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Backtesting and Simulating Lottery SystemsPrev TopicNext Topic
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Since Basic is the most mentioned computer language here, I adapted the Roulette Simulation from TASC magazine to simulate a Pick3 Game. You should be able to use the source code below to experiment with other simulations. The code is simple because it merely outputs one number for each Trial (Person), leaving the graphics, if wanted, to Excel, or any other program you might prefer. I loaded it into Excel and produced a Histogram similar to those I scanned from the magazine above. The first picture is a pure bar chart based on the frequencies of Equity segments in the data.
If you're smiling at the crudeness and lack of good formatting and labels in this chart, then you are one of the people I'm hoping will give us some tips on how to better utilize Excel for charting!
This second graph is a screen capture describing the same data, but is using mean and standard calculations of the descriptive statistics module I have installed im my Excel. It's called Analyze-It. I've been told that newer versions of Excel can accomplish a lot of what it does, so this is just FWIW.
In this run, among other things, I found the following:
Of the 50,000 "People" who played for 13.7 years...
1012 Broke even (Ended up with their original $5000)
539 were ahead $500
240 were ahead $1000
37 were ahead $1500
6 were ahead $2000
4 were ahead $2500
I'll leave it up to you to calculate the fate of the rest!
The source code below tells you what this data means.
I don't have time now to discuss this, so I'll leave it for you to mull over for a while. What I'm hoping you will eventually be convinced that fair and purely random lotteries can result in people winning far above average expectations, even in Pick3s, WITH NO MORE THAN CHANCE to assist them!
Here's a link to the output of a run of the program below:
http://www.box.net/shared/sign4r88k3
Here's the source code of the Basic code. Basic is not my "Native" language, so please check it carefully.
'
' Simulation of a Pick-3 Lottery Game
'
' Adapted by Jimmy4164 from Phil Abel's
' Roulette Simulation in Casino Trading,
' TASC Magazine, November, 2003
'
' Assumes that 50,000 People each buy one $1 Straight
' ticket per day for 5000 Days, or about 13.7 Years.
' A Win pays $500.
DIM Equity AS LONG
DIM Person AS LONG
DIM DDraw AS INTEGER
DIM LP AS INTEGER ' Lottery's Pick
DIM QP AS INTEGER ' Player's QP
' Print results to an Excel file for further analysis
OPEN "PICK3.CSV" FOR OUTPUT AS #3
PRINT #3, "Equity"
RANDOMIZE 11 ' Try different seeds and observe results
FOR Person = 1 TO 50000 ' 50,000 "People"
Equity = 5000 ' $5000 Starting Equity
FOR DDraw = 1 TO 5000 ' Cycle through the Draws
' Buy a Ticket
QP = 100 * INT(RND * 10) + 10 * INT(RND * 10) + INT(RND * 10)
' Pay the Clerk!
Equity = Equity - 1
' Let the Balls Fly!
LP = 100 * INT(RND * 10) + 10 * INT(RND * 10) + INT(RND * 10)
IF QP = LP THEN Equity = Equity + 500
NEXT DDraw
' Write each Person's Equity to the file
PRINT #3, Equity ' $5000 - Costs + Winnings
IF Person MOD 500 = 0 THEN PRINT Person, Equity, QP, LP 'Halo?
NEXT Person
CLOSE #3 ' Close the file
ENDJimbooble!!!!!
VERY nice! No kidding. Haven't played with it yet, but I will.
Don't know what version of Excel you have, but 2007, (under Insert) there are plenty of options to make chart, line, bar, pie, area, column......don't use them much myself.
Nice explanation of what does what too!
Thanks for sharing it. Now I'll give this post 5
. (Sorry for the 4. My thumbulator is pushing the thingabob on the widget too fast. Did I mention I hate Vista?) -
Jimbooble!!!!
Had fun playing with the code. Thanks for posting it!!!
My complaints: NONE OF THIS IS YOUR FAULT!!
1) The output screen is lacking any explanantion. It shows the number of draws, the ending balance (Equity after the 5000 draws), and then it shows the last QP number and last lottery draw. There were 4999 other draws not shown! Can't figure why that was done.
2) It would have been much more realistic to dimension 50,000 (or at least 100 people with one QP each) for each LP of the 5000 draws.
3) These 50,000 people are not all playing the same game! The way the program is written it runs 5000 draws for person one, then 5000 draws for person 2, 5000 more for person 3, all the way to 50,000.
4) Each of these 50,000 people are playing $1 a night on one QP. (I know that's picky, but even I, the guy who plays out of a change spittoon, have never l played less than $1.50 and three numbers).
