United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 3, 2010, 10:16 pm - IP Logged

The Quest for a Blockbuster System

In a couple of my earlier posts, I mentioned that I had 12,200 Draw results for the Pennsylvania Daily Number game (Evening). This was incorrect. I hadn't finished grabbing all 33.4 years from the PA website, so I multipled 33.4 by 365 and rounded to 12,200. In fact, PA did not draw Daily Numbers on Sundays for nearly 2 years. So, now that I'm done, what I have are 11,563 rows from March 1, 1977 to today, August 3, 2010.

Theoretically, according to probability as I learned it, a particular 3 digit number is expected to be drawn, on average, once every 1000 draws, provided there is no human or mechanical interference in the selection process. This theory can be tested easily at the PA website by merely entering the number of interest in the Daily Number (Evening) "Has my number ever hit before" boxes, and clicking Search. Now, since there have been approximately 12,000 draws, we should expect each number to be drawn around 12 times, give or take. The give or take is measured in standard deviations, which I have not yet calculated. However, more often than not, I observe the number of hits to fall in the range 9 to 15 over the 33.4 year period, which looks normal. For example, 328 had 13 hits, 493 had 11, and 473, 12. Some results that some here will not want to believe are 111:12 hits, 888:13, and 000:14. The results are all public information at the PA Official site.

Which brings us to some more complicated backtests, those that aren't available seamlessly at the PA site. For starters, I just wrote a tiny program which scans the 11,563 lines in the file to answer some of the easier questions. The first question I asked was, What would have happened if each day I had bought a straight ticket on the PA Daily Number (Evening) , and religously chose the WINNING NUMBER OF THE PREVIOUS DAY? So, here is our first SYSTEM in the Fooled by Randomness thread!Always buy the previous day's winning number. (Send out a Toad Alert!)

Hopefully this will be the prelude to testing some of themore sophisticated Systems published here for 3 digit lotteries.

According to the same probability theory used to calculate the number 12 above, for more or less random selections, the results for yesterday's winners should be the same! On any given day, in a fair game, the odds of a specific number hitting is 1:1000. Now, will this apply to a choice like "Yesterday's Winner?" We will soon see. But first, I'd like to satisfy my curiosity by staging a Poll here. I've never done one, so I'm not sure where it will be seen when I initiate it from this Forum/Thread. This site is pretty cool, so I'm sure it will work out.

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 6, 2010, 1:09 pm - IP Logged

Quote: Originally posted by GASMETERGUY on August 6, 2010

So, here is our first SYSTEM in the Fooled by Randomness thread!Always buy the previous day's winning number. (Send out a Toad Alert!)

Why should I buy the previous day's winning number?

GASMETERGUY,

I didn't say you should. This is just an exercise to prove that buying yesterday's winning number Straight will result in approximately the same number of hits over 33+ years as you would expect buying QPs. Stay tuned!

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 7, 2010, 12:22 am - IP Logged

Quote: Originally posted by GASMETERGUY on August 6, 2010

Always buy the previous day's winning number.

Sorry. My bad. I read "always" and assumed you meant "You should".

You're right, I should have been more clear about what that boldfaced sentence really was. RedToad had been complaining about my lack of a System in this Forum and this was my [I guess confusing] way of pulling his chain a little. Thanks for your interest and comments.

NASHVILLE, TENN United States Member #33372 February 20, 2006 1044 Posts Offline

Posted: August 7, 2010, 10:55 am - IP Logged

Speaking of Red Toad, IMHO he was only trying to provoke you into revealing your thoughts instead of your results. I coult be wrong; I often am; but that is the way I read his posts.

I, too, am only interested in your thoughts. Results (i.e. the posting of numbers) means nothing. I could do that for myself. How you achieved those numbers is the main interest. Being the kind, patient person that I am (I pulled a muscle patting myself on the back for that one) I will wait upon your pleasure. I am sure you will reveal your thinking in your own good time.

Kentucky United States Member #32652 February 14, 2006 7344 Posts Offline

Posted: August 7, 2010, 9:49 pm - IP Logged

Quote: Originally posted by jimmy4164 on August 3, 2010

The Quest for a Blockbuster System

In a couple of my earlier posts, I mentioned that I had 12,200 Draw results for the Pennsylvania Daily Number game (Evening). This was incorrect. I hadn't finished grabbing all 33.4 years from the PA website, so I multipled 33.4 by 365 and rounded to 12,200. In fact, PA did not draw Daily Numbers on Sundays for nearly 2 years. So, now that I'm done, what I have are 11,563 rows from March 1, 1977 to today, August 3, 2010.

