Atlassino Academy · Slots · Lesson 8
Due, hot, cold and the stop button
What people do when an hour at a machine has given back next to nothing — and what that hour tells you about the next spin.
A machine has taken your money for forty minutes and given you next to nothing back. Is it closer to paying now than it was when you sat down?
The short answer
No. The chance on the spin you are about to make is the chance the machine gave your first spin, and the chance it gave every spin in between. What forty minutes of pressing changed is your own pressing and nothing else: how many spins you have made, and how much of your money those spins have sent through the machine.
- Spins you made in forty minutes400at 600 spins an hour
- Your money through the machine400 unitson a 1 unit spin
- The chance on your next spinunchangedthe same chance the machine gave your first spin
Mayaformer floor supervisor · manners, money and breaks
“It’s due.” “It’s hot.” “It’s cold.” “You have to press it at the right moment.” I have heard all four of those sayings out loud on the floor, and almost never from somebody being silly. You sit in one place for an hour watching the same thing happen, and your head starts hunting for the pattern. That is what heads are for. A slot machine simply is not the kind of object that has a pattern in it.
So this is not about being wrong, and I am not going to tell you the thought is foolish. What I can tell you is what the thought costs, and the cost is not luck and not a jinx. The cost is the extra spins you make while you wait for the machine to do what you have decided it owes you, and the money those extra spins send through the machine.
Four things people say, and the one belief under all four
“It’s due”, “it’s hot”, “it’s cold” and “you have to press it at the right moment” sound like four different claims about four different situations. All four sayings say one and the same thing: that the machine is in some state right now, that the state is either good for you or bad for you, and that you can read which state it is in from what the machine has just been doing.
| What gets said | What it claims | What is there |
|---|---|---|
| “It’s due” | the quiet stretch is building towards something | nothing is stored |
| “It’s hot” | a payout makes the next one likelier | nothing is stored |
| “It’s cold” | a payout makes the next one further off | nothing is stored |
| “Press it right” | the moment of the press can be aimed | the result is already picked |
A machine on this floor is not allowed to announce a next payout on its screen: the rule gives the example of three times the payout that is about to appear. The rule is not a verdict on the people who say “it’s due” out loud at a machine. It is there because the thought behind it is so reliable that a machine could be built to feed it, and a machine that announced the next payout would be selling you a state the machine does not have.
There are no hot machines and no cold ones, and sitting at one machine longer does not improve the odds on any spin of that machine. The machine takes the same amount on the spin you make in the fortieth minute as it took on the spin you made in the first minute, and what it is taking is your credits (what a machine counts your money in on screen, which is not the same as cash until you cash out).
The climbing line is what people picture when they say a machine is due; the flat line is what a machine actually draws.
Leoformer dealer · rules and maths
I dealt cards rather than fixing machines, but I walked past the same rows every shift. What you notice from the aisle is that the quiet machines and the loud ones swap places all evening long, and nobody walking that aisle can tell you which machine will be the loud one a minute from now. Neither can the person already sitting at that machine, and that person is closer to it than anybody else in the building.
What an hour with nothing back actually looks like
Take two machines that give back the same share of everything staked over their lifetimes, and let them do it at two different rhythms. The machine that pays often gives back small amounts many times an hour; the machine that holds its money back gives nothing at all for long stretches and then one large payout. Neither machine is real: both are written out one possible result at a time, which is what makes every figure about the two machines something to be worked out rather than guessed at.
| Teaching machine | How often a spin pays | Longest stretch with nothing back, in a typical hour | Chance the next spin pays, after 100 spins with nothing back |
|---|---|---|---|
| The machine that pays often | 30.0% | 15 spins | 30.0% |
| The machine that holds its money back | 5.1% | 72 spins | 5.1% |
How often a spin pays and the chance after a hundred spins with nothing back come out the same: those hundred spins leave the machine exactly where it started.
On the machine that holds its money back, a stretch of 72 spins with nothing back is the middle of an hour rather than the bad end of it: half of all hours on that machine contain a dead stretch at least that long.
- 50 spins in a row with nothing back93.0%of hours on that machine hold a stretch at least that long
- 72 spins in a row with nothing back50.5%of hours on that machine hold a stretch at least that long
- 100 spins in a row with nothing back13.5%of hours on that machine hold a stretch at least that long
- 150 spins in a row with nothing back0.9%of hours on that machine hold a stretch at least that long
The machine you walked away from, and the award somebody else took
The version of the belief that hurts most — the belief that a machine carries something forward from one spin to the next — is not something people say while they are still playing. It is what they say afterwards. You stand up after two hours at a machine, somebody else sits down in the seat you have just left, and three spins later that person takes the largest award the machine has.
