Do cards, dice and wheels remember?

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

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?

Leoformer dealer · rules and maths

Count what is in front of you, not what has already happened. A double-zero wheel has 38 pockets: 18 red, 18 black and 2 green. Red is 18 pockets of 38 — 47.4%.

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 47.4% 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?

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?

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.

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 6 decks.

Twenty cards have gone into the discard tray and not one of them was a ten-card, so all 96 ten-cards are still in the shoe. What has changed is the crowd those 96 ten-cards are standing in: 292 cards now, where it was 312 at the start. 96 of 292 is 32.9%.

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 32.9% 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.

A second kind of wheel is played here as well, with 37 pockets on it instead of 38. Which of the two wheels you sit at changes what an evening at roulette costs you, and it changes nothing whatever about memory: neither wheel remembers a single spin.

The two wheels differ by one green pocket, and that single pocket nearly doubles the share of every even-money bet the house keeps. What the two wheels have in common is not printed in either tile, because the line would read the same on both of them: what the spin before this one leaves behind is nothing at all.

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 every dollar bet 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 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:

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.

How far the share moves depends on how many decks are being dealt from

The number of decks in front of the dealer is not the same at every table, and the same twenty cards are a thick slice of a few decks and a sliver of many. Take the same twenty cards out of each size, with no ten-card among the twenty in any of them:

Every row of that table starts at the same 30.8%, however many decks are being dealt from, because every deck holds 16 ten-cards among 52 cards and shuffling more of them together changes neither figure. What the number of decks decides is how far the same twenty cards move that share once they are lying in the tray.

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.

Both tiles are the same twenty cards leaving the same shoe of 6 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: 96 ten-cards share the shrinking shoe against 24 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.

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.

Your wheel, and further reading

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 — Game plan is where that decision is easiest to make, before you sit.

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.

Further reading

• Criminal Code, section 207: permitted lotteries · Justice Laws Website, Government of CanadaThe section that lets a province, and only a province, conduct and manage a lottery scheme — the sentence every casino in the country stands on.
• About Casinos BC · British Columbia Lottery Corporation (Casinos BC)Who conducts the gaming in one province and who runs the room, in the corporation’s own two sentences.
• Annual Report 2024–25 · Ontario Lottery and Gaming CorporationWhat a provincial gaming corporation publishes about itself: what it conducts, and what share of the money brought to the tables it keeps.
• Protecting the public · Independent Gambling Control Office, Province of British ColumbiaWhat a provincial regulator does, who is allowed to run the games, and where a complaint about a casino goes.
• Minimum Technical Standards for Gaming — 11. Game Behaviour · Alcohol and Gaming Commission of OntarioThe floor one regulator sets under a slot machine’s return, and its rule that the floor holds for every bet configuration.
• The house edge of casino games · Wizard of OddsWhere the house edge is defined, and the rating table of rounds an hour this track uses for every game.

How it’s worked out