Theoretically, according to probability as I learned it, a particular 3 digit number is expected to be drawn, on average, once every 1000 draws, provided there is no human or mechanical interference in the selection process. This theory can be tested easily at the PA website by merely entering the number of interest in the Daily Number (Evening) "Has my number ever hit before" boxes, and clicking Search. Now, since there have been approximately 12,000 draws, we should expect each number to be drawn around 12 times, give or take. The give or take is measured in standard deviations, which I have not yet calculated. However, more often than not, I observe the number of hits to fall in the range 9 to 15 over the 33.4 year period, which looks normal. For example, 328 had 13 hits, 493 had 11, and 473, 12. Some results that some here will not want to believe are 111:12 hits, 888:13, and 000:14. The results are all public information at the PA Official site.

Which brings us to some more complicated backtests, those that aren't available seamlessly at the PA site. For starters, I just wrote a tiny program which scans the 11,563 lines in the file to answer some of the easier questions. The first question I asked was, What would have happened if each day I had bought a straight ticket on the PA Daily Number (Evening) , and religously chose the WINNING NUMBER OF THE PREVIOUS DAY? So, here is our first SYSTEM in the Fooled by Randomness thread!Always buy the previous day's winning number. (Send out a Toad Alert!)

Hopefully this will be the prelude to testing some of themore sophisticated Systems published here for 3 digit lotteries.

According to the same probability theory used to calculate the number 12 above, for more or less random selections, the results for yesterday's winners should be the same! On any given day, in a fair game, the odds of a specific number hitting is 1:1000. Now, will this apply to a choice like "Yesterday's Winner?" We will soon see. But first, I'd like to satisfy my curiosity by staging a Poll here. I've never done one, so I'm not sure where it will be seen when I initiate it from this Forum/Thread. This site is pretty cool, so I'm sure it will work out.

Look for the Poll soon!

"Theoretically, according to probability as I learned it, a particular 3 digit number is expected to be drawn, on average, once every 1000 draws, provided there is no human or mechanical interference in the selection process."

I have a program that tracks past result but doesn't include all the past drawings so I could only look at the past 5400 in the PA evening drawing. The mean would be 5 draws so I counted the numbers with less than 5 hits and there were 395. This tells us that about 40% of the numbers didn't average 1 hit every 1000 drawings. And 20 of those numbers only hit once so while probability says each number, including the previous drawing should hit once every 1000 drawings, it doesn't mean they will.

On the other side of the coin, 6 numbers did repeat so your starter system did do better than once every 1000 drawings in that time frame!

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 8, 2010, 1:27 pm - IP Logged

Quote: Originally posted by Stack47 on August 7, 2010

"Theoretically, according to probability as I learned it, a particular 3 digit number is expected to be drawn, on average, once every 1000 draws, provided there is no human or mechanical interference in the selection process."

I have a program that tracks past result but doesn't include all the past drawings so I could only look at the past 5400 in the PA evening drawing. The mean would be 5 draws so I counted the numbers with less than 5 hits and there were 395. This tells us that about 40% of the numbers didn't average 1 hit every 1000 drawings. And 20 of those numbers only hit once so while probability says each number, including the previous drawing should hit once every 1000 drawings, it doesn't mean they will.

On the other side of the coin, 6 numbers did repeat so your starter system did do better than once every 1000 drawings in that time frame!

NASHVILLE, TENN United States Member #33372 February 20, 2006 1044 Posts Offline

Posted: August 8, 2010, 2:28 pm - IP Logged

I have a program that tracks past result but doesn't include all the past drawings so I could only look at the past 5400 in the PA evening drawing. The mean would be 5 draws so I counted the numbers with less than 5 hits and there were 395. This tells us that about 40% of the numbers didn't average 1 hit every 1000 drawings. And 20 of those numbers only hit once so while probability says each number, including the previous drawing should hit once every 1000 drawings, it doesn't mean they will.

Because your results are skewed and are opposite what theory says should be, I went to the PA website to find out if the game was ball drop or RNG. While the information was not straightforward, I am lead to believe that particular game is RNG. Feel free to correct me if I am mistaken.

Being RNG, is anyone surprised by the skewed results? Should you be?

This, as far as I am concerned, is further evidence that states manipulate RNG to their benefit.

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 8, 2010, 8:39 pm - IP Logged

Quote: Originally posted by GASMETERGUY on August 8, 2010

I have a program that tracks past result but doesn't include all the past drawings so I could only look at the past 5400 in the PA evening drawing. The mean would be 5 draws so I counted the numbers with less than 5 hits and there were 395. This tells us that about 40% of the numbers didn't average 1 hit every 1000 drawings. And 20 of those numbers only hit once so while probability says each number, including the previous drawing should hit once every 1000 drawings, it doesn't mean they will.

