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Atlassino Academy · How casinos work · Lesson 4

Do cards, dice and wheels remember?

Whether the last spin, roll or card changes the next one — and why the honest answer is different for a shoe of cards than for a wheel.

  • About 22 minutes
  • Illustrated hosts: Leo and Maya
  • Last checked 18 October 2026

A roulette wheel has come up red eight times in a row. The player beside you doubles his bet on black.

Before we start: what would you do?

Nothing is scored here. We come back to it at the end.

The short answer

A wheel and a pair of dice carry nothing at all into the next round: red is still 18 of 37 pockets after eight reds, and a seven is still 6 of 36 combinations after ten rolls without one. A shoe of cards is the one exception on the whole casino floor, because a card that has been dealt stays out of the shoe until the shuffle. What moves the share of ten-cards left in a shoe is which cards have gone into the discard tray, and never how many of them have gone.

A single-zero wheelEight reds in a row

The chance of red before the run started
48.6%
The chance of red on the next spin
48.6%

The eight reds carried nothing over.

Two diceTen rolls with no seven

The chance of a seven before those ten rolls
16.7%
The chance of a seven on the next roll
16.7%

The ten rolls carried nothing over.

A shoe of 8 decksTwenty cards out, not one of them a ten-card

The share of ten-cards before those twenty left
30.8%
The share of ten-cards among the cards left now
32.3%

The twenty cards themselves carried over: they are out of the shoe until the shuffle.

Leo turns an open palm toward a clear discard tray half filled with face-down cards while Maya stands beside the card shoe at the other end of the same empty table.
Leo smiling, explaining with an open hand.

Leoformer dealer · rules and maths

I dealt cards for years, and the question I heard most was this one: is it due? For the wheel, the dice and the machine the answer is a short no. For the shoe of cards it is not a flat no.

You do not need to know how roulette, craps or blackjack is played to follow any of it, because every answer here is a count of what is sitting in front of you. Three tables in a row: I count the wheel out loud, we count the dice together, and the shoe is yours to count.

Three tables, worked through

One: the wheel

Eight reds in a row. What are the chances of red on the next spin?

The wheel
37 pockets: 18 red, 18 black and 1 green one
The board
the last 8 results, oldest first: red, red, red, red, red, red, red, red
This spin
not spun yet
The board above the wheel, with the eight reds on it. The wheel itself has read the same all evening.
Leo pointing at a chart with an open hand.

Leoformer dealer · rules and maths

Count what is in front of you, not what has already happened. A single-zero wheel has 37 pockets: 18 red, 18 black and 1 green. Red is 18 pockets of 37 — 48.6%.

Now the only question worth asking. Did those eight reds change how many pockets are on this wheel, or how many of the pockets are red? Neither number moved, because the ball does not remember where it landed and the wheel has nowhere to write down where it landed. The chance of red on the next spin is the same 48.6% it was before the run of reds started.

Two: the dice, together

Ten rolls have gone by with no seven. Your turn — what are the chances the next one is a seven?

Leo raising one finger, thinking something through.

Leoformer dealer · rules and maths

I will do the first half of the count. Two dice, six faces on each, and every face of one die can land beside every face of the other die: that makes 36 combinations in all, and 6 of those combinations add up to seven.

Your half of the count: did those ten rolls without a seven take away any of the 36 combinations, or any of the 6 that make seven?

The six combinations that add up to seven: one and six, two and five, three and four, and each of those three the other way round. Which of the two dice shows which number is what makes six combinations out of three pairs of numbers.

You: neither of the two numbers moved. Ten rolls took nothing away, because two dice are two objects with a shape and a weight, and a shape and a weight are the whole of what they have.

Every combination two dice can land on, one square each: 36 squares in all, and the 6 shaded ones are the six pairs drawn above. Ten rolls without a seven take no square off this picture, because the dice are thrown fresh every time.

So a seven is 16.7% on the next roll, exactly as it was on every roll before it. And ten rolls in a row without a seven is not a strange thing to sit through: a stretch that long comes up on its own 16.2% of the time, which is often enough to see at a craps table on an ordinary evening.

Three: the shoe, yours

Twenty cards have come out of the shoe at a blackjack table, and not one of them was a ten-card. What are the chances the next card off the shoe is a ten-card?

Same method: count what is in the shoe (the box the dealer deals from, holding several decks shuffled together). At this table the shoe holds 8 decks.