The spin you would have taken
A press made at the instant your own thumb would have chosen, with the largest award standing at 1 in 262,144 on that press.
The spin the next player took
A press made at the instant the next player’s thumb chose, three spins after sitting down, with the largest award standing at 1 in 262,144 on that press as well — and on that press the three symbols came up.
One machine, and two presses made at two different instants. What changes from picture to picture is the instant the button went down and the symbols that instant brought up on the payline. What does not change is the machine — three reels of 64 symbols, with the symbol that matters appearing once on each reel — and the chance of the largest award, which stands at the same figure under both pictures. Standing up did not hand the next player an award that had been waiting for you: standing up changed which instants got pressed, and a press a thousandth of a second apart is a different spin, not the same spin caught better or caught worse.
The belief that a machine carries something forward runs just as often in reverse: the machine has paid heavily, so it must be empty now. A machine that has just paid out a large jackpot can pay another large jackpot on the very next spin. Nothing was taken out of a store when the machine paid, because there is no store inside a machine to take anything out of.
What people picture inside a machine
A store that fills up while the machine is quiet and drains when the machine pays, so that a long quiet stretch leaves a full store waiting for whoever sits down next.
What is actually inside a machine
A program that keeps every result the machine can produce available at the start of each game. One result is drawn at each press, and the program is exactly the same after that draw as it was before it.
And the explanation people reach for when a good stretch ends is that the machine adjusted itself to what it has just paid. A game may not do that for its bonus: it may not change the chance of a bonus on the strength of the payouts before it, so that games do not adapt their theoretical return to the player from earlier payments. And every combination that can pay or lose has to be available for random selection at the start of each game.
The number generator inside the machine ran through the whole of your two hours, and through every idle minute before you arrived, and it kept no score of any of it.
Practice: read the machine
A machine has no decision left in it once the button is down, so not one of these moments asks you to spin a machine. Each moment asks about the three things you really do decide — which machine you sit at, what you stake, when you get up — and then it checks the reason you gave for deciding, because at a machine the reason is the only part of a decision that anybody can check.
The lesson is one run: every square on the strip below is one moment of it, and they are all there from the start. Level 1 is the button alone. Level 2 is what you do after a machine pays somebody else. Only your first answer on each moment counts, and when a level’s squares are full the next one begins by itself, with no button in between.
Nothing here keeps a balance, pays credits or makes a sound. There is no money in it at all.
Lesson done
Review my mistakes (0)
Progress stays in this browser; nothing is sent anywhere.
The practice table needs JavaScript. Here is one moment from it, with the answer.
Level 1 · The button
The button · you stopped the reels yourself
- The machine
- a reel machine, one payline
- This spin
- already picked, still turning
- You did
- held the button down until the reels snapped still
The reels snap still the moment you hold the button down. What did that change?
The answer: How long I watched, and nothing else.
The button shortens the show. The result it shows you was picked at the start of the game, and the machine may not make a second decision that changes it.
Tras la selección del resultado de la partida, la máquina de juego no hará una decisión secundaria variable, que afecte el resultado mostrado al jugador; por ejemplo, el generador de números aleatorios opta por un resultado donde la partida se perderá.Free translation: After the game outcome has been selected, the gaming machine shall not make a variable secondary decision that affects the outcome shown to the player; for example, the random number generator opts for an outcome in which the game will be lost.
IPLyC Buenos Aires (Sistema de Normas) · Resolución 705/13: requisitos para máquinas electrónicas de juegos de azar · section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4) · readLevel 2 · The one you left
Afterwards · the seat you gave up
- You
- stood up after an hour
- The next player
- took the largest award three spins later
You stood up, someone sat down, and three spins later they took the largest award. Do you go back to it?
The answer: Go back or not, but not because of that spin.
Leaving changed which spin got taken, not whether one paid. The chance on that spin was 1 in 262,144 for them and would have been 1 in 262,144 for you.
El generador de números aleatorios deberá funcionar en un ciclo continuo como fondo (background) entre las partidas y durante las jugadas a una velocidad, que no pueda ser cronometrada por el jugador.Free translation: The random number generator must operate in a continuous cycle in the background between games and during plays at a speed that cannot be timed by the player.
