Quote: Originally posted by jimmy4164 on Dec 27, 2012
I know what you're guessing, and what you're not guessing. I wonder how many other readers here know too, but are, for some reason, afraid to admit it? Oh well, here goes again...
Standard Deviation
In the spirit of the old adage "A Picture Is Worth A Thousand Words," I offer the following to help lift the fog that seems to have settled on this thread. Please excuse the use of * to produce this picture, and the rounding used to scale it. It is based on the output of a Monte Carlo style computer simulation I wrote to show what randomness is capable of producing in the lottery world, using Pick-3 as the vehicle.
In words, the simulation is of 25,000 players buying Five(5) $1.00 Straight Quick Pick tickets per day for Five(5) Years, or 1825 Days. The payoff is $500 when they win. Somewhat arbitrarily, I chose to start each player on day 1 with a "Stake" of $9125.00, which allows them to lose every bet they make over the five years without having to borrow from their friends.
Each row in the output below represents a subset of the 25,000 people whose results were the same.
In each row, the 3 numerical columns represent:
Win The amount in $ left to the players in their subset at the end of the five years
ROI The Return On Investment of the people in their subset ==> (100*(Win - 9125) / 9125)
# The number of people in the subset. (The summation of all rows is 25,000)
* Each asterisk represents 27 people in its respective row. You will notice roundoff error
which resulted from scaling to avoid distorting the "picture" through wrap around. It's not
really important, since the scale used here is fine enough to show you what's going on.
The most obvious roundoff errors are in the "tails" of the distribution. For example, 35
people (out of the 25,000) ended up with $500 at the end of the five years. 35 divided by
27 is ~1.3, which rounds off to 1. Thus 1 * in the 2nd row.
Study these results for a while, and then look below for further discussion. (2)
Win ROI #
0 -100 3 *
500 -95 35 *
1000 -90 99 ***
1500 -84 311 ***********
2000 -79 765 ****************************
2500 -73 1426 ****************************************************
3000 -68 2171 ********************************************************************************
3500 -62 2958 *************************************************************************************************************
4000 -57 3176 *********************************************************************************************************************
4500 -51 3346 ***************************************************************************************************************************
5000 -46 3065 *****************************************************************************************************************
5500 -40 2551 **********************************************************************************************
6000 -35 1825 *******************************************************************
6500 -29 1318 ************************************************
7000 -24 823 ******************************
7500 -18 535 *******************
8000 -13 283 **********
8500 -7 152 *****
9000 -2 83 ***
9500 4 36 *
10000 9 21 *
10500 15 4 *
11000 20 8 *
11500 26 2 *
12000 31 1 *
13500 47 1 *
14000 53 1 *
15500 69 1 *
For our (practical) purposes, we can treat this distribution as Normal. The Mean(1) of the Win column is 4560, with a Standard Deviation of 1501.50. As expected(approximately), the Mean ROI was 50.6 with a SD of 16.5. So, about 76% of the 25,000 people ended up holding between $3000 and $6000. Look above, and you can see what this looks like graphically. But remember, they all started out with $9125, so all of these 19,092 people were losers, losing between $3125 and $6125 over their 5 years of play. Which brings us to the BIG losers, and, TA! TA! The WINNERS! Yes, randomness produces winners, even over long periods of time. I'll let you peruse the data and absorb how many BIG losers there were, and how much they lost. What I want you to play close attention to, though, is the small group of winners that resulted. There were 75 people who ended up with more than the $9125 they started out with! But let's focus on the 18 people who ended up with from $10,500 to $15,500, representing gains from $1375 through $6375. Now, let's use our imaginations for a minute. Let's pretend that our Old Uncle Craig was the sole person out of the 25,000 who ended up with $15,500, for a return on his investment of 69% Let's assume further that he had devised a "System" for playing Pick-3 prior to the 5 years of play described above.
Here is the most important part of this posting! If Old Uncle Craig doesn't know anything about Means and Standard Deviations, or doesn't "Believe" they apply to flying lottery ping pong balls, DO YOU THINK ANYONE WILL EVER BE ABLE TO CONVINCE HIM THAT HIS WINNINGS WERE MERELY THE RESULT OF THE LUCK OF THE DRAW, OF RANDOMNESS?
(1) The Means and Std. Deviations mentioned here were calculated on 25,000 rows, so don't expect to get the same results from the data listed above. This data is a summary, calculated to allow you to view the distribution.
(2) I ran this simulation multple times, using different Random Number Generator Seeds, and the results were strikingly similar.
--Jimmy4164
P.S.
Boney526:
Since I've taken the time to write this program and present the results, I hope I can count on you to help explain it.
Anyone who has not yet posted in this thread:
If you understand this post, and agree with its conclusions, don't be bashful. It would be wonderful to discover that there are others here besides Boney526 and myself who are not Fooled By Randomness!