Because your results are skewed and are opposite what theory says should be, I went to the PA website to find out if the game was ball drop or RNG. While the information was not straightforward, I am lead to believe that particular game is RNG. Feel free to correct me if I am mistaken.

Being RNG, is anyone surprised by the skewed results? Should you be?

This, as far as I am concerned, is further evidence that states manipulate RNG to their benefit.

GASMETERGUY,

PA "Daily Number" MidDay is computer selected, the Evening draw is Live Ping Pong Balls. I'm using the (Evening) data.

Please double check me on that, but I'm pretty sure that's the way it is. (I wouldn't have chosen that game if I new it was computerized.)

We watch the Daily Number (Evening) here on Local TV at 7PM.

Skewed? What do you mean? You looked at 5,400 drawings, I'm looking at nearly 12,000. This is why I'm expecting 12 hits, and you should be expecting 5. I also expect there will be numbers that hit more or less than 12 times(5 in your case.) Did you count how many hit MORE than 5 times? If I have time, I will calculate the mean and standard deviation of the "Number of Hits" for each of the 1000 numbers (000-999) in my Aprox. 12,000 draws. That result plus the distribution of the hits resulting from playing "Yesterday's Winner" should clear this up for you.

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 8, 2010, 9:46 pm - IP Logged

Quote: Originally posted by jimmy4164 on July 31, 2010

The name of this Thread is the name of one of my favorite books, written by Nicholas Taleb. If you read it, you will know why I chose This Title, in This Forum. It's too late for me to elaborate further at this time. Tomorrow is another day.

Harry C. Edwards, a reviewer at Amazon, had this to say:

"If the prescriptions for getting rich that are outlined in books such as The Millionaire Next Door and Rich Dad Poor Dad are successful enough to make the books bestsellers, then one must ask, Why aren't there more millionaires? In Fooled by Randomness, Nassim Nicholas Taleb, a professional trader and mathematics professor, examines what randomness means in business and in life and why human beings are so prone to mistake dumb luck for consummate skill. This eccentric and highly personal exploration of the nature of randomness meanders from the court of Croesus and trading rooms in New York and London to Russian roulette, Monte Carlo engines, and the philosophy of Karl Popper. Part of what makes this book so good is Taleb's ability to make seemingly arcane mathematical concepts (at least to this reviewer) entirely relevant in evaluating and understanding everything from the stock market to the success of those millionaires cited in the aforementioned bestsellers. Here's an articulate, wise, and humorous meditation on the nature of success and failure that anyone who wants a little more of the former would do well to consider."

--Highly recommended

--Jimmy

OK All,

I'm pressed to go to my other life shortly, so this will be shorter than I planned. (I'm sure you all know about that problem!) I will elaborate more later or tomorrow if comments warrant it. On the Poll, the correct answer was 12. 7 out of 9 people got it right, which is great! I'd like to know why people picked the 3 and 100 options. Please don't be reluctant. Rest assured, you are not alone. Books have been written about this. Take the title of this Thread, for example!

You will be justified if you complain that in the Poll Question I did NOT specify the number of hits EXPECTED, which is what 12 is. In reality, with this specific Lottery data, the actual result was 14! So Shoot me! I think everyone will still see the point here.

I really have to leave now, so let me ask another Poll qustion, without a formal Poll: What do you think the results will look like if we change the "System" to be: Every day, play the winner from two(2) days ago (instead of one)? (This is a hypothesis, not a command!)

I also promised someone in another thread that I would calculate the Mean & Standard Deviation of the "Number of Hits" for each of the 1000 numbers, over the 12,000(approximate) Draws. That will be in the next post along with the results for the above question.

Please alert me to anything that would indicate a problem with my data, or programs. You know the old saying, "Garbage in, garbage out!"

--Jimmy

---------------

PA Lottery Daily Number (Evening) [3 digits, 000-999]

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: August 9, 2010, 2:56 am - IP Logged

Quote: Originally posted by jimmy4164 on August 3, 2010

The Quest for a Blockbuster System

In a couple of my earlier posts, I mentioned that I had 12,200 Draw results for the Pennsylvania Daily Number game (Evening). This was incorrect. I hadn't finished grabbing all 33.4 years from the PA website, so I multipled 33.4 by 365 and rounded to 12,200. In fact, PA did not draw Daily Numbers on Sundays for nearly 2 years. So, now that I'm done, what I have are 11,563 rows from March 1, 1977 to today, August 3, 2010.