IPLyC Buenos Aires (Sistema de Normas) · Resolución 705/13: requisitos para máquinas electrónicas de juegos de azar · section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4) · readEvery moment is worked out the same way. The machines are teaching machines, enumerated in full: the run lengths come from the same arithmetic as our streaks tool, and the largest award is three reels of 64 with the symbol once on each. The workings are in “How it’s worked out” at the end of this page.
How the practice table works
What is being marked. The action is not marked; the reason is. Staying, moving and stopping are all fine, and more than one answer to a moment can be right — “I would rather play the other machine” counts, because a preference is not a claim about chance. What does not count is a reason read off the strip of past games.
Where the machines come from. They are ours, and the page says so wherever their figures appear. No operator we could read publishes how often a real machine pays, so every run length here is worked out from a teaching machine we enumerate in full, using the same arithmetic as our streaks tool.
One strip, no rounds. Every square is one moment of this lesson, and your first answer fills it. Practising a mistake turns a cross into “fixed in practice” and does not change the count. Progress stays in this browser; nothing is sent anywhere.
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.
The question we opened with. The machine is not closer to paying than it was forty minutes ago. Forty minutes that leave you with next to nothing to show for them is one of the ordinary shapes forty minutes at a machine takes, and the machine has no way of knowing those forty minutes happened at all. What those forty minutes did settle is how much of your money went through the machine, and that figure is the one that keeps climbing for as long as you sit there.
Where to check this
18+ under each province’s rules · Play responsibly · the helplines for every province are at the end of this page
Further reading
- Resolución 705/13: requisitos para máquinas electrónicas de juegos de azar · Instituto Provincial de Lotería y Casinos de la Provincia de Buenos AiresThe technical rules a machine must meet: independent random draws, no “near miss” tricks, a minimum payout set by law.
- Resolución 00296-P/2023: Reglamento de Salas Tragamonedas · Instituto de Juegos y Casinos de Jujuy (InProJuy)Jujuy’s slot-room rules: a theoretical return of at least 90 %, and what a machine must display.
- 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.
Mayaformer floor supervisor · manners, money and breaks
If you take one thing away, take this: believing a machine is due never changes the odds on a single spin, so the only way the belief can reach your evening is through the clock and through the money going into the machine while you wait. That is what makes it easy to handle. Decide the hour while you are still at home, and “it has to be close by now” stops being an argument you are obliged to answer at two in the morning.
And if the pull to stay is the loud part of your evening rather than a passing thought, that is worth talking to somebody about. The lines below are for exactly that.
If it stops being fun
If gambling stops being entertainment, help is available. Minimum entry age: each province sets its own. Where we found the rule or regulator that sets it, we cite it on the page; those we found set it at 18. More on responsible gaming.
Show all provinces
If you are thinking about suicide, call 135 or 0800 345 1435 from anywhere in the country
How it’s worked out
Sources, numbers and hosts
Sources. Every quoted rule and every operator’s sentence on this page sits behind the source button next to it, with its publisher, the section it comes from and the date we read it. Rules written by a province’s regulator are quoted as that, and not as a statement about any single casino.
Numbers. None of the figures here describes a real machine, and none of them could: no operator or regulator we read publishes how often a machine pays. The two teaching machines are ours, enumerated result by result, built to return the same share over their lifetimes and to do it at different rhythms. Run lengths come from the same function that powers our streaks tool, as an exact calculation rather than a simulation. The pace figures — 600 spins an hour, and about half as many again with the stop button — come from a published study of machines, not from an operator.
What the money columns are. They are turnover: money that passes through the machine. They are not what an evening costs on average, which is a different quantity and a different lesson.
Hosts. Maya and Leo are illustrated characters. Their backstories, a former floor supervisor and a former dealer, 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. Nothing on this page says an evening at a machine is a good idea for you, and nothing here suggests any way of coming out ahead. Every belief it takes apart is one that costs money to hold; none of them is replaced by a better one, because there is no better one.
When the result of a spin is chosen
Tras la selección del resultado de la partida, la máquina de juego no hará una decisión secundaria variable, que afecte el resultado mostrado al jugador; por ejemplo, el generador de números aleatorios opta por un resultado donde la partida se perderá.Free translation: After the game outcome has been selected, the gaming machine shall not make a variable secondary decision that affects the outcome shown to the player; for example, the random number generator opts for an outcome in which the game will be lost.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
Machines are never due
El uso de un generador de números aleatorios resultará en la selección de símbolos de la partida o la producción de resultados de las partidas. La selección deberá: * Ser estadísticamente independiente; * Cumplir con la distribución aleatoria deseada; * Pasar varias pruebas estadísticas reconocidas; * Ser impredecible.Free translation: The use of a random number generator shall result in the selection of the game's symbols or the production of the game's results. The selection shall: * Be statistically independent; * Meet the desired random distribution; * Pass several recognized statistical tests; * Be unpredictable.