1010JJJQQQKKK
A ten, a jack, a queen and a king are the ten-cards, and every deck holds four of each. A shoe of 8 decks therefore starts with 128 ten-cards among 416 cards — 30.8%, or near enough one card in three.

Twenty cards have gone into the discard tray and not one of them was a ten-card, so all 128 ten-cards are still in the shoe. What has changed is the crowd those 128 ten-cards are standing in: 396 cards now, where it was 416 at the start. 128 of 396 is 32.3%.

The shoe as it was dealt from the start: 128 ten-cards among 416 cards

30.8%

After twenty cards, not one of them a ten-card: 128 ten-cards among 396 cards

32.3%

Leo smiling, giving a thumbs-up.

Leoformer dealer · rules and maths

The move you have just counted is the whole lesson, and look how small it is: 30.8% at the start of the shoe against 32.3% now. Small, but not nothing — and at the wheel and at the dice the move was nothing exactly, not nearly nothing. There is no luck in the shoe either. A card that has been dealt is lying in the discard tray, and it cannot come out of the shoe a second time.

What a wheel carries into the next spin

A wheel, a pair of dice and a slot machine have nowhere to keep a tally of what has already happened, and a tally is exactly what the word “due” would need in order to mean anything. Nothing is written down anywhere on any of the three between one round and the next.

Where the belief turns into money

Being wrong about a wheel costs nothing until the belief makes your bet bigger. One spin takes the whole bet or pays you; over many spins the casino keeps the house edge (the share of all the money bet that the casino keeps on average, over many rounds). The bet times that share is what one spin costs on average, so double the bet and you double that cost, whatever the board shows.

The bet you sat down meaning to make10 units on red

An hour of those spins costs about 9.46 units on average.

The bet the run talks you into25 units on black, because black is “overdue”

The extra 15 units rides the same house edge as the first 10 units did, and costs 0.41 units a spin on average — every time the thought comes back.

The spin you sit outNothing down, and you watch

Sitting a spin out costs 0 units, because nothing multiplied by any house edge is nothing. Sitting out is allowed at every table in the room.

The first amount is an hour of spins; the other two are one spin each, and the bets are examples rather than suggestions. Price of an hour works it out for the bet you would actually put down.

The shoe, and what it keeps a record of

The only memory on a casino floor sits inside one object, and that object is the shoe. Cards that have been dealt go into the discard tray standing beside it, and they stay in that tray until the dealer shuffles. A shoe’s memory is nothing more than the cards lying in that tray, because those are exactly the cards that cannot come off the shoe next.

The shoe does not remember how many cards have gone. It remembers which cards have gone. Take the same shoe and deal twenty cards out of it three separate times, changing nothing at all except which twenty cards they were:

Ten-cards left in the shoe after twenty cards, by which cards they were
The twenty that leftTen-cards leftCards leftShare that are ten-cards
Nothing dealt yet12841630.8%
Not one of them a ten-card12839632.3%
The ordinary share, 6.2 of them ten-cards6.2 fewer39630.8%
Every one of them a ten-cardtwenty fewer39627.3%

Look again at the row where the ordinary share of ten-cards went into the tray, because that row is the one people do not expect. Twenty cards have gone and the share of ten-cards is exactly where it started — not nearly, exactly. An ordinary twenty cards carry off 6.2 ten-cards, which is precisely the share ten-cards had in the shoe to begin with, so what is left behind is mixed the same way it was before. What moves the share of ten-cards is how lopsided the cards that left were, and never how many of them left.

Ten-cards are not the only rank that moves. Every rank in the shoe moves at the same moment and each one moves by an amount of its own, and how far any rank moves depends on how many cards of that rank were in the shoe at the start.

1010JJJQQQKKK

Ten-cards16 in every deck, 128 in this shoe

The share of ten-cards at the start
30.8%
After twenty cards, none of them a ten-card
32.3%
AAAAAAAA

Aces4 in every deck, 32 in this shoe

The share of aces at the start
7.7%
After the same twenty cards, none of them an ace
8.1%

Both tiles are the same twenty cards leaving the same shoe of 8 decks, and neither a ten-card nor an ace was among the twenty. The ten-cards move the further of the two because there are more of them to be moved: 128 ten-cards share the shrinking shoe against 32 aces.

Putting the cards back

A shoe’s record is only the cards lying in the discard tray. The dealer sweeps those cards up, shuffles every one of them back in and loads the shoe again, and the tray beside it is empty: ten-cards are back at 30.8%, exactly where they would be if nobody had played a hand there all night.

