How to calculatte roulette standard deviation, the best answer

question

#1

Here is result of 120 spins. How to calculate standard deviation across the best 7 numbers to play?

image
0 3
1 6
2 3
3 5
4 1
5 3
6 3
7 1
8 6
9 6
10 4
11 7
12 5
13 6
14 5
15 6
16 4
17 3
18 4
19 6
20 3
21 3
22 3
23 5
24 2
25 2
26 1
27 1
28 1
29 3
30 2
31 1
32 0
33 1
34 1
35 3
36 1

#7

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.

Normal%20standard%20deviation

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.

z-score

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.

image

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.


How to calculate roulette advantage using ball jumps chart and prediciton data?
#2

Looks like the same wheel, about which we talked in neighbour posts , i writed formula how to calculate…


#13

While z-score or how we like to say amount if standard deviations tells us probability we can easy calculate our possible winnings based on the ball jumps data.

In our example we have 39 hits on the sector of 7 pockets in 120 spins we played.
If we play 7 numbers sector for 120 spins we would play;

7 x 120 = 840 units
We would win 36 units 39 times therefore
36 x 39 = 1404
And profit 1404 – 840 = 564 units

If we divide profit with units we invested we get advantage
564 / 840 = 0.67
It is 67% advantage
It means for each $100 we place on the table we would profit $68
We actually changed the casinos – 2.7% advantage, so the total change is about 70%.

On same principle we can calculate casinos advantage for the particular bet

For a single number

Chance to win is W = 1/37
Chance to lose L= 36/37
35 is amount of units we win
W = 1/37 x 35 = 0.027 x 35 = 0.945
1 is amount of units we lose
L= 36/37 x 1 = 0.972
We subtract L form W.
Advantage = 0.945 – 0.972 = - 0.027; or – 2.7%

On a same way we can calculate it for a spit bet

On a split bet we would win 17 units, 2 times on 37 spins and lose 35 times 1 unit;
Advantage = W – L = (2/37 x 17) – (35/37 x 1) = 0.918 – 0.945 = - 0.027

Someone may get confused and say but on a split bet I win 18 units because I get my chip as well. It is truth but then you wouldn’t lose one unit 35/37 but 37/37 times and calculation would be;
Advantage = W – L = (2/37 x 18) – 37/37 = 0.972 - 1 = -0.027 = - 2.7%


#3

I would like to know this as well
:slight_smile: Can you link to that “neighbor” post? Or is it private?

Thank you


#6

What wheel is that data from? And what ball? Looks kind of similar to my jump chart.

I think the best is ~15


#4

Almost same, but notice this is a question. When creating post there is tag area , if you write question the thread gets another format. Also members can give votes to answers they like.

You can replay to each post, or you can answer. Also the answers get sorted by highest vote.

Not sure who would be the best for this subject perhaps @Snowman.


#9

Good writed and good will be will write source.

But here is again the same problem , that we to all look after all happend. So we have data - find best place and for it we look how much sigmas we have…


#5

I think not private…


#8

It is , just an example data.


#12

1 SD has its meaning. The point is that you could see how with more numbers it increasing. We already made decision to look numbers next to each other but not just any with highest hits. That makes it different from what bias player may do.


#10

Should reply to the answer instead of making the answer but commenting it.
I am not sure, if looking only 2 numbers at any place than yes. But if looking next to each other numbers where most of them have significantly higher hits it is a different story.

If the chart looks as yours it would be close to impossible to be a coincidence, that next same amount of spins the pick gets shifted ~ ,9,18, 27 pockets. Few points in the high area may change in value but whole still should be there. For bias is different you look say 2 numbers at any place, in say 3x37 spins each one should get 3 hits but if 2 numbers get 5 it means nothing but if 0-18 mostly all are above average it already have meaning.


#14

Great post Forester!


#11

Still you must look in advance - in front, so calculate only for predicted place. If will look all overal and will select best - then will have maybe every time 3 STD, but such not be when will start play in casino for money…

That is this chart only counted in groups of 9 pockets.

image
And here is all recalculated acordingly mine methodic if to count direct we will get in pick 3.1 STD if i good remember.
With this data all will be good if not holes near to positive area in 5-8 zone and 27-29.
here are few moments - we do mistakes when colect data and second is that i can change only few distances to theese holes and all will be other. Enough to remove 3 distances from central place to theese holes and we see different picture. So this i try to recalculate - what can be and get what i get and that is usually very exact, so after such recalculations left only 1STD what is not enough for me, I play from something near to 2STD recalculated…