# South Africa's lottery probed as 5, 6, 7, 8, 9 and 10 drawn and 20 win

#### nsaspook

Joined Aug 27, 2009
9,444
https://www.bbc.com/news/world-africa-55154525

Tuesday's PowerBall lottery saw the numbers five, six, seven, eight and nine drawn, while the PowerBall itself was, you have guessed it, 10.
The organizers say the sequence is often picked. But some have alleged a scam and an investigation is under way.
If the system is random then that sequence of number is just as likely as any other possible sequence of numbers randomly drawn. The fact that 20 people won with those numbers says a lot more about the human fixation with simple sequences than possible fraud.

#### Delta Prime

Joined Nov 15, 2019
1,326
human fixation with simple sequences
Is that akin to seeing faces or animals in clouds?

#### Marley

Joined Apr 4, 2016
468
In fact I am surprised anyone chose 5, 6, 7, 8 and 9 as their numbers. I think a lot of people would say "that would never come up" when of course, the chance of that is the same as any other sequence.

#### BobTPH

Joined Jun 5, 2013
4,749
My bridge partner, every now and then, would open his hand and exclaim “Wow, this hand is one in 600 billion!”

Bob

#### Marley

Joined Apr 4, 2016
468
Knowing something about chance and probability is why I don't do gambling and lotteries!

#### atferrari

Joined Jan 6, 2004
4,576
Knowing something about chance and probability is why I don't do gambling and lotteries!
If you consider the frustration of never wining like the DC component in a function, the rest is the thrill and where the fun resides. And yes, basically you have to pay for it.

#### xox

Joined Sep 8, 2017
674
In fact I am surprised anyone chose 5, 6, 7, 8 and 9 as their numbers. I think a lot of people would say "that would never come up" when of course, the chance of that is the same as any other sequence.
Assuming each number has been drawn from a random distribution then the likelihood of drawing 9, given 8, given 7, etc, is actually extremely low.

Think of how a Galton board works.

Had you to constructed the numbers from a sequence of coin tosses (assigning, say, 64 bits to each number) then you'd actually see what a likely sequence might look like. The numbers 5, 6, 7, 8, and 9 are 3 to 4 bit numbers in a much larger space of 64 bits, so they could only ever occur VERY rarely in sequences pulled from random distributions (in ANY order). The balls at the very edges in the Dalton board represent those really unlikely sequences.

Code:
#include <stdio.h>
#include <stdlib.h>

int main(void)
{
FILE* pool = fopen("/dev/urandom", "rb");
size_t drawing;
for(int count = 0; count < 100; ++count)
{
printf("%zu, ", drawing);
}
puts("");
}
Output:

6572567561348488469, 7856962240734473823, 15482074707068412154, 12301282909526002858, 6878620608761634902, 4566982616094158700, 7581684543793300689, 8306023012610511870, 645050035323876702, 18284986536795687056, 1134092509357230841, 8201576040792171715, 4927617414793519388, 12240521024785874998, 959023656288354228, 2600197629769201122, 1782120095419890880, 4338646118552757416, 15150293780501307555, 7837302699635543891, 9794470691089399471, 5339305383240830012, 15664483181821866569, 5669928970320719566, 7609324124015069844, 4778045966151980163, 11039079233713472014, 9434063894603193159, 4677487635204951685, 5937542348105956437, 14296407800545187180, 11070826778348763219, 5336895398860585487, 13691456951696929834, 12039700856646904963, 12889241456529695803, 12658525950839309187, 13987478296898370191, 9339917404859293864, 9809451362137888122, 12051298359130051497, 3381614809038358578, 15367462081084105608, 16583753904611042104, 3391486731932765289, 14331680477184916002, 1385683823368457228, 17474509175656737468, 2305143898079249668, 8119910560376290075, 16669787200762797982, 8471575367925615151, 7927451435072496461, 14184906915822927224, 1838565656025395994, 17640143262393500679, 15146948963591934192, 12660433928857351585, 8332280043565068119, 16227660319925514611, 940525084228016342, 17320025975300020179, 7671678496407195248, 739758746545059388, 3605901704883070848, 6959479771298520333, 4514063285540630335, 11716026969693956907, 12059434711804620621, 16444585218902632657, 9858385205332228574, 1171742219962788373, 13071787832367697760, 929991841374390627, 17994605014876627489, 2652149740164180550, 4778761250100601366, 5697529438174129951, 16037983608138345037, 2631818177940747590, 5414190422671929525, 18128389637770418417, 10996047557991947882, 17520766722327515946, 12027577274600957506, 9102120447796262213, 7005126816856970605, 3677053835402643665, 2179836192586187800, 235345567311696604, 6586935402784971750, 4832121421944483967, 9546078603221183342, 16489549878760436483, 4655164390361820590, 18240647677826950288, 6918593769062157883, 9180033961761287591, 2535036870071753196, 15998362942904342112
Don't worry - 5, 6, 7, 8, 9 will eventually come up...just not in another thousand years!

