American and European Wheel Sequences

Written by Boris Atanasov
With more than 4+ years of experience in the iGaming industry, Boris Atanasov writes exciting content about slots, video poker, roulette and blackjack.
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People approaching the roulette table for the first time may overlook one crucial detail. Most roulette players focus solely on the table layout when placing their bets, without considering how the numbers are arranged on the wheel. This is a significant oversight.

Upon closer inspection, aspiring roulette players will notice that there is a significant difference between the wheel and the betting layout on the table. Make no mistake: this is not a coincidence. The numbers are deliberately arranged to make the results as random as possible. This prevents even the most observant players from predicting the pocket in which the ball will land.

The most obvious example is the alternation of the pocket colors. Red and black always alternate on the wheel. This is not the case on the layout, where two red or two black numbers may sit next to each other. While the numbers appear in sequential order on the betting layout, they are distributed in a seemingly random manner on the wheel.

This peculiarity forces players making section bets to spread their wagers across the layout when betting on specific wheel segments. The following sections examine the number sequences used on the two types of roulette wheels and the logic behind them.

Number Arrangement

Double-Zero Wheels

Single-Zero Wheels

Single-Zero Wheel Asymmetries

The main difference between European and American wheels becomes apparent as soon as you approach an American roulette table. This variant contains an additional pocket for the double zero (00), alongside numbers 0 through 36. This brings the total to 38 numbered segments on the wheel.

The American wheel uses the following clockwise sequence for its numbers: 00, 27, 10, 25, 29, 12, 8, 19, 31, 18, 6, 21, 33, 16, 4, 23, 35, 14, 2, 0, 28, 9, 26, 30, 11, 7, 20, 32, 17, 5, 22, 34, 15, 3, 24, 36, 13, 1.

There are 18 black pockets and 18 red pockets. The single-zero and double-zero pockets are green, and their presence results in a house edge of 5.26%. Some American wheels use blue instead of green for the zero pockets.

If you inspect the double-zero wheel closely, you will notice several regularities. The order of the numbers is pseudo-random. This arrangement is designed to ensure arbitrary outcomes and eliminate predictability.

The first noticeable pattern is that an odd number almost always directly faces an even number. Consider the red 25 pocket, for instance. It sits on the opposite side of the wheel, directly across from the black 26 pocket. A similar arrangement can be observed with most other even and odd numbers, although the two green zeros disrupt the pattern slightly.

The second pattern relates to the colors of the numbers. Red and black alternate around the wheel, and the color of each numbered pocket matches the color shown on the betting layout. Interestingly, red numbers sit across from black ones, with very few exceptions. Likewise, the green single zero is placed directly opposite the double zero.

Opposite numbers are usually sequential in value. On the double-zero wheel, 13 black is positioned across from 14 red, 15 black faces 16 red, 29 black faces 30 red, and so on.

In addition, odd numbers and even numbers tend to appear in pairs on the wheel. For example, 25 sits next to 29, 12 sits next to 8, and 19 sits next to 31. This pairing is interrupted only near the zero sectors.

The double zero separates the odd-number pair 27 and 1. Moving to the right from the 00 pocket, odd 27 sits next to even 10. The single zero separates the even-number pair 2 and 28. Moving to the left from the 0 pocket, even 28 sits next to odd 9.

A pattern can also be discerned among low numbers (1 to 18) and high numbers (19 to 36). The wheel is arranged so that pairs of low numbers alternate with pairs of high numbers.

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The Reasoning Behind the Number Distribution on Roulette Wheels

1To achieve randomness

The two types of wheels use entirely different sequences, yet both have their numbers arranged in a seemingly random order. Randomness is defined as “the absence of predictability and patterns in events.”

Nevertheless, closer inspection reveals certain patterns on the roulette wheel. This arrangement is deliberate. The numbers are distributed in this manner to accomplish two main goals.

2To eliminate predictability

The seemingly chaotic sequence makes it difficult for most players to find any relationship between the wheel’s sectors and the numbers on the betting layout. Detecting biases toward specific sectors is extremely difficult, if not impossible, on such a wheel.

3To balance the wheel

The sequence ensures that numbers sharing similar properties are evenly dispersed. First, the numbers in two adjacent pockets are never the same color. Red and black alternate, balancing the color distribution across the wheel.

Second, high and low numbers alternate as evenly as possible. This balance is achieved with great success on the European wheel, where there is only one exception: the adjacent low numbers 5 and 10. In contrast, double-zero wheels contain more adjacent pairs in which both numbers are low or both are high. As a result, the American wheel is not as balanced as the European one.

The same principle applies to the distribution of odd and even numbers. The wheels are designed so that the numbers are spread out evenly in terms of parity. You will find no more than two adjacent odd or even numbers on the wheel. This pseudo-randomness reinforces the idea that roulette is based entirely on chance.

Which Wheel to Play?

The question arises which wheel should roulette players go for, the one with the single-zero or the one with the double-zero? To provide a satisfactory answer, we need to first explain why roulette is not a fair game, i.e. a game where both the player and the house share the same advantage and have equal odds of winning.

This would have been the case if the roulette wheel featured only pockets 1 through 36 for 18 red/even/low numbers and 18 black/odd/high numbers. Playing one such neutral game is pretty much the same as flipping a coin and betting on the outcome. The odds of winning the coin toss are the same as those of losing or 50%.

Unfortunately, gambling operators are not in the habit of running neutral games. Casino games always have a negative expected value for the players because their odds are titled in favor of the house. All tables inevitably yield a profit, a portion of which is used to pay the personnel that operates the games.

In roulette, the zero pocket skews the probabilities in favor of the house. All outside bets on dozens, columns, and number properties like parity, range, and color lose to the zero. It does not share any of these characteristics and is part neither of the dozens nor of the columns.

When you do win with a bet on red, for example, the house pays you at even odds (1 to 1) despite the fact the true odds of winning are lower than 50% because you have 18 winning and 19 losing pockets. The same applies to all roulette bets, including those on individual numbers.

Players are paid at a ratio of 35 to 1 when their number hits. This would have been okay if there were indeed only 36 sections on the wheel. Instead, you have 37 pockets in European roulette and 38 in the American variation.

 

Single-Zero Wheel House Edge
Double-Zero Wheels House Edge

The difference between the payouts and the true odds of winning represents the house edge. The advantage casinos derive from straight up bets at their single-zero tables is -1 x (36/37) + 35 x (1/37) = -0.0270 x 100 = -2.70%.

You end up losing $0.027 out of every dollar you wager in single-zero roulette. If the La Partage or En Prison rules are applicable at the table, they lead to a further reduction of the house edge.

The bottom line is you are bound to lose money to roulette in the long run regardless of which wheel you play. The real question here is do you prefer to lose money at a faster or a slower rate? We think the answer is pretty much obvious.

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The second green pocket with the double zero on American wheels almost doubles the casino's edge. For straight up bets, it stands at -1 x (37/38) + 35 x (1/38) = -0.0526 x 100 = -5.26%.

You are fighting these edges for all roulette bets bar the five number bet, which is available only in American roulette. It has an overwhelming casino advantage of 7.90% and should never be made. The minus sign in front of the two percentages clearly shows both roulette variations yield negative expectation for the player.

Players incur long-term losses of around $0.053 per every dollar they wager at the double-zero tables.

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