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Wheel arithmetic

The zero belongs in the calculation

A single-zero wheel has 37 pockets and pays a straight-up bet 35 to 1. Put those two numbers in one sum and every standard bet loses about £0.27 for each £10 staked.

Worked arithmetic · Sources checked

Pocket 0 — the zero is one of 37 pockets, and it sets the edge

A single-zero roulette wheel has 37 pockets: the numbers 1 to 36, and one zero, so a straight-up bet on a single number wins once in 37 spins. The published payout is 35 to 1, which means a £10 bet on that number loses about £0.27 on average.

That gap between 37 pockets and a 36-unit return is the house edge: the share of each stake the table keeps over many spins. It comes to 1/37 of the stake, or about 2.70%.

We read the Massachusetts Gaming Commission's published roulette rules on 22 September 2026. They give a payout table and say what happens to an even-money bet when the ball lands in zero.

Sources: Massachusetts roulette rules; Gambling Commission: return to player.

The numbers this page works with

Pockets on the wheel
37: the numbers 1 to 36 and one zero, each treated as equally likely.Massachusetts roulette rules · as checked on
Straight-up payout
35 to 1, the minimum a licensed table may pay on a single number.Massachusetts roulette rules · as checked on
Average loss per £10 staked
£0.27 on every standard bet in the table, because each one pays one unit short of its true odds.Massachusetts roulette rules · as checked on
The zero on an even-money bet
On a single zero wheel, the rules state that bets on red, black, odd, even, 1 to 18 and 19 to 36 are lost when the ball rests in zero.Massachusetts roulette rules · as checked on
What an average is
The Gambling Commission calls a return-to-player figure an average over many plays, not a result you should expect in one session.Gambling Commission: return to player · as checked on

Payout odds as the Massachusetts rules print them, read on 22 September 2026. Pocket counts are for the 37-pocket wheel modelled here.

Pocket 1 — the payout table, exactly as the rules print it

The Massachusetts rules carry one table of payout odds. The line above it sets a floor, not a target: no licensee 'shall pay off winning wagers at the game or roulette at less than the odds listed below'.

So the printed odds are the least a licensed table pays, and an operator may pay more. Nothing in the rules prevents that, and nothing in them promises it either.

The rows below are copied from that page, read on 22 September 2026. The pocket counts beside them are ours, worked for the 37-pocket wheel; the same document also covers a double-zero wheel, which is a different sum.

Sources: Massachusetts roulette rules.

Seven bets from one published table

Payout odds as printed in the Massachusetts roulette rules, read 22 September 2026, with the winning pockets and the average loss per £10 staked worked for a 37-pocket single-zero wheel. The loss column is our arithmetic, not the regulator's figure.
Bet, as the rules name itPayout oddsWinning pockets (of 37)Average loss (per £10 staked)Evidence
Straight35 to 11£0.27 · Massachusetts roulette rules
Split17 to 12£0.27 · Massachusetts roulette rules
Three Numbers11 to 13£0.27 · Massachusetts roulette rules
Six Numbers5 to 16£0.27 · Massachusetts roulette rules
Dozen2 to 112£0.27 · Massachusetts roulette rules
Red1 to 118£0.27 · Massachusetts roulette rules
Seven Numbers4 to 17£0.54 · Massachusetts roulette rules

Six of these seven bets lose the same £0.27. The Seven Numbers row does not, and the section below shows why.

Pocket 2 — the straight-up sum, worked in pounds

Take a £10 bet on one number: it wins once in 37 spins and returns 35 units of profit alongside the original £10 stake, and it loses on the other 36 spins.

So the expected value is (35 × £10 × 1/37) − (£10 × 36/37). That is £9.46 minus £9.73, or about −£0.27 for each £10 staked.

Expected value here means the average result per spin over many spins. It is not a forecast for your next spin, and no single spin can return £0.27.

Sources: Massachusetts roulette rules.

Pocket 3 — the same sum, run for every standard bet

Now run that same sum again for the other rows of the published table. A Split pays 17 to 1 and wins on 2 pockets, while a Three Numbers bet pays 11 to 1 and wins on 3.