A shuffle is also the plainest way to say what a wheel and a pair of dice are doing all evening. They behave as though somebody gathered them up and shuffled them after every single round — which is why nothing you watched on the last spin or the last roll is of the slightest use on the next one.

Slot machines, and what is left for later

A slot machine looks like the one place on the floor where “due” ought to be true, and a slot machine is the furthest thing from it. What a spin lands on is settled at the moment the spin is started, by a generator of random numbers, and the spin before it is not one of the things that generator is given.

Two hundred spins with no bonus round leave nothing behind either. No symbol has been used up, nothing inside the machine is keeping a count of what it has not paid out yet, and the two hundred spins that have gone are not among the things that decide the next one.

Practice: memory or not?

A moment at a table, three answers, and after each answer the counting that answer rests on. Level 1 is a wheel and a pair of dice, where the chance on the next round is always the same number as it was on the last one. Level 2 is a shoe, where it is not — and where the moments worth slowing down over are the ones in which the share of ten-cards does not move after all. The lesson is one run: every square on the strip below is one moment of it, and every square is there from the start. Only your first answer on each moment counts, and when a level’s squares are full the next level begins by itself.

The practice table needs JavaScript. Here is one moment from it, with the answer.

Level 1 · Nothing was written down

Roulette · single-zero wheel

The wheel
37 pockets: 18 red, 18 black and 1 green one
The board
the last 8 results, oldest first: red, red, red, red, red, red, red, red
This spin
not spun yet

Eight reds in a row. You were going to put 10 units on red. The player beside you says black is overdue and is moving to 25 units. What goes down?

The answer: The same 10 units, on whatever I was going to play.

A wheel keeps no record: the same 37 pockets and the same 18 reds on this spin as on the one before the run started, which is 48.6%. What a run can do is make a larger bet feel reasonable, and that is where it costs money — the extra 15 units is 0.41 units a spin on average.

cualquiera de los treinta y siete (37) números en que está dividido el tablero.

Free translation: any of the thirty-seven (37) numbers into which the board is divided.

Lotería de Córdoba · Reglamento de Ruleta · section Art. 5 · read

Level 2 · The shoe keeps a little

Blackjack · a shoe of 8 decks

The shoe at the start
8 decks shuffled together: 416 cards, 128 of them ten-cards
In the discard tray
20 cards, not one of them a ten-card
Left in the shoe
396 cards
The next card
not dealt yet

Twenty cards have gone into the discard tray, and not one of them was a ten-card. What are the chances the next card off the shoe is a ten?

The answer: About 32.3% — a little more than the 30.8% it started at.

Up a little: 128 ten-cards among 396 left is 32.3%, against 30.8% at the start. That is the whole difference between a shoe and a wheel, and it is not a large number.

Serán utilizados para este Juego como mínimo 8 (ocho) mazos de naipes de tipo "Francés"

Free translation: A minimum of 8 (eight) decks of "French" type playing cards shall be used for this Game

Lotería de Córdoba · Reglamento del juego «Black Jack» · section Cartas a utilizar y valores de las mismas · read

Every moment is worked out the same way: a wheel and a pair of dice by counting the pockets and the thirty-six combinations, a shoe by counting the cards left in the shoe. The workings are in “How it’s worked out” at the end of this page.

How the practice table works

Where the answers come from. Every figure on every moment is worked out when the page is built: the wheel from its pockets, the dice from the thirty-six combinations, the shoe by counting the cards left in it. The size of the shoe and the make-up of the wheel come from the published rules behind the source buttons on this page, so a document that changes changes the moments with it.

No money in this table. Three games share these moments and they carry three different house edges; one running total across them would be wrong for two of the three. Where a belief costs money the moment says so in its own reason, in amounts worked out for an example bet, and that is the only place amounts appear.

One strip, no rounds. Every square on the strip is one moment of this lesson, and they are all there from the start. Your first answer fills the square; when a level’s squares are full the next level begins by itself, with no button in between. Practising a mistake turns a cross into “fixed in practice” and does not change the count: only first answers do. Progress stays in this browser; nothing is sent anywhere.

Check yourself

Maya with a finger raised and a knowing look.

Mayaformer floor supervisor · manners, money and breaks

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

A question marked “New situation” asks you to use the lesson on a case it did not show.

