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Law of averages
States that the more you draw the greater the chance at error.
There the least you draw the better are your chances at winning.
If a coin is tossed 10 the chance error is less that it would be heads 50% of the time. If you toss the coin 100x the chances error is greater. therefore go with the chance error that is least.
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Box Model
Help see chance variability
The tickets in the box show the various amount that can be won or lost on a single play.
The chance of drawing any particular number form the box must equal the chance of winning or losing that amount on a single play. both +1 or -1
- Example:
- A gambler play a game of roulette where there are 38 numbers. He selects 2 numbers next to each other that will pay 17 to 1 on either number if he hits. If he lands, on any other number beside the 2 he selected he wins -1 (losses)
- Solution:
- Chances of winning each is roll is like drawing tickets from a box. 2 = 17, 17, and 36 = -1.
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Expected value Formula
Sum of Draws
(Number of Draws) x (Average of Box)
- Box = [1,2,3,4,5,6,7]
- Draws = 300
- (1+2+3+4+5+6+7)/7 = 4 (average of box)
4 x 300 = 1200
- Note: Roulette
- Be sure to add up the number of losses and the number of wins.
- In roulette there are 38 numbers. You can win on 18 (18 Red, 18 Black) and lose on -20, (0,00).
- Solution 18-20 = -2/38 (numbers) = -.05
- expected value of 100 draws x average $-.05
- is 100 x $-.05 = $-5
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(Standard Error) SE Formula
- Box =1,2,3,4,5,6,7
- Draws = 100
- SD = 2
Answer; 10 x 2 = 20
SE= 20
Note: If there is a lot of spread in the box the sd will be big and it's harder to predict how the draws will turn out
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Observe Value
Observe Value is like flipping a coin 100 times and getting an Observe Value of heads 54. Repeating the process you get a observed value of 47 and so on.
It's the total value that is observed after so many draws. This number can fluctuate.
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Expected Value & Chance Error
- The expected value (EV)= 150 [draws x averages of box]
- Chance Error is the (square root # of draws) Multiplied by its SD.
- Example:
- qaaq
- Box = [12345] Box Ave =3
- Draws = 50
- Observed Value = Least 50 (50 x 1), Max = 250 (50x5)
Note: Observed Values are usually less than 2 or 3 SE. think of Normal Curve (1 SD = 68%, 2 sd= 75%, 3 SD =98%)
The expected value (EV)= 150 [draws x averages of box]
SE =
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Using the Normal Cruve
Convert values to Standard units using the (Expected Value and Standard Error).
- The Standard error = SD
- Expect Value is Average
- Obsevered value = Range
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Short Cut SD Formula
(big number) - (small numbers) x [square root (fraction of big number) x (fraction of small number)]
Box = 5,1,1,1
(5-1) x (Square-root of
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Adding and Classifying
When it comes getting the SE of a single Number in a Set, You need to isolate the number and see who many times it is likely to happen against how many times it is not likely to happen.
- Set: 123456
- Draws=100
- SD = 1.71
EV of only 6 = 1/6 x 100 = 16.5
SD of only 6= 1/6 it goes up or 5/6 change it stay the same (Important)
Use SD Short Cut
SE =
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