Six Numbers pays 5 to 1 and wins on 6 pockets. A Dozen pays 2 to 1 and wins on 12, and Red pays 1 to 1 and wins on 18. Each one returns 36 units where the wheel has 37 pockets.

That is why the loss column repeats itself. Every one of those bets returns £9.73 of each £10 staked, so the identical £0.27 goes to the table whichever square you choose.

Sources: Massachusetts roulette rules.

Pocket 4 — the one row in the table that breaks the pattern

One row does not follow the pattern, because the rules allow a table to offer a Seven Numbers wager and the payout table gives it 4 to 1.

Seven pockets out of 37 win. A winning £10 bet returns 4 × £10 of profit, so the sum is (£40 × 7/37) − (£10 × 30/37). That comes to about −£0.54 for each £10 staked.

So this bet keeps twice as much as the others in the same table. The refrain on this site is that every bet has the same edge; the published odds show exactly where that stops being true.

Sources: Massachusetts roulette rules.

Pocket 5 — what the zero actually does to an even-money bet

The zero is not a neutral pocket, and on a single-zero wheel the published rules are blunt about it in a single sentence.

A double-zero wheel is handled differently in the same document. There a licensee may take either half of each even-money bet or the whole of it when zero or double zero comes up, and must display which option is in force.

That choice is worth reading before you sit down, because it halves or doubles what the zero costs an even-money bet. A UK table may instead apply la partage, which is a rule that returns half the stake on a zero.

Sources: Massachusetts roulette rules.

The single-zero rule, in the regulator's words

When roulette is played on a single zero wheel and the roulette ball comes to rest in a compartment marked zero (0), wagers on red, black, odd, even, 1 to 18, and 19 to 36 shall be lost.

Roulette rules, Massachusetts Gaming Commission · Section 2(c), payout odds · Massachusetts roulette rules · read on

Pocket 6 — a losing run is not the zero catching up

Each spin is drawn from the same 37 pockets. The Gambling Commission's guide puts the same point in plain terms for random machines: the odds in the current game are constant and are not affected by wins or losses in earlier games.

So a run of eight reds changes nothing about the ninth spin, and the £0.27 does not accumulate anywhere and come back later.

A losing run is the ordinary shape of independent draws, not a sign that a win is near. If a run has taken more than you planned, GamCare's helpline is 0808 8020 133.

Sources: Gambling Commission: return to player.

Pocket 7 — how to check any wheel's numbers yourself

You do not need us for this, because the sum takes only two numbers from the game rules and one line of arithmetic.

The five steps below are the ones this page used. Write each number down as you take it, with the date you read it.

Step five says what the answer means, because a percentage on its own is easy to misread.

Sources: Massachusetts roulette rules.

How to work out what a roulette bet costs

Five steps, in order. The last one says what the result does and does not tell you.

  1. Count the pockets

    Open the game rules and count the compartments on the wheel. A single-zero wheel has 37; a double-zero wheel has 38, and the sum changes.

    The Massachusetts rules cover both, and say which wager belongs to which wheel.

  2. Count the pockets that win your bet

    A Dozen wins on 12 pockets. A Split wins on 2. Take the number from the rules, not from the layout's artwork.

  3. Read the payout odds from the table

    The rules print the odds as a ratio, such as 35 to 1 or 2 to 1. Those are the minimum a licensed table pays.

  4. Work the sum on a £10 stake

    Multiply the payout by 10 and by the winning chance, then subtract £10 times the losing chance. A Dozen gives (£20 × 12/37) − (£10 × 25/37).

  5. What the result means

    You get an average loss per £10 staked, over many spins. It is not what one spin will cost and it does not tell you when a number is due, because nothing is due.

Pocket 8 — what the Gambling Commission says an average is

The Commission's guide is written about gaming machines, but its warning about averages carries straight over. It defines the return to player as the part of the money paid in that is given back as prizes.

It then says the figure is an average achieved over a significant number of game plays, and not each time the machine is played. Its own example is blunt: at 85% RTP you should not expect to win an average of 85p for every £1 staked in a session.