1Eight reds in a row on a single-zero wheel. The chance of red on the next spin is…

Show the answer

Answer: 18 of 37, or 48.6% — the same as on the spin before the run started. 18 of 37 is the whole answer. How long a run has to be before it is genuinely unusual, and why runs feel so much rarer than they are, is something Runs and streaks counts for the wheel in front of you.

  • Higher: red is running tonight The same belief with the sign changed. A wheel cannot favour a colour it has no record of.
  • 18 of 37, or 48.6% — the same as on the spin before the run started The pockets do not move and the ball does not remember. Both numbers are the same on every spin of this wheel.
  • Lower: eight reds is a lot, and black is behind The wheel keeps no count. And the run is not the rarity it looks: over 105 spins, an evening’s worth, a run of eight or more of one colour turns up 27.9% of the time.
2Twenty cards have come out of a shoe of 8 decks, and not one of them was a ten-card. The share of ten-cards among the cards left is…

Show the answer

Answer: Up a little: 30.8% to 32.3%. The same number of ten-cards, spread among fewer cards: 128 ten-cards among 396 cards now, where they were 128 among 416 at the start of the shoe.

  • Down: cards have left the shoe Which cards left is what decides the answer, and cards leaving on its own decides nothing. All 128 ten-cards stayed in the shoe here, so the share of ten-cards went up rather than down.
  • Unchanged — cards have no memory either A single card has no memory; a shoe of cards does. A card that has been dealt out of a shoe does not go back into it until the shuffle, and that one fact is the whole of the difference between this table and the wheel.
  • Up a little: 30.8% to 32.3% There are still 128 ten-cards, and now only 396 cards for them to be among.
3The same table, another twenty cards — and this time 6.2 of the twenty were ten-cards, which is the ordinary share of them. Where does that leave the share of ten-cards among the cards still in the shoe?

Show the answer

Answer: 30.8% — exactly the share the shoe started at. Keep one sentence out of all of it: what moves the share of ten-cards is how lopsided the cards that left were, and never how many cards left. Twenty ordinary cards leave 30.8% behind, which is the share the shoe began with.

  • Higher, because twenty more cards have gone How many cards have gone says nothing about the share of ten-cards on its own. Twenty cards moved the share in the question before this one only because of which twenty cards they were.
  • Lower, because 6.2 ten-cards have gone Those 6.2 ten-cards did go, and fourteen cards that were not ten-cards went with them. In the ordinary mixture the two exactly cancel, which is what “the ordinary mixture” means.
  • 30.8% — exactly the share the shoe started at Twenty cards in the ordinary mixture carry off the ordinary share of ten-cards along with them, and taking out a share exactly equal to the one already there leaves the share behind untouched.
4The same shoe and the same twenty cards, and this time not one of them was an ace. Aces start at 7.7% of the shoe. Where are the aces now? new situation

Show the answer

Answer: Up, to about 8.1%. The same rule, with a different number of cards underneath it. A shoe shifts every rank at the same moment, and how far it shifts any one rank depends on how many cards of that rank were in the shoe to begin with.

  • Up to about 32.3%, the same as the ten-cards That is the answer for the ten-cards. A deck holds 4 aces against 16 ten-cards, so the same twenty cards move the aces and the ten-cards by different amounts.
  • Up, to about 8.1% All 32 aces are still in the shoe, among 396 cards instead of the 416 they started among.
  • Unchanged at 7.7% The aces move for the same reason the ten-cards do: whatever stays in a shrinking shoe becomes a larger share of what is in it.
5A slot machine has run two hundred spins without a bonus round. The chance of a bonus round on the next spin is… new situation

Show the answer

Answer: Exactly what it was on the first of those two hundred spins. Each spin comes out of a generator of random numbers, and the spin before it is not one of the things that generator is given. A slot machine has no discard tray either: nothing comes out of the machine, so nothing is left behind by it. Why “it is due” feels so strong at a machine is the slots track’s own lesson.

  • Lower, because the machine is cold and it is better to move on Moving to another machine is allowed and it costs nothing at all, so the choice is fine; the reason behind it is not. The two hundred spins that have gone are not among the things that decide the next spin.
  • Higher, because the bonus round is due by now Being due would need something inside the machine counting what the machine owes, and there is nothing in there counting. This is the wheel mistake wearing different clothes.
  • Exactly what it was on the first of those two hundred spins What a spin lands on is settled at the moment the spin is started, by a generator of random numbers, and nothing inside the machine is keeping a tally of what it has not paid out yet.

