slot machines: instructions in Spanish, minimum bets and independent results.
- Preguntas frecuentes · Superintendencia de Casinos de JuegoThe regulator’s answer on slot odds: a minimum 85% return over about 100 million plays, and why it is not the chance of a prize.
- Catálogo de Juegos · Superintendencia de Casinos de JuegoThe national catalogue of casino games: the kinds of slot machine it names, among them multi-position machines such as electronic roulette and video versions of live games.
- PAR sheets, probabilities, and slot machine play · Kevin Harrigan and Mike Dixon, Journal of Gambling Issues (2009)What a manufacturer’s PAR sheet says about a machine: how often it pays, how much the payback swings, and the several versions of one game.
- Key terms relating to live return to player performance monitoring of games of chance · UK Gambling CommissionA regulator’s definition of volatility: the standard deviation of the game, and what “very large but rare” and “small and often” prizes mean.
- 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.
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 our own engine: 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, 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
Los jugadores pueden aprender a jugar y conocer los premios que se pueden obtener con las jugadas a través de las instrucciones disponibles en la misma máquina de juego. Estas instrucciones deben estar siempre en idioma castellano.Free translation: Players can learn how to play and find out the prizes that can be obtained from the plays through the instructions available on the gaming machine itself. These instructions must always be in Spanish.
Tenga presente que las máquinas exigen una apuesta mínima, que puede ser mayor o igual al valor de la moneda.Free translation: Please note that the machines require a minimum bet, which may be greater than or equal to the value of the coin.
Superintendencia de Casinos de Juego (SCJ) · Funcionamiento de los juegos: Máquinas de azar · read
Todas las combinaciones ganadoras y las reglas que se aplican al juego de una máquina de azar deberán estar disponibles en todo momento, aún cuando ésta se encuentre en descanso;Free translation: All winning combinations and the rules that apply to the play of a slot machine must be available at all times, even when it is idle;
Las ilustraciones artísticas deberán explicar al jugador las reglas correspondientes a la característica o bonificación, inclusive el premio grande y las alternativas de selección disponible.Free translation: The artwork must explain to the player the rules corresponding to the feature or bonus, including the top prize and the selection alternatives available.
Section 3.2.34–3.2.35 (retorno y premio máximo); 3.7.3 (contadores de la pantalla de juego); 3.8.17 (tablas de pagos); 3.8.24 (Doble o nada); 3.13 (RNG); 3.14 (funcionalidad de los progresivos); 4.2.5 (instrucciones de la tabla de pagos); 4.3.11 (características y bonificaciones)
Superintendencia de Casinos de Juego (SCJ) · Estándares para Máquinas de Azar (edición julio 2019) · read
What a machine must show before a bet
Los jugadores pueden aprender a jugar y conocer los premios que se pueden obtener con las jugadas a través de las instrucciones disponibles en la misma máquina de juego. Estas instrucciones deben estar siempre en idioma castellano.Free translation: Players can learn how to play and find out the prizes that can be obtained from the plays through the instructions available on the gaming machine itself. These instructions must always be in Spanish.
Tenga presente que las máquinas exigen una apuesta mínima, que puede ser mayor o igual al valor de la moneda.Free translation: Please note that the machines require a minimum bet, which may be greater than or equal to the value of the coin.
Superintendencia de Casinos de Juego (SCJ) · Funcionamiento de los juegos: Máquinas de azar · read
Todas las combinaciones ganadoras y las reglas que se aplican al juego de una máquina de azar deberán estar disponibles en todo momento, aún cuando ésta se encuentre en descanso;Free translation: All winning combinations and the rules that apply to the play of a slot machine must be available at all times, even when it is idle;
Las ilustraciones artísticas deberán explicar al jugador las reglas correspondientes a la característica o bonificación, inclusive el premio grande y las alternativas de selección disponible.Free translation: The artwork must explain to the player the rules corresponding to the feature or bonus, including the top prize and the selection alternatives available.
Section 3.2.34–3.2.35 (retorno y premio máximo); 3.7.3 (contadores de la pantalla de juego); 3.8.17 (tablas de pagos); 3.8.24 (Doble o nada); 3.13 (RNG); 3.14 (funcionalidad de los progresivos); 4.2.5 (instrucciones de la tabla de pagos); 4.3.11 (características y bonificaciones)
Superintendencia de Casinos de Juego (SCJ) · Estándares para Máquinas de Azar (edición julio 2019) · read
Volatility, in a regulator’s own words
Most commonly the standard deviation of the game is used to represent the game’s volatility.
A highly volatile game will have a larger tolerance and might be comprised of prizes falling into the ‘very large but rare’ category.
A low volatility game will be much more predictable and mostly comprised of prizes falling into the ‘small and often’ category.
This is an unavoidable consequence of the mathematics of the game — the in-built set of probabilities of winning different prizes, including the standard deviation (the ‘volatility’) of the game.
Productivity Commission (Australian Government) · Gambling, Inquiry Report no. 50, volume 1 (2010) · read
“VI” stands for “volatility index,” and is an indication of how much the game's payback percentage will vary for a given number of games played.
Games with a high volatility index have a larger variance in the payback percentage per gambling session than do games with a low volatility index.
Four real machines, in the study behind these figures,
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
Los jugadores pueden aprender a jugar y conocer los premios que se pueden obtener con las jugadas a través de las instrucciones disponibles en la misma máquina de juego. Estas instrucciones deben estar siempre en idioma castellano.Free translation: Players can learn how to play and find out the prizes that can be obtained from the plays through the instructions available on the gaming machine itself. These instructions must always be in Spanish.
Tenga presente que las máquinas exigen una apuesta mínima, que puede ser mayor o igual al valor de la moneda.Free translation: Please note that the machines require a minimum bet, which may be greater than or equal to the value of the coin.
Superintendencia de Casinos de Juego (SCJ) · Funcionamiento de los juegos: Máquinas de azar · read
Todas las combinaciones ganadoras y las reglas que se aplican al juego de una máquina de azar deberán estar disponibles en todo momento, aún cuando ésta se encuentre en descanso;Free translation: All winning combinations and the rules that apply to the play of a slot machine must be available at all times, even when it is idle;
Las ilustraciones artísticas deberán explicar al jugador las reglas correspondientes a la característica o bonificación, inclusive el premio grande y las alternativas de selección disponible.Free translation: The artwork must explain to the player the rules corresponding to the feature or bonus, including the top prize and the selection alternatives available.
Section 3.2.34–3.2.35 (retorno y premio máximo); 3.7.3 (contadores de la pantalla de juego); 3.8.17 (tablas de pagos); 3.8.24 (Doble o nada); 3.13 (RNG); 3.14 (funcionalidad de los progresivos); 4.2.5 (instrucciones de la tabla de pagos); 4.3.11 (características y bonificaciones)
Superintendencia de Casinos de Juego (SCJ) · Estándares para Máquinas de Azar (edición julio 2019) · read
Bigger jackpots, fewer payments
A highly volatile game will have a larger tolerance and might be comprised of prizes falling into the ‘very large but rare’ category.
Varying the probability of different pictures on the slot machines means that they can have virtually any possible prize structure, including many small to medium prizes with rare huge jackpots.
the jackpot prize could be as rare as 1 in 137 million