A roulette dozen bet covers one consecutive block of 12 numbers and pays 2 to 1:
- first dozen: 1–12;
- second dozen: 13–24;
- third dozen: 25–36.
Zero, double zero, and any additional green pocket are outside all three dozens. That exclusion creates the house edge. On a single-zero wheel, one dozen wins on 12 of 37 pockets and has a 2.70% edge. On a double-zero wheel, it wins on 12 of 38 and has a 5.26% edge.
Where the chip goes
The three dozen boxes appear in the outside-bet area of the felt, normally labeled 1st 12, 2nd 12, and 3rd 12. A chip placed fully inside one box covers only that dozen.
Dozens are not the same as columns:
- a dozen is a consecutive numerical block;
- a column contains every third number down one vertical line of the table grid.
Both cover 12 numbers and normally pay 2 to 1, but they cover different sets. The roulette table layout shows the exact chip positions, while column bet odds handles the neighboring wager.
Single-zero probability and expected value
A single-zero wheel has 37 pockets. A chosen dozen wins on 12 and loses on 25.
For a one-unit wager:
[ P(win)=\frac{12}{37}=32.4324% ]
[ P(loss)=\frac{25}{37}=67.5676% ]
The posted net payout is 2 units. Expected value is:
[ EV=\left(\frac{12}{37}\times2\right)-\left(\frac{25}{37}\times1\right) =-\frac{1}{37} ]
So:
[ HE=\frac{1}{37}=2.7027% ]
A $30 first-dozen bet therefore has expected loss:
[ EL=$30\times0.027027=$0.81 ]
That does not predict the next spin. The actual result is either a $60 profit or a $30 loss. Expected loss is the long-run average across repeated identical wagers.
Fair odds are slightly higher than 2 to 1
Fair net odds equal losing outcomes divided by winning outcomes:
[ \text{Fair odds}=\frac{25}{12}=2.0833\text{ to }1 ]
The casino pays 2 to 1. The missing 0.0833 unit on a fair winning payout creates the single-zero edge.
On a double-zero wheel:
[ \text{Fair odds}=\frac{26}{12}=2.1667\text{ to }1 ]
The payout remains 2 to 1, so the deficit is larger.
| Wheel | Total pockets | Win probability | Fair net odds | Posted odds | House edge |
|---|---|---|---|---|---|
| Single zero | 37 | 12/37 = 32.43% | 25/12 = 2.0833:1 | 2:1 | 2.70% |
| Double zero | 38 | 12/38 = 31.58% | 26/12 = 2.1667:1 | 2:1 | 5.26% |
| Triple zero | 39 | 12/39 = 30.77% | 27/12 = 2.25:1 | 2:1 | 7.69% |
The ordinary payout does not improve when the casino adds another zero. The denominator changes while the prize stays fixed.
A payout example
A player wagers $25 on the second dozen.
- If 19 wins, the net profit is $50 and the $25 stake is returned, for $75 total back.
- If 8, 31, 0, or 00 wins, the $25 is lost.
“Two to one” means two units of profit for each unit wagered. It does not mean a two-unit total return.
Official procedures such as the Massachusetts roulette rules identify dozens as 12-number wagers, specify the standard payout, and set the order for closing betting and settling the layout.
Betting two dozens does not create a safer edge
A common system places one unit on two different dozens. That covers 24 ordinary numbers.
On a single-zero wheel:
- 24 covered numbers produce one winning dozen and one losing dozen;
- 12 numbers in the uncovered dozen lose both wagers;
- zero also loses both wagers.
With $1 on each of two dozens, total stake is $2. A covered number creates $2 profit on the winner and a $1 loss on the other bet, so the net result is +$1. An uncovered result loses $2.
[ EV=\left(\frac{24}{37}\times1\right)-\left(\frac{13}{37}\times2\right) =-\frac{2}{37} ]
That is an expected loss of 2/37 unit per spin on $2 total action. Dividing by the $2 wagered gives the same 2.70% edge.
The system changes the result shape:
- more spins produce a small win;
- fewer spins produce a larger loss;
- the average percentage cost remains unchanged.
A progression that increases the two-dozen stake after a loss also keeps the same edge while increasing dollar exposure.
Betting all three dozens is not neutral
If one unit is placed on every dozen, total stake is three units.
When any number from 1 to 36 wins:
- the winning dozen earns two units;
- the other two dozen stakes lose two units;
- net result is zero.
When zero wins, all three units lose.
On a single-zero wheel:
[ EV=\left(\frac{36}{37}\times0\right)+\left(\frac{1}{37}\times-3\right) =-\frac{3}{37} ]
The player has constructed a wager that usually pushes and occasionally loses everything. The edge on the three units remains 2.70%.
On double-zero roulette, both green pockets lose all three wagers, doubling the frequency of the full loss.
Rotating dozens cannot predict the wheel
Players often switch among first, second, and third dozen based on recent results. That changes which 12 numbers are covered, not the probability structure.
On a fair wheel, the next spin is independent of the previous spin. A dozen that has missed repeatedly is not due. A dozen that has appeared several times is not mechanically hot. The selected dozen still covers 12 pockets and excludes every zero.
Changing the bet may make a session feel active, but it cannot remove the payout deficit.
La Partage and En Prison usually do not protect dozens
French-style rules can reduce the cost of qualifying even-money wagers when zero appears. Dozens pay 2 to 1 and are not even-money bets. They normally lose in full on zero.
Do not assume that a single-zero French layout gives a 1.35% edge on every outside wager. The reduced figure applies only when the posted rule protects eligible bets such as red/black, odd/even, or high/low. See La Partage house edge for the exact calculation.
Dozens versus other roulette wagers
Under one standard wheel and payout schedule, most ordinary bets carry the same percentage edge. Their variance differs.
| Bet | Numbers covered | Net payout | Single-zero hit rate |
|---|---|---|---|
| Straight-up | 1 | 35:1 | 2.70% |
| Six-line | 6 | 5:1 | 16.22% |
| Dozen | 12 | 2:1 | 32.43% |
| Column | 12 | 2:1 | 32.43% |
| Even-money | 18 | 1:1 | 48.65% |
A dozen produces fewer wins than an even-money wager but larger winning profits. It produces more wins than an inside bet but smaller payouts. That is a volatility choice, not an advantage.
Operational and dispute points
A dozen wager should be completely inside the intended box before the dealer announces no more bets. Common problems include:
- a chip touching the border between two dozen boxes;
- confusion between a dozen and the adjacent column area;
- a late wager placed after betting closed;
- an electronic bet not confirmed before the timer expired;
- payout confusion between 2 to 1 profit and total return;
- a player believing zero is protected by La Partage;
- several players’ cash chips stacked without clear ownership.
If a dispute occurs, do not move the chips. Ask the dealer to stop before the layout is cleared. The floor should confirm the chip position, accepted amount, winning number, wheel type, and active table rule. Electronic roulette should have an accepted-bet record and result log.
Session cost
If a player makes a $20 dozen wager for 60 spins on a single-zero wheel:
[ H=$20\times60=$1,200 ]
[ EL=$1,200\times\frac{1}{37}=$32.43 ]
On a double-zero wheel:
[ EL=$1,200\times\frac{2}{38}=$63.16 ]
The same stake and spin count cost almost twice as much in expectation because of one extra green pocket.
Use the roulette odds calculator to compare wheel types and the expected-loss calculator to price repeated action.
A dozen bet is easy to understand: 12 numbers, 2-to-1 profit. The decision that matters most is not which dozen appeared recently. It is which wheel you are playing, how much total action you create, and whether you accept the zero cost built into the payout.