### Author Topic: Expected Standard Deviation  (Read 3722 times)

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#### Paul

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##### Expected Standard Deviation
« on: November 24, 2015, 03:53:27 PM »
Hi everyone,
Could someone check my calculations below and let me know if my figures are correct?

The expected standard deviation for 18 numbers on a single 0 wheel over 148 spins.

Step 1. The Probability Figure
= Square root (148 x (18/37) x (19/37
= Square root (148 x (0.486486) x (o.513514)
= Square root (148 x 0.249817
= Square root 36.97297
= 6.08054

Step 2. The Mean
= spins / 37 x 18
= 148 / 37 x 18
= 72

Step 3, Standard Deviation
1 Positive Standard Deviation   = 72 + 6.08054 = 78.08054
1 Negative Standard Deviation = 72 - 6.08054 = 65.91946
2 Positive Standard Deviation   = 72 + (6.08054 x 2) = 84.16108
2 Negative Standard Deviation = 72 – (6.08054 x 2) = 59.83892
3 Positive Standard Deviation   = 72 + (6.08054 x 3) = 90.24162
3 Negative Standard Deviation = 72 – (6.08054 x 3) = 53.75838
4 Positive Standard Deviation   = 72 + (6.08054 x 4) = 96.32216
4 Negative Standard Deviation = 72 – (6.08054 x 4) = 47.67784

With thanks,
Paul

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#### Reyth

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##### Re: Expected Standard Deviation
« Reply #1 on: November 24, 2015, 05:06:28 PM »
Awesome question!  I look forward to seeing the answers you receive as I have always wanted to make these calculations for myself as well. : )

#### kav

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##### Re: Expected Standard Deviation
« Reply #2 on: November 25, 2015, 05:42:05 AM »
Hi Paul,

Good question.
For calculating standard deviations for different bets the little program I posted in this topic is invaluable:
http://rouletteforum.roulette30.com/index.php/topic,543.msg6686.html#msg6686

So I suggest you compare your findings with it's results.

#### Harryj

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##### Re: Expected Standard Deviation
« Reply #3 on: November 25, 2015, 01:47:12 PM »
Hi Paul,
Your basic formula was spot on, but you should take into account the Varince. ie

For 68.3% of the time V = 1 SD of E(Expected result)
For 95%    of the time V = 2 SD of E
For 99.7% of the time V = 3SD of E

For the remaining  0.3% of the time the SD will be greater than 3.

I don't know if this is of importance to your calculations.

Harry

#### Real

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##### Re: Expected Standard Deviation
« Reply #4 on: November 25, 2015, 02:11:33 PM »
Just a quick note.

A standard deviation can't really be "negative".  What you want to really say is that it's "above" or "below" the mean or norm.  Saying that it's negative is kind of slang.  I'm definitely guilty of using the slang too, and most people will know what you mean when you say it's a  "negative standard deviation" but die hard mathematicians will sometimes snicker.
« Last Edit: November 25, 2015, 02:13:10 PM by Real »

#### Reyth

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##### Re: Expected Standard Deviation
« Reply #5 on: November 25, 2015, 06:09:22 PM »
Kewl thought!  Reminds me of the stock or commodity markets where downward movement does not mean loss and upward movement does not mean gain but that it is movement that actually matters. : )

People have a hard time of conceptualizing how to make money when you sell a position (as the initial transaction) but its "easier" to see how you make money when  you buy.
« Last Edit: November 25, 2015, 06:13:13 PM by Reyth »

#### Real

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##### Re: Expected Standard Deviation
« Reply #6 on: November 25, 2015, 06:44:15 PM »
1.Calculating standard deviation on the red/black/odd/even is pointless.

2. However...calculating it to measure whether or not a wheel is defective and testing individual numbers and sections is something entirely different.

Be smart.  Choose number two.

#### weird

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##### Re: Expected Standard Deviation
« Reply #7 on: November 26, 2015, 03:06:40 AM »
Hi Real,
Seems that u are very fond about the 'defective' , or rather 'tilted', or 'biased' wheel?

Then how are u detect a defective wheel???

The popular ways, are, slicing the wheel into six sections,[ ignore the green], [or six stars numbers, and  ignore the the green]...and then see how the section, or sections, that keep being hit, after a certain amount of spins.

How to slice the wheel into six section, on say, euro wheel.

1]count clockwise, from zero, 1,2,3,4,5,6,, that 1st section, [or simply 'section A']

then 1,2,3,4,5,6, again, that section B, and so on, till whole 36numbers spliced into six sections, of ABCDEF.

Thus after a certain amount of spins, you could see, which section, will have more hit, then the others.

And you may see that...
1]Wheel are balanced, which mean the sections will have almost equal hits after  a long spins.

2]A particular section, or 2, or 3 sections, will have more hits than the others...

And u act or bet accordingly...

#### Paul

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##### Re: Expected Standard Deviation
« Reply #8 on: November 26, 2015, 04:24:18 PM »
Hi Harry,
Thank you for your input. Knowing what you can expect in regarding deviation from the mean is a great advantage to the intelligent player. The percentage of expected results also gives the player an insight into the swings he may encounter. This is of assistance in working the size of the bank required to ride out the swings and is even more help in knowing when to stop play.
Regards,
Paul

#### Harryj

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##### Re: Expected Standard Deviation
« Reply #9 on: November 27, 2015, 06:11:36 AM »
No sweat Paul. Welcome to the forum,

Good Luck.
Harry