Chapter 16 and 17 (Law of Averages) (Expected Value Error)

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.

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.

(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

• 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

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.

• 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 = 

Convert values to Standard units using the (Expected Value and Standard Error).

• The Standard error = SD
• Expect Value is Average
• Obsevered value = Range

(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

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 =