Theoretically, according to probability as I learned it, a particular 3 digit number is expected to be drawn, on average, once every 1000 draws, provided there is no human or mechanical interference in the selection process. This theory can be tested easily at the PA website by merely entering the number of interest in the Daily Number (Evening) "Has my number ever hit before" boxes, and clicking Search. Now, since there have been approximately 12,000 draws, we should expect each number to be drawn around 12 times, give or take. The give or take is measured in standard deviations, which I have not yet calculated. However, more often than not, I observe the number of hits to fall in the range 9 to 15 over the 33.4 year period, which looks normal. For example, 328 had 13 hits, 493 had 11, and 473, 12. Some results that some here will not want to believe are 111:12 hits, 888:13, and 000:14. The results are all public information at the PA Official site.

Which brings us to some more complicated backtests, those that aren't available seamlessly at the PA site. For starters, I just wrote a tiny program which scans the 11,563 lines in the file to answer some of the easier questions. The first question I asked was, What would have happened if each day I had bought a straight ticket on the PA Daily Number (Evening) , and religously chose the WINNING NUMBER OF THE PREVIOUS DAY? So, here is our first SYSTEM in the Fooled by Randomness thread!Always buy the previous day's winning number. (Send out a Toad Alert!)

Hopefully this will be the prelude to testing some of themore sophisticated Systems published here for 3 digit lotteries.

According to the same probability theory used to calculate the number 12 above, for more or less random selections, the results for yesterday's winners should be the same! On any given day, in a fair game, the odds of a specific number hitting is 1:1000. Now, will this apply to a choice like "Yesterday's Winner?" We will soon see. But first, I'd like to satisfy my curiosity by staging a Poll here. I've never done one, so I'm not sure where it will be seen when I initiate it from this Forum/Thread. This site is pretty cool, so I'm sure it will work out.

Look for the Poll soon!

On with the Quest for the Blockbuster System!

First, here are the results of betting on the Two(2) day old Winner:

(This is PA Daily Number (Evening) [000-999] 3/01/1977 thru 08/08/2010)

(Remember, this lottery did not have daily draws in all years - Note the 1st entry.)

Kentucky United States Member #32652 February 14, 2006 7344 Posts Offline

Posted: August 9, 2010, 12:14 pm - IP Logged

Quote: Originally posted by jimmy4164 on August 8, 2010

And what does this lead you to conclude?

Had I played the previous number for $1 in 5400 drawings and hit 6 times, I would have lost $2400 because the lotteries have a statistical payoff edge over any pick-3 bet. There probably are money management methods where betting the same number could show a slight profit, but realistically it's better to find something with a higher statistical probability than slightly better than average.

Basically you found something in the past that statistically exceeded the average for that time period without any guarantee it will continue into the future.

Kentucky United States Member #32652 February 14, 2006 7344 Posts Offline

Posted: August 9, 2010, 1:52 pm - IP Logged

Quote: Originally posted by GASMETERGUY on August 8, 2010

I have a program that tracks past result but doesn't include all the past drawings so I could only look at the past 5400 in the PA evening drawing. The mean would be 5 draws so I counted the numbers with less than 5 hits and there were 395. This tells us that about 40% of the numbers didn't average 1 hit every 1000 drawings. And 20 of those numbers only hit once so while probability says each number, including the previous drawing should hit once every 1000 drawings, it doesn't mean they will.

Because your results are skewed and are opposite what theory says should be, I went to the PA website to find out if the game was ball drop or RNG. While the information was not straightforward, I am lead to believe that particular game is RNG. Feel free to correct me if I am mistaken.

Being RNG, is anyone surprised by the skewed results? Should you be?

This, as far as I am concerned, is further evidence that states manipulate RNG to their benefit.

The PA evening pick-3 drawing is and has always been done by live ball drawings.

There is much more to probability than assuming each number should be drawn one time every 1000 drawings and the results show this. Looking at the last 1000 PA evening drawings, the digit 9 appeared 81 times in the first position meaning it was impossible for for at least 19 numbers starting with the digit 9 to be drawn in those 1000 drawings. The digit 2 was drawn 91 times and 6 was drawn 92 giving another 17 numbers. In the second digit position there were 5 digits failing to be drawn 100 times so add at least another 34 numbers. The third position had at least another 33 numbers for a total of at least 103 numbers (10%) that had no chance of being drawn.

Simply put, any digit in any position must be drawn at least 100 times before all 100 numbers using that digit can be drawn. It's cause and affect because if one digit in any position is drawn more than average at least one other digit will be drawn less than average meaning it's impossible for at least one 3 digit number to be drawn.

Comparing PA's live ball drawing results to TN RNG drawing, PA had at least 103 impossible numbers and TN had 111. To get the best comparison we would need to compare all the live ball drawing with all the RNG drawings, but for now comparing two is should be sufficient because of the time it would take.