El juego no deberá ajustar la probabilidad de que ocurra una bonificación, basándose en el historial de premios obtenidos en partidas previas (esto es, los juegos no adaptarán su ganancia teórica al jugador basándose en pagos previos);Free translation: The game must not adjust the probability of a bonus occurring based on the history of prizes obtained in previous games (that is, games shall not adapt their theoretical gain to the player based on previous payouts);
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
No announcement of the next payout
El juego no deberá publicar “próximas ganancias”, por ejemplo tres (3) veces el pago próximo a aparecer.Free translation: The game must not display “upcoming wins”, for example three (3) times the next payout to appear.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
A large payout can repeat
El uso de un generador de números aleatorios resultará en la selección de símbolos de la partida o la producción de resultados de las partidas. La selección deberá: * Ser estadísticamente independiente; * Cumplir con la distribución aleatoria deseada; * Pasar varias pruebas estadísticas reconocidas; * Ser impredecible.Free translation: The use of a random number generator shall result in the selection of the game's symbols or the production of the game's results. The selection shall: * Be statistically independent; * Meet the desired random distribution; * Pass several recognized statistical tests; * Be unpredictable.
El juego no deberá ajustar la probabilidad de que ocurra una bonificación, basándose en el historial de premios obtenidos en partidas previas (esto es, los juegos no adaptarán su ganancia teórica al jugador basándose en pagos previos);Free translation: The game must not adjust the probability of a bonus occurring based on the history of prizes obtained in previous games (that is, games shall not adapt their theoretical gain to the player based on previous payouts);
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
No hot and no cold machines
El uso de un generador de números aleatorios resultará en la selección de símbolos de la partida o la producción de resultados de las partidas. La selección deberá: * Ser estadísticamente independiente; * Cumplir con la distribución aleatoria deseada; * Pasar varias pruebas estadísticas reconocidas; * Ser impredecible.Free translation: The use of a random number generator shall result in the selection of the game's symbols or the production of the game's results. The selection shall: * Be statistically independent; * Meet the desired random distribution; * Pass several recognized statistical tests; * Be unpredictable.
El juego no deberá ajustar la probabilidad de que ocurra una bonificación, basándose en el historial de premios obtenidos en partidas previas (esto es, los juegos no adaptarán su ganancia teórica al jugador basándose en pagos previos);Free translation: The game must not adjust the probability of a bonus occurring based on the history of prizes obtained in previous games (that is, games shall not adapt their theoretical gain to the player based on previous payouts);
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
A different instant is a different spin
El generador de números aleatorios deberá funcionar en un ciclo continuo como fondo (background) entre las partidas y durante las jugadas a una velocidad, que no pueda ser cronometrada por el jugador.Free translation: The random number generator must operate in a continuous cycle in the background between games and during plays at a speed that cannot be timed by the player.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
The generator never stops
El generador de números aleatorios deberá funcionar en un ciclo continuo como fondo (background) entre las partidas y durante las jugadas a una velocidad, que no pueda ser cronometrada por el jugador.Free translation: The random number generator must operate in a continuous cycle in the background between games and during plays at a speed that cannot be timed by the player.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
No announcement of the next payout
El juego no deberá publicar “próximas ganancias”, por ejemplo tres (3) veces el pago próximo a aparecer.Free translation: The game must not display “upcoming wins”, for example three (3) times the next payout to appear.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
No hot and no cold machines
El uso de un generador de números aleatorios resultará en la selección de símbolos de la partida o la producción de resultados de las partidas. La selección deberá: * Ser estadísticamente independiente; * Cumplir con la distribución aleatoria deseada; * Pasar varias pruebas estadísticas reconocidas; * Ser impredecible.Free translation: The use of a random number generator shall result in the selection of the game's symbols or the production of the game's results. The selection shall: * Be statistically independent; * Meet the desired random distribution; * Pass several recognized statistical tests; * Be unpredictable.