It also gives a definition we use above. The house edge is 'the percentage that a casino would expect to keep, on average, from each hand or spin, given normal patterns of play'.

Sources: Gambling Commission: return to player.

Pocket 9 — what an operator has to publish before you bet

The Commission's remote technical standards set the disclosure. RTS 3 exists, in its own words, 'to enable customers to make informed decisions about whether to gamble based on their chances of winning'.

Requirement 3A says the rules must be easily available before a customer commits to gamble, and accurate enough to explain how to take part. Requirement 3C adds the chances: a house edge, a return-to-player percentage or the probability of a winning event.

So a table that shows none of those three is not giving you the second number this page needs. That is worth noticing before the first spin, not after it.

Sources: Gambling Commission: RTS 3.

Before you accept a percentage, check these five lines

Each line comes from a page read on 22 September 2026. Tick marks stay in your browser and are not sent anywhere.

  • Without it, a quoted percentage cannot be checked.

  • The rules must be available before you commit to gamble, not after.

Ticks are kept only in this browser and are never sent anywhere.

What the wheel cannot tell you

These figures describe a model: 37 equally likely pockets and the payouts as printed. A worn wheel, a different payout or a house rule on the zero would each need the sum run again.

We have not measured any wheel, online or in a venue, and we make no claim about how any particular table behaves. The arithmetic is checkable; a physical wheel is not, from here.

Nothing above makes one bet preferable to another; it prices them, which is a different and considerably duller thing.

Sources: Massachusetts roulette rules; Gambling Commission: return to player.

Words used on this page

Pocket
One numbered compartment on the wheel. The rules call it a compartment; a single-zero wheel has 37 of them.
House edge
The Gambling Commission's guide defines it as the percentage a casino would expect to keep, on average, from each hand or spin, given normal patterns of play.
Expected value
The average result of one bet across many repeats of it, written here as pounds lost per £10 staked.
Return to player (RTP)
The part of the money paid in that is given back as prizes, measured as an average over a large number of plays.
La partage
A roulette rule under which half of an even-money stake is returned when the ball lands in zero. It is not in the Massachusetts table quoted here.
RTS
The Gambling Commission’s remote gambling and software technical standards. RTS 3 is the one covering rules, game descriptions and the likelihood of winning.

Look up more terms in the Casino Lexicon dictionary

Sources checked 22 September 2026

Three pages were read on 22 September 2026. Two are Gambling Commission pages and one is the Massachusetts Gaming Commission's published roulette rules.

Sources checked 22 September 2026. Each page is listed below with the date it was read, so you can open the same page and start again.

If a payout table changes, the sums above should be run again before anyone quotes them. That is the only maintenance a page like this needs. If any of this has been useful, or if you find an error in the arithmetic, tell us and we will check it.

Sources: Massachusetts roulette rules; Gambling Commission: return to player; Gambling Commission: RTS 3.

Questions answered

Why does the zero give the house an edge?

Because the wheel has 37 pockets and the payout is built on 36. A straight-up bet pays 35 to 1, so a winning £10 returns £360 of a £370 pool. The missing unit is 1/37 of the stake, about 2.70%.

Do some roulette bets have a lower house edge than others?

Not among the six standard bets worked here. Straight, Split, Three Numbers, Six Numbers, Dozen and Red all lose about £0.27 per £10 staked on a 37-pocket wheel, because each pays one unit short of its true odds.

Which bet in the published table costs more?

The Seven Numbers wager. The Massachusetts rules pay it 4 to 1, and it wins on 7 of 37 pockets, so the average loss is about £0.54 per £10 staked. That is double the others in the same table.

What happens to a bet on red when the ball lands in zero?

On a single-zero wheel the Massachusetts rules say it is lost, along with black, odd, even, 1 to 18 and 19 to 36. On a double-zero wheel the licensee may instead take only half the bet, and must display which option applies.

Does a percentage tell me what a session will cost?

No. The Gambling Commission describes a return-to-player figure as an average over a significant number of plays, not a result to expect each time. Its own example says an 85% machine will not hand back 85p of every £1 in one session.

Rule sources

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