I made some changes in the program so that everyone could see what was actually happening. Here's the program with the changes:
' Simulation of a Pick-3 Lottery Game
' Adapted by garyo1954 from Jimmy4164's adaptation from Phil Abel's
' Roulette Simulation in Casino Trading,
' TASC Magazine, November, 2003
' Assumes that 50,000 People each buy one $1 Straight (for different games)
' ticket per day for 5000 DIFFERENT Days, or about A DIFFERENT 13.7 Years.
' A Win pays $500. VERY IMPORTANT: These people are not playing the same game at the same time!!!!!DIM Equity AS LONG
DIM Person AS LONG
DIM DDRAW AS INTEGER
DIM LP AS INTEGER ' Lottery's Pick
DIM QP AS INTEGER ' Player's QP' Print results to an Excel file for further analysis
OPEN "H:\QB64\PICK3\DATA\MCSIM3.CSV" FOR OUTPUT AS #3
PRINT #3, "Equity"RANDOMIZE TIMER ' Try different seeds and observe results (changed to use TIMER)
FOR Person = 1 TO 50000 'starts 50,000 repetitions of 5000 draws (outside loop)
Equity = 5000 ' $5000 Starting Equity (YOUR $$$$$)
FOR DDRAW = 1 TO 5000 '(starts 5000 draw cycle; nested loop/inside loop)
' Buy a Ticket (one person, one number, each draw)
QP = 10 * INT(RND * 100) + INT(RND * 10)
' Pay the Clerk! (He wants your $1)
Equity = Equity - 1
' Let the Balls Fly! (draw here)
LP = 10 * INT(RND * 100) + INT(RND * 10)IF QP = LP THEN Equity = Equity + 500
' New lines for output screen here:
IF QP = LP THEN Match = Match + 1 'added to count WINS
PRINT "Person"; Person; SPC(2); "Draw"; DDRAW; SPC(2); "Equity-1"; Equity; SPC(2); "QP"; QP; SPC(2); "LP"; LP; SPC(2); "Win"; Match 'shows the result of each draw
FOR J = 1 TO 50000: NEXT J 'slows output screen; add 0's to slow it more, delete 0's to speed it up, or delete whole line.NEXT DDRAW '(sends program back to FOR DDRAW for next draw; nested loop/inside loop)
' Write each Person's Equity to the file
PRINT #3, Person, Equity, Match ' $5000 - Costs + Winnings (added Person number and Match to file)
IF Person MOD 500 = 0 THEN PRINT Person, Equity, QP, LP 'Halo? (?!? Don't know. Would make more sense IF Equity = 0 THEN PRINT Person, Equity, QP, LP)
Match = 0
NEXT Person '(send program back to FOR Person to start another 5000 draws for next player; end of outside loop)
CLOSE #3 ' Close the file
ENDIt's a nice simulation as long as everyone understands this is not 50,000 people playing $1 each draw on the same game. This is 50,000 people playing $1 a draw on different games or different draws.
BTW, 10 wins break even! Anybody playing a single $1 a draw would have to be VERY lucky with QPs to do that.
MY compliments for posting it Jimbooble!!!! May work on the output file part, REVISED SCREEN LOOKS LIKE:
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Since Basic is the most mentioned computer language here, I adapted the Roulette Simulation from TASC magazine to simulate a Pick3 Game. You should be able to use the source code below to experiment with other simulations. The code is simple because it merely outputs one number for each Trial (Person), leaving the graphics, if wanted, to Excel, or any other program you might prefer. I loaded it into Excel and produced a Histogram similar to those I scanned from the magazine above. The first picture is a pure bar chart based on the frequencies of Equity segments in the data.
If you're smiling at the crudeness and lack of good formatting and labels in this chart, then you are one of the people I'm hoping will give us some tips on how to better utilize Excel for charting!
This second graph is a screen capture describing the same data, but is using mean and standard calculations of the descriptive statistics module I have installed im my Excel. It's called Analyze-It. I've been told that newer versions of Excel can accomplish a lot of what it does, so this is just FWIW.
In this run, among other things, I found the following:
Of the 50,000 "People" who played for 13.7 years...
1012 Broke even (Ended up with their original $5000)
539 were ahead $500
240 were ahead $1000
37 were ahead $1500
6 were ahead $2000
4 were ahead $2500
I'll leave it up to you to calculate the fate of the rest!
The source code below tells you what this data means.
I don't have time now to discuss this, so I'll leave it for you to mull over for a while. What I'm hoping you will eventually be convinced that fair and purely random lotteries can result in people winning far above average expectations, even in Pick3s, WITH NO MORE THAN CHANCE to assist them!
Here's a link to the output of a run of the program below:
http://www.box.net/shared/sign4r88k3
Here's the source code of the Basic code. Basic is not my "Native" language, so please check it carefully.
'
' Simulation of a Pick-3 Lottery Game
'
' Adapted by Jimmy4164 from Phil Abel's
' Roulette Simulation in Casino Trading,
' TASC Magazine, November, 2003
'
' Assumes that 50,000 People each buy one $1 Straight
' ticket per day for 5000 Days, or about 13.7 Years.