#### bogosort

Joined Sep 24, 2011
678
Assuming each number has been drawn from a random distribution then the likelihood of drawing 9, given 8, given 7, etc, is actually extremely low.
That's true for any given sequence, whether (7, 8, 9) or (20183, 4, 998376). The probability of drawing any sequence is the same, so there's no advantage in favoring or avoiding any particular sequence.

#### nsaspook

Joined Aug 27, 2009
9,444
"Everything not forbidden is compulsory."
https://en.wikipedia.org/wiki/Gambler's_fallacy
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the erroneous belief that if a particular event occurs more frequently than normal during the past it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been less than the usual number of sixes.

#### joeyd999

Joined Jun 6, 2011
4,465
Think of how a Galton board works.
I think you are confusing Normal (Gaussian) Probability Distribution with Uniform Probability Distribution.

Joined Apr 16, 2011
547
Don't forget that with a lottery - the prize may need to be shared (as in the case described by OP)

For example, avoiding the "lucky" number 7 increases your chances of having the whole pot to yourself.

Picking numbers higher than 31 might decrease chances of having to share, since birthday dates are popular.

Or maybe one day people will cop-on and 32 might become the most popular choice, because it may be statistically the least likely choice. All depends on understanding current psychology and knowing how "lottery picker" software works.

Probably the best way to win is not to participate, as suggested earlier. I already saved more than £10,000 by not investing £5 a week in the lottery - for 40 years. If only I had not invested £500 a week - I could have avoided wasting so much more money ... (yes I know - this ignores the occasional £10 win)
I plan on not buying another 5 Ferraris next year - a further massive saving, I recommend negotiating the highest possible price with the most expensive car dealer before not buying.

Last edited:

#### joeyd999

Joined Jun 6, 2011
4,465
I already saved more than £10,000 by not investing £5 a week in the lottery - for 40 years.
Exactly.

I save (earn!) even more by keeping my wife locked up in the basement.

#### Hymie

Joined Mar 30, 2018
1,079
There was another strange lottery result in one of the American State lotteries some years back.

Six random numbers were drawn, however 6 people matched 5 of those random numbers (nothing strange you might think); but all 6 winners had the same 5 winning numbers and they all chose the same loosing number.

This caused the lottery organisers to investigate how this could happen.

Before reading below, you might like to think how this happened.

#

#

#

The investigation found that all 6 winners had entered their lottery numbers from those on a Chinese fortune-cookie. The fortune-cookie company was found to print the same lucky numbers on all their fortune-cookies – which were lucky for those who entered them that week.

#### xox

Joined Sep 8, 2017
674
That's true for any given sequence, whether (7, 8, 9) or (20183, 4, 998376). The probability of drawing any sequence is the same, so there's no advantage in favoring or avoiding any particular sequence.
Code:
#include <stdio.h>
#include <stdlib.h>

size_t draw()
{
static FILE* pool = NULL;
if(pool == NULL)
if((pool = fopen("/dev/urandom", "rb")) == NULL)
exit(1);
size_t drawing;
return drawing;
}

int main(void)
{
size_t count = 0;
puts("Waiting for the sequence of a 5 followed by a 6:");
for(;;)
{
if(++count % 100000000 == 0)
printf("...%zu tries...\n", count);
if(draw() == 5 && draw() == 6)
break;
}
puts("Wow, you must have waited a very long time!");
}

#### bogosort

Joined Sep 24, 2011
678
Code:
puts("Waiting for the sequence of a 5 followed by a 6:");
...
puts("Wow, you must have waited a very long time!");
Replace 5 and 6 with any two numbers and the result is the same.

#### xox

Joined Sep 8, 2017
674
Replace 5 and 6 with any two numbers and the result is the same.
Precisely. And only after one million iterations per second for one million years you'd churn out a sequence like that. So not very likely at all.

#### bogosort

Joined Sep 24, 2011
678
Precisely. And only after one million iterations per second for one million years you'd churn out a sequence like that. So not very likely at all.
But the same is true of any sequence, whether sequentially ordered or not. So, there's zero difference in probability of winning between choosing (1,2,3,4,5,6,7) or any other possible 7-number sequence. That's the entire point of a uniform distribution.

#### xox

Joined Sep 8, 2017
674
But the same is true of any sequence, whether sequentially ordered or not. So, there's zero difference in probability of winning between choosing (1,2,3,4,5,6,7) or any other possible 7-number sequence. That's the entire point of a uniform distribution.
Fine, so now run the program with those constraints and then see how long till it completes. The counter may well roll over several times before you'd get a sequence like that.