To answer this question I will first calculate SD for each number hit.

From that we get:

Probability to win for a single number on roulette would be 1/37

Probability to lose for a single number on roulette would be 36/37 or (1 - Probability to win = 1 - 1/36 )

Trails is 120 spins.

From that we get

SD = SQRT (1/36 x 36/37 x 120)

SD = SQRT (3.15)

SD = 1.77

The Mean, (expected hits on each number for even distribution) for 120 spins on 37 numbers is 120/37 = 3.24

Let’s look from our data position the highest hit rate position 11.

It has 7 hits.

Now let’s calculate how it lies from the mean?

It is called Z-score

z = ( 7 – Mean) / SD

z = (7 – 3.24) / 1.77

z = 2.12

Position 11 with value 7 has z-score value of 2.12.

Values within one standard deviation of the mean have 68% chance to happen;

two standard deviations of the mean about 95%;

and within three standard deviations about 99.7%.

You can see it on this chart.

From that chart we can only approximate so here is a table with values.

**How to find our z-score = 1 in the table?**

Scroll down to find in blue 1 row then go left to find in green 0.00.

You should find value 0.8413

z-score can be and negative number but in the table we don’t have data for such case. You can make one but it is basically in this case 1 - 0.8413 = 0.1587. So number 1 minus whatever is on positive side.

*If you look chart you can see that z-score 0 has value 0.5. Of course it is in middle and there is a 50:50 chance for each side.*

If i deduct 0.1587 from 0.8413 i get

0.8413 = 0.1587 = 0.6826

which means 68% of hits will be within 1 SD.

That matches previously stated

Values within one standard deviation of the mean have 68% chance to happen;

Now if we look our z = 2.12 in the table we find 0.9826

Position 11 has highest value than 98% of expected values of the other positions.

We can look z-score for all numbers.

**Now lets look sections of 7 pockets.**

For that I extended data on each side by 3 pockets as on the picture.

Before 0 copied 34,35,36 and after 0 copied 0,1,2, it makes it easier to add ends of data.

Added 7 cells together and divided by 7 which gives me an average.

To find how much hits are from an average in this case 120/37=3.24

Subtract from amount of hits 3.24

Then divide result with 3.24.

Bingo

Make a chart and you get something as this.

Showing 72% advantage at 11,12

Median would be in middle of green area so 14 which could be safer to play.

**So let’s look now SD across 7 pockets sector**

SQRT (7/37 x 30/37 x 120) = SQRT 18.4 = **4.29**

It is higher.

But Mean in this case would be (120 / 37) x 7 = 22.7

And around position 12 on 7 pockets sector we have 39 hits.

So let’s check z-score;

Z = (39 – 22.7) / 4.29 = **3.79**

You can see z-score is much higher even the normal SD distribution is higher.

**It tells you that almost there is no chance that so much higher amount of hits across 7 pockets is just a coincidence.**