The Law of the Third

A good roulette strategy or system should be based on hard facts, or true insights of the roulette wheel. Everything else might well be wishful thinking. First we must identify a truth about the game. Then we must analyze it extensively and then comes the most difficult part: take advantage of it and make a profit. Easier said than done. But let us try and see if we can build a roulette strategy on the Law of the third.

Each experienced roulette player knows that it is impossible for the roulette wheel to produce in 37 (or 38) spins all 37 roulette numbers (or 38 numbers in the case of the American wheel). 37 different numbers in 37 roulette spins probably never occurred in the long history of roulette. This fact represents a mathematical reality.

This empirical insight, which can also be proven mathematically with probability theory, is called Law of Third, and it says that in average: in 37 or 38 spins, 1/3 of the numbers (roughly 12 numbers) do not appear. Or reversely: in 37 spins only the 2/3 of the numbers appear (roughly 24 numbers). That again means that some numbers must appear several times within 37 spins. After statistical analysis of many thousands of roulette spins on a real roulette wheel and not RNG, we receive on average the following results:

Within 20 spins we have 16 different roulette numbers
4 numbers appeared twice-within 37 spins we have 23 or 24 different numbers do appear on the average,
10 numbers appear twice
and 2 or 3 numbers appear three times.
Within 110 spins we have on average 35 different numbers,
of which 28 appear twice,
from these 28 numbers 20 appear three times,
from these 20 numbers 12 appear four times,
from these 12 numbers 6 appear five times,
from these 6 numbers 3 appear six times and
from these 3 finally 1 number appears seven times.

The table below shows the complete outline of the appearance of the numbers from spin 1 up to spin 111. To keep the table short we have omitted the spin lines where nothing happens. The table is easy to read: For example with spin 12 one number appeared twice and with spin 21 already 16 numbers appeared once and 4 numbers twice.

If you understand the logic in the above statistics, it is easy to apply the same logic to other bets, like the streets, the lines and even the dozens. The law of the third holds true in any bet. Hope this little insight, was inspirational to you, to try and devise a new roulette strategy or system. It goes without saying that such a law depends on mathematics and is valid, for both physical and (fair) online roulette games.