El juego no deberá ajustar la probabilidad de que ocurra una bonificación, basándose en el historial de premios obtenidos en partidas previas (esto es, los juegos no adaptarán su ganancia teórica al jugador basándose en pagos previos);Free translation: The game must not adjust the probability of a bonus occurring based on the history of prizes obtained in previous games (that is, games shall not adapt their theoretical gain to the player based on previous payouts);
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
A different instant is a different spin
El generador de números aleatorios deberá funcionar en un ciclo continuo como fondo (background) entre las partidas y durante las jugadas a una velocidad, que no pueda ser cronometrada por el jugador.Free translation: The random number generator must operate in a continuous cycle in the background between games and during plays at a speed that cannot be timed by the player.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
A large payout can repeat
El uso de un generador de números aleatorios resultará en la selección de símbolos de la partida o la producción de resultados de las partidas. La selección deberá: * Ser estadísticamente independiente; * Cumplir con la distribución aleatoria deseada; * Pasar varias pruebas estadísticas reconocidas; * Ser impredecible.Free translation: The use of a random number generator shall result in the selection of the game's symbols or the production of the game's results. The selection shall: * Be statistically independent; * Meet the desired random distribution; * Pass several recognized statistical tests; * Be unpredictable.
El juego no deberá ajustar la probabilidad de que ocurra una bonificación, basándose en el historial de premios obtenidos en partidas previas (esto es, los juegos no adaptarán su ganancia teórica al jugador basándose en pagos previos);Free translation: The game must not adjust the probability of a bonus occurring based on the history of prizes obtained in previous games (that is, games shall not adapt their theoretical gain to the player based on previous payouts);
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
A game may not adapt to earlier payouts
El uso de un generador de números aleatorios resultará en la selección de símbolos de la partida o la producción de resultados de las partidas. La selección deberá: * Ser estadísticamente independiente; * Cumplir con la distribución aleatoria deseada; * Pasar varias pruebas estadísticas reconocidas; * Ser impredecible.Free translation: The use of a random number generator shall result in the selection of the game's symbols or the production of the game's results. The selection shall: * Be statistically independent; * Meet the desired random distribution; * Pass several recognized statistical tests; * Be unpredictable.
El juego no deberá ajustar la probabilidad de que ocurra una bonificación, basándose en el historial de premios obtenidos en partidas previas (esto es, los juegos no adaptarán su ganancia teórica al jugador basándose en pagos previos);Free translation: The game must not adjust the probability of a bonus occurring based on the history of prizes obtained in previous games (that is, games shall not adapt their theoretical gain to the player based on previous payouts);
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
Every outcome is available at the start of the game
Cada posible permutación o combinación de elementos de juego que produzcan resultados ganadores o perdedores deberán estar disponibles para la selección aleatoria al inicio de cada partida, a menos que se describa de otra manera en el juego;Free translation: Each possible permutation or combination of game elements that produce winning or losing outcomes must be available for random selection at the start of each game, unless otherwise described in the game;
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
The generator never stops
El generador de números aleatorios deberá funcionar en un ciclo continuo como fondo (background) entre las partidas y durante las jugadas a una velocidad, que no pueda ser cronometrada por el jugador.Free translation: The random number generator must operate in a continuous cycle in the background between games and during plays at a speed that cannot be timed by the player.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
Every outcome is available at the start of the game
Cada posible permutación o combinación de elementos de juego que produzcan resultados ganadores o perdedores deberán estar disponibles para la selección aleatoria al inicio de cada partida, a menos que se describa de otra manera en el juego;Free translation: Each possible permutation or combination of game elements that produce winning or losing outcomes must be available for random selection at the start of each game, unless otherwise described in the game;
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
When the result of a spin is chosen
Tras la selección del resultado de la partida, la máquina de juego no hará una decisión secundaria variable, que afecte el resultado mostrado al jugador; por ejemplo, el generador de números aleatorios opta por un resultado donde la partida se perderá.Free translation: After the game outcome has been selected, the gaming machine shall not make a variable secondary decision that affects the outcome shown to the player; for example, the random number generator opts for an outcome in which the game will be lost.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)
The generator never stops
El generador de números aleatorios deberá funcionar en un ciclo continuo como fondo (background) entre las partidas y durante las jugadas a una velocidad, que no pueda ser cronometrada por el jugador.Free translation: The random number generator must operate in a continuous cycle in the background between games and during plays at a speed that cannot be timed by the player.
Section Requisitos de la máquina de juego, software: reglas de juego, generador de números aleatorios, porcentajes de pago, juegos con bonificación (4-1 a 4-4)