' A Win pays $500.
DIM Equity AS LONG
DIM Person AS LONG
DIM DDraw AS INTEGER
DIM LP AS INTEGER ' Lottery's Pick
DIM QP AS INTEGER ' Player's QP
' Print results to an Excel file for further analysis
OPEN "PICK3.CSV" FOR OUTPUT AS #3
PRINT #3, "Equity"
RANDOMIZE 11 ' Try different seeds and observe results
FOR Person = 1 TO 50000 ' 50,000 "People"
Equity = 5000 ' $5000 Starting Equity
FOR DDraw = 1 TO 5000 ' Cycle through the Draws
' Buy a Ticket
QP = 100 * INT(RND * 10) + 10 * INT(RND * 10) + INT(RND * 10)
' Pay the Clerk!
Equity = Equity - 1
' Let the Balls Fly!
LP = 100 * INT(RND * 10) + 10 * INT(RND * 10) + INT(RND * 10)
IF QP = LP THEN Equity = Equity + 500
NEXT DDraw
' Write each Person's Equity to the file
PRINT #3, Equity ' $5000 - Costs + Winnings
IF Person MOD 500 = 0 THEN PRINT Person, Equity, QP, LP 'Halo?
NEXT Person
CLOSE #3 ' Close the file
END -
-
I made a small modification to the Pick-3 simulation code [posted earlier in this thread] to produce output that should be more familiar to most people here. Rather than output the Equity remaining from $5000 after 5000 $1 bets, I converted to Prize Ratio notation. So, a Prize Ratio of 50 corresponds to $2500 Equity remaining in the earlier posting. Here's a screen shot of the transformed results in Excel.
I wrote a throw-away program to compress the 50,000 lines of output from the simulation to produce this frequency chart, and in the process discovered an error in my earlier posting. When I said "6 were ahead $2000," I should have said "16 were ahead $2000." This line corresponds to the 140% Prize Ratio in the chart immediately above.
Hopefully, seeing the results displayed in this way will demonstrate more seamlessly what is going on in this random process, including the breadth of outcomes that are possible. For example, we usually make casual references to the fact that in Pick-3 games, the average prize ratio is expected to be 50%. However, as you can see, in this simulation of 50,000 people making 5000 bets each, only 8,872 actually got this 50% score. Note also that because the lottery payouts are so low, a 100% Prize Ratio is required to break even, moneywise. I'll leave it to you to look over the rest of the entries above, and draw further conclusions. What I hope you are beginning to see is that randomness can result in big losers AND big winners! And this is all possible with, or without, a system...
There have been complaints that my code is not valid because it doesn't pit the 50,000 people against the same lottery draw, but rather gives each person their own draw for each bet. The program is simpler the way it is, and I think you will eventually see that the results will be the same either way, but we can do it the other, just for fun! I think JADELOTTERY's (1) simulation and proof in the 10 ticket/1 draw vs 1 ticket/10 draw Thread should preclude the need for another Pick-3 run, but WHY NOT?!
I would like to be including the revised source code here, but because of what happened when I posted the original, I need more time to figure out how to get the code to people seriously interested without having it torn apart and changed in dubious ways. I'm trying to write code for this thread that can be understood by non-programmers, so there will be no attempt to use tricky algorithms or output fancy graphics. The core ideas in Monte Carlo simulations are really quite simple. Don't worry; the revised program is nearly identical to the original, and I'll keep it safe until we can determine a safe way to publish it.
So, next up will be a run where each of the 50,000 "People" will bet against 1 Lottery Draw, 5000 times. And if all goes well, we might smoothe out the graphs a little by including the more complex BOX calculations in subsequent runs.
--Jimmy4164
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This is not what I said I would be posting next here. But after considering Stack47's comments in the Poll Thread on this Topic, I think it's more important to continue looking at the effects on the distribution of winnings when the number of trials is increased or decreased. Besides, if JADELOTTERY's simulation of One Ticket / Ten Draws vs Ten Tickets / One Draw does not convince you that the way we stage the draw / people loops here is irrelavent, I doubt if I'll change your mind. But time permitting, we WILL try to do it eventually.
Stack47 is interested in 100 Draws, but first, let's go the other way. This graph depicts the frequency distribution of the Prize Ratios resulting from quadrupling the number of draws for each of the 50,000 players from 5,000 to 20,000. Other than this change, the code is identical.
