Roulette Number Sequences

Roulette is a semi-random game. And in case a particular number has not been a winner after a considerable number of wheel spins, say more than 70, it would seem that the number is set to win soon enough. Many people tend to believe this, as they do not understand that every ball spin has absolutely nothing to do with events in the past. It is preposterous to think that a roulette wheel have memory, or records of historical data! There is no mechanism to store information which of the numbers was a winner at the prior spin or the one before it, or at any of the earlier spins. Every time a ball is spun, the outcome is not linked with past outcomes, just like the case with a pair of dice. Therefore, each ball spin is an independent event.

If we take the American roulette wheel, at every spin of the ball the probability of a specific number winning is 1/38 (1 chance out of 38). Let us presume that the number 20 emerged as a winner two consecutive times. At the third spin the probability for the number 20 to win is again 1/38, or the exact probability as any of the remaining numbers on the wheel. If we presume that the number 20 has not won in the past 85 wheel spins, the probability for this number to win at the 86th spin is again 1/38!

Repeating numbers

The combined probability of the number 20 winning two times in a row is a result of individual probabilities. Or we have 1/38 x 1/38 = 1/1444. The combined probability of the number 20 winning three times in a row is 1/38 x 1/38 x 1/38 = 1/ 54 872. The combined probability of the number 20 winning four times in a row is 1/38 x 1/38 x 1/38 x 1/38 = 1/2 085 136. The chances for this event to occur diminish more and more with every repetition!

There may be those who believe that the fourth time the number 20 emerges as a winner, it has to deal with larger odds. That is not the case, because the odds were overcome on the first three wheel spins. The first three spins combined dealt with a probability of 1/54 872. In order to win on the fourth spin, the number 20 only has to overcome a probability of 1/38. If indeed this happens, the combined probability of all four spins is 1/ 54 872 x 1/38 = 1/2 085 136.

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These odds will be correct, regardless of what has occurred on prior spins, because the wheel has no memory of past events. On each separate wheel spin the probability remains 1/38. The table below presents the expected probabilities of repeating numbers.

Repeats Any Number Pre-selected Number
1 1 / 1 1 / 38
2 1 / 38 1 / 1444
3 1 / 1444 1 / 54 872
4 1 / 54 872 1 / 2 085 136

It is not a rare occurrence for any number to repeat itself. A repeat is likely to happen every 38 spins, or 2-3 times within one hour.

Repeating Numbers in Roulette

Number Sequences

An effective betting technique usually requires the placement of bets on groups of adjacent numbers all over the roulette wheelhead. The minds, that invented the number sequences for the French and the American wheels were obviously quite aware of that. They devised the wheels in a way, so that if one is to place a bet on contiguous sectors, he/she will need to scatter his/her chips across the betting layout. The majority of roulette computer programs usually are number-sequence sensitive, which means that a program adjusted to the American number sequence will probably not function with the French number sequence.

When playing on a particular wheel, one needs to know whether it uses the French or the American number sequence. Even if a particular wheel features only a single zero, this is not indicative of the number sequence it uses. For instance, there are casinos located in the Asian-Pacific region, which have roulette wheels with 37 numbers, only a single zero, but using the American number sequence (hybrid wheels).

Number Spans

If we consider the American roulette wheel, the most popular contiguous bet combination is based on the center column. The latter features the span (in a clockwise manner) from the numbers 23 to 5 with five gaps (0, 7, 9, 28, 30). In addition, two other numbers remain outside of the span (8 and 29). This bet covers a span width of 15 numbers, which represents almost 2/5 of the wheel perimeter.

This bet is usually placed in one of the following ways:

1. A player may place one chip on each of the numbers 0, 7, 9, 28, 30 and then place a stack of four chips (or more) on the center column;

American Roulette Center Column Straight Up

2. A player may place one chip on the row including 7, 8, 9, one chip on the row including 28, 29, 30, and then place two chips (or more) on the center column;

American Roulette Center Column and Street

3. A player may bet right on the center column, while hoping the ball will not come to rest on one of the five gaps.

American Center Column Bet Roulette

A curious fact is that two combinations of street (row) bets on the American wheel are often used by professional players. These combinations tend to be quite effective, because they cover eight-number spans and no gaps.

The first span extends from 22 to 1 and includes 4 street bets as follows: one on 1, 2, 3, one on 13, 14, 15, one on 22, 23, 24 and one on 34, 35, 36. We should note that there is also a secondary span of four numbers at the opposite side of the wheel. It includes the numbers 23, 35, 14, 2.

American Roulette Street Bets

The second span extends from 19 to 4. It includes one street bet on 4, 5, 6, one street bet on 31, 32, 33 and after that two split bets – one on 16-19 and one on 18-21. Only two numbers remain outside of the major span – 32 and 5.

American Roulette Street and Split Bets

If we consider the French wheel, the only easy way for one to place a contiguous-number bet is to demand a neighbors bet, which we already discussed.

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