American and European Wheel Sequences

People who approach the roulette table for the first time sometimes fail to take notice of one very crucial detail. Most roulette players focus solely on the table layout when making their bets without taking into consideration the numbers’ arrangement on the wheel. A big oversight on their behalf.

Upon closer inspection, aspiring roulette players will undoubtedly notice there is a huge difference between the wheel and the betting layout on the table. Make no mistake – this is not a coincidence. It is done deliberately to ensure the ultimate randomization of results. This hinders more observant players from predicting in which pocket the ball will land.

The most obvious way of achieving this is through the alternation of the pockets’ color. Red always follows black on the wheel, which is not the case on the layout where two red or two black numbers sometimes sit next to each other. Also, the numbers are listed in sequential order on the betting layout but are spread out in a seemingly random manner on the wheel.

This peculiarity of the game forces section bettors to spread their action all over the layout when wagering on specific wheel segments. Let’s have a closer look at the number sequences for 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 is staring you right in the face as soon as you approach the American roulette table. There is one additional pocket with a double-zero (00) plus numbers 0 through 36. This makes for a total of 38 numbered segments on the wheel.

The American wheel uses the following clockwise sequence for its numbers00, 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 ones. Green color is used for the single-zero and the double-zero, which represent the house edge of the game (5.26%). Some American wheels use blue instead of green color for their zeros.

If you inspect the double-zero wheel up close, you are bound to notice certain regularities. The order of the numbers is, in fact, pseudo-random. Ironically, this pseudo-randomness aims at ensuring completely arbitrary outcomes and eliminating predictability.

The first regularity that strikes you is that an odd number is almost always directly facing each even number. Look at number 25 red, for instance. It is sitting on the opposite side of the wheel directly against 26 black. A similar pattern can be observed with the majority of the other even and odd numbers. The two green zeros appear to disrupt this pattern ever so slightly.

This brings us to the second pattern that concerns the color characteristics of the numbers. Of course, red and black always alternate on the wheel. It also makes sense that the color of the numbered pockets coincides with the color of the numbers spread over the betting layout. The interesting thing here is that red numbers sit across black ones, with very few exceptions. Similarly, the green single zero is placed directly across the double zero.

Opposite numbers are usually sequential in terms of value. Check the double-zero wheel and you will see 13 black is positioned across 14 red, 15 black sits against 16 red, 29 black faces 30 red, and so on.

Also, odd and even numbers tend to appear in pairs on the wheel. For example, 25 sits next to 29, 12 sits next to 8, 19 is placed next to 31, etcetera. A disruption of this pattern occurs only near the sectors with the zeros.

The double zero separates the pair of odd numbers 27 and 1. Respectively, you have odd 27 next to even 10 on the right of the 00 pocket. The single zero divides numbers 2 and 28, so you have even 28 next to odd 9 to the left of the 0 pocket.

One can discern a pattern when it comes to low (1-18) and high (19-36) numbers as well. The spread of the wheel appears to be such 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

As you can see, the two types of wheels use entirely different sequences but both have their numbers ordered in a seemingly random way. If you check a dictionary, you will see the word randomness is defined as “the absence of predictability and patterns in events”.

However, one can discern some patterns on the roulette wheel upon closer inspection, albeit with some difficulty. This is anything but coincidental. The numbers are spread out in this manner for the purpose of accomplishing two main goals.

2To eliminate predictability

The seemingly chaotic sequence makes it difficult for most players to find any relations between the wheel sectors and the numbers on the layout where the bets are placed. Noticing biases toward specific sectors is extremely hard, if not entirely impossible, on one such wheel.

3To balance the wheel

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

Secondly, numbers from the high and low range must alternate as evenly as possible. This is achieved with great success on the European wheel where there is only one exception to this rule for the adjacent low numbers 5 and 10. In contrast, there are more pairs of neighboring low and high numbers on double-zero wheels. As a result, the American wheel is not as balanced as the European one.

The same pertains to the distribution of the odd and even numbers. The wheels are devised in such a way so that the numbers spread out evenly in terms of parity. You will find no more than two adjacent odd or even numbers on the wheel layout. This pseudo-randomness reinforces the concept 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.

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.