Here is the Excel data compressed from the 50,000 Prize Ratios output from the Basic program:
Prize_Ratio, Frequency
12.5 , 12
15.0 , 13
17.5 , 24
20.0 , 50
22.5 , 75
25.0 , 193
27.5 , 534
30.0 , 855
32.5 , 1158
35.0 , 1956
37.5 , 2858
40.0 , 3332
42.5 , 3816
45.0 , 4294
47.5 , 4638
50.0 , 4496
52.5 , 4108
55.0 , 3797
57.5 , 3322
60.0 , 2757
62.5 , 2279
65.0 , 1878
67.5 , 1319
70.0 , 792
72.5 , 396
75.0 , 345
77.5 , 359
80.0 , 163
82.5 , 114
85.0 , 60
87.5 , 7---------------------------------------
Now, compare the graph and the frequency counts to their counterparts above in the last Post with 5000 Draws:What do you see as the primary difference?What happened to the 445 people who went completely bust in 5000 Draws?What happened to the 4 people who scored a 150% PR in 5000 Draws?What do you see happening to the shape of the curve in the graph as Draws are increased?Did anyone come out ahead in $ winnings in 20,000 Draws?--Jimmy4164 -
This is not what I said I would be posting next here. But after considering Stack47's comments in the Poll Thread on this Topic, I think it's more important to continue looking at the effects on the distribution of winnings when the number of trials is increased or decreased. Besides, if JADELOTTERY's simulation of One Ticket / Ten Draws vs Ten Tickets / One Draw does not convince you that the way we stage the draw / people loops here is irrelavent, I doubt if I'll change your mind. But time permitting, we WILL try to do it eventually.
Stack47 is interested in 100 Draws, but first, let's go the other way. This graph depicts the frequency distribution of the Prize Ratios resulting from quadrupling the number of draws for each of the 50,000 players from 5,000 to 20,000. Other than this change, the code is identical.
Here is the Excel data compressed from the 50,000 Prize Ratios output from the Basic program:
Prize_Ratio, Frequency
12.5 , 12
15.0 , 13
17.5 , 24
20.0 , 50
22.5 , 75
25.0 , 193
27.5 , 534
30.0 , 855
32.5 , 1158
35.0 , 1956
37.5 , 2858
40.0 , 3332
42.5 , 3816
45.0 , 4294
47.5 , 4638
50.0 , 4496
52.5 , 4108
55.0 , 3797
57.5 , 3322
60.0 , 2757
62.5 , 2279
65.0 , 1878
67.5 , 1319
70.0 , 792
72.5 , 396
75.0 , 345
77.5 , 359
80.0 , 163
82.5 , 114
85.0 , 60
87.5 , 7---------------------------------------
Now, compare the graph and the frequency counts to their counterparts above in the last Post with 5000 Draws:What do you see as the primary difference?What happened to the 445 people who went completely bust in 5000 Draws?What happened to the 4 people who scored a 150% PR in 5000 Draws?What do you see happening to the shape of the curve in the graph as Draws are increased?Did anyone come out ahead in $ winnings in 20,000 Draws?--Jimmy4164 -
-
-
This is not what I said I would be posting next here. But after considering Stack47's comments in the Poll Thread on this Topic, I think it's more important to continue looking at the effects on the distribution of winnings when the number of trials is increased or decreased. Besides, if JADELOTTERY's simulation of One Ticket / Ten Draws vs Ten Tickets / One Draw does not convince you that the way we stage the draw / people loops here is irrelavent, I doubt if I'll change your mind. But time permitting, we WILL try to do it eventually.
Stack47 is interested in 100 Draws, but first, let's go the other way. This graph depicts the frequency distribution of the Prize Ratios resulting from quadrupling the number of draws for each of the 50,000 players from 5,000 to 20,000. Other than this change, the code is identical.
Here is the Excel data compressed from the 50,000 Prize Ratios output from the Basic program:
Prize_Ratio, Frequency
12.5 , 12
15.0 , 13
17.5 , 24
20.0 , 50
22.5 , 75
25.0 , 193
27.5 , 534
30.0 , 855
32.5 , 1158
35.0 , 1956
37.5 , 2858
40.0 , 3332
42.5 , 3816
45.0 , 4294
47.5 , 4638
50.0 , 4496
52.5 , 4108
55.0 , 3797
57.5 , 3322
60.0 , 2757
62.5 , 2279
65.0 , 1878
67.5 , 1319
70.0 , 792
72.5 , 396
75.0 , 345
77.5 , 359
80.0 , 163
82.5 , 114
85.0 , 60
87.5 , 7---------------------------------------
Now, compare the graph and the frequency counts to their counterparts above in the last Post with 5000 Draws:What do you see as the primary difference?What happened to the 445 people who went completely bust in 5000 Draws?What happened to the 4 people who scored a 150% PR in 5000 Draws?What do you see happening to the shape of the curve in the graph as Draws are increased?Did anyone come out ahead in $ winnings in 20,000 Draws?--Jimmy4164 -
With only a finite number of chances to be on the "correct" side of the bell curve, I'd play for higher prizes.
P3 ain't it. That's like grinding shares for 1/16th of a point gains.
In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency. -
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