The question we opened with. Putting down whatever you were going to put down anyway and putting nothing down at all are both sound answers, and they are sound for the same reason: red is 48.6% on that spin whatever the board above the wheel says, so playing your own bet and sitting the spin out are equally defensible. Following him onto black rests on something a wheel cannot do, and it is the only one of the three answers that costs anything at all. Going from 10 units to 25 units puts an extra 15 units on the same house edge as the first 10 units, which comes to 0.41 units a spin on average.

Your wheel, and further reading

Maya with a hand on her chest, speaking gently and seriously.

Mayaformer floor supervisor · manners, money and breaks

One thing to take away from all of this, and it is not a number. “It is due” is a feeling, and the feeling is real even though the fact behind it is not. Treat it as a signal to stop for the evening rather than a signal to put more down.

Playing on to get an evening back has a name: chasing losses (playing on to get back what the evening has cost, which raises the cost rather than returning it). If that is where tonight has gone, the lines below are what they are for, and they are open now.

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
0800-666-6006Buenos Aires City (CABA) · Línea de orientación por juego problemático (LOTBA) · Monday to Friday, 9 to 17
0800-444-4000Buenos Aires Province · Programa de Prevención y Asistencia al Juego Compulsivo (IPLyC)
0800-777-2983Cordoba · Línea 0800-777-AYUDA (Lotería de Córdoba) · 24 hours
0800-268-5640Santa Fe · Línea gratuita de la APRECOD (Santa Fe) · Every day, 8 to 24
0800-888-2202Entre Rios · Departamento Juego Responsable (IAFAS, PREVENJUEGO)
0261-424-7536Mendoza · Programa de Juego Responsable (IPJyC) · Monday to Friday, 8 to 14
0800-888-5836Misiones · Programa de Juego Responsable del IPLyC S.E. (0800-888-LUDO)
0800-888-2008Chaco · Línea de Juego Responsable (Lotería Chaqueña)
0299-403-8900Neuquen · Líneas de contacto, orientación y tratamiento (IJAN, juego responsable) · Monday to Friday, 8 to 15
0800-222-1700Rio Negro · Línea de Orientación al Jugador Problemático (Lotería de Río Negro)
02901-433515Tierra del Fuego · Departamento Juego Responsable (IPRA, Ushuaia)
0800-555-7678Tucuman · Juego Responsable, Ley 8986 (Caja Popular de Ahorros)
0800-999-1314San Juan · Línea gratuita del Programa Provincial de Juego Responsable (Caja de Acción Social) · Monday to Friday, 08 to 12

If you are thinking about suicide, call 135 or 0800 345 1435 from anywhere in the country

Further reading

How it’s worked out

The counting behind every figure on this page

The wheel. 37 pockets, 18 of them red: the chance of red on one spin is 18 divided by 37, or 48.6%, and one named number is 2.70%. The house edge of 2.70% is the gap between what a successful bet is paid and what the chance is worth, worked out by the same code as House edge of every bet. How often a run of a given length turns up over an evening is counted spin by spin, by the same code as Runs and streaks.

The dice. Two dice have 36 combinations, and 6 of them total seven, so a seven is 16.7% of rolls. Ten rolls with no seven is that chance multiplied by itself ten times: 16.2%.

The shoe. A deck of 52 cards holds 16 ten-cards and 4 aces. A shoe of 8 decks therefore starts with 128 ten-cards among 416 cards. After twenty cards have been dealt, the share of ten-cards among the cards left is the ten-cards still in the shoe divided by 396; the rows of the table differ only in how many of the twenty were ten-cards — none of them, the ordinary share of 6.2, or all twenty. The bars under that table are those same four shares drawn to length, and no number is printed on them. The number of decks is not written into this page. It is read from the published rules behind the source buttons above, and every figure here is recomputed from it, which is why the same page in another country would show different numbers rather than these.

Amounts. Amounts are in betting units, not pesos: a unit can stand for any amount, and the arithmetic is the same at any scale. The cost of raising a bet is the extra amount multiplied by the house edge of that wheel; the cost of an hour is the bet multiplied by the edge and by the number of spins an hour this course uses for the game. Both are long-run averages on an example bet, not a forecast for one evening, and the example is an example rather than a suggested bet.

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. Nothing on this page is a way of doing better at any of these games. Two of the three tables here have nothing to read at all, and the third changes by less than the width of the question people usually ask about it.

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