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

WBahn

Joined Mar 31, 2012
29,976
I refer to my previous answer,
If we can not agree that the memory you refer to is provided by the observer, and not by the coins as you imply, then there is no further discussion to be had.

Once again, thank you for your time and input
its been very interesting and informative in many ways.

Have a good day
Fine. Let's stipulate that this "memory" is provided by the observer.

Will you NOW describe how this observer's memory somehow influences the outcome of future coin flips based on what they have observed in prior coin flips?

Or will you continue to duck the question?
 

402DF855

Joined Feb 9, 2013
271
If your random number generator always returns zero, then how can it produce anything other than a string of either all heads or all tails (depending on what 0 maps to)?

Please provide the simple program you used.
Uhhm, hopefully it was obvious my "generator" was rhetorical. My simulation used rand() from the C library.
C:
    DWORD nt=0;
    DWORD z=0;
    DWORD counts[15] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
    for(;z<1000;z++) {
        DWORD j;
        nt=0;
        for(j=0;j<14;j++) {
            int bT = (rand()&4)==0;
            if (bT)
                nt++;
        }
        counts[nt]++;
    }
    for(z=0;z<15;z++) {
        printf("%d %d\n",z,counts[z]);
    }
    return 0;
 

bogosort

Joined Sep 24, 2011
696
A quick simulation of flipping 14 times shows the odds of seeing 8 tails as about 18% or 1 in 6.
You're moving the goal posts. There are a little more than 3,000 different sequences of 14 flips with 8 tails in them, so the chance of flipping any one of them is about 18%. What is the probability of flipping precisely one of those? 1 in 16384.

Note that you can apply your argument in the original context of the lotto. We (presumably) know that the probability of drawing (5,6,7,8,9,10) is the same as any other sequence. But if we consider the set of all recognizable drawings, then the probabilities increase significantly. One pattern of recognizable drawings includes:

(1,2,3,...) or
(2,3,4,...) or
(3,4,5,...) or
...
(20,21,23,..) or
(21,22, 23,..) or
...
(..., 48,49,50)

Another pattern includes:

(1,3,5,...) or
(3,5,7,..) or
...

Yet another:

(2,4,6,...) or
(4,6,8,...) or
...

Taking the union of all such sets, the probability of drawing a recognizable ("suspicious") sequence of balls is still low, but significantly higher than one might think.
 

WBahn

Joined Mar 31, 2012
29,976
Uhhm, hopefully it was obvious my "generator" was rhetorical. My simulation used rand() from the C library.
C:
    DWORD nt=0;
    DWORD z=0;
    DWORD counts[15] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
    for(;z<1000;z++) {
        DWORD j;
        nt=0;
        for(j=0;j<14;j++) {
            int bT = (rand()&4)==0;
            if (bT)
                nt++;
        }
        counts[nt]++;
    }
    for(z=0;z<15;z++) {
        printf("%d %d\n",z,counts[z]);
    }
    return 0;
It wasn't obvious (to me) at all. You offered up your PNG and then said that you performed a simulation using your PNG.

The rand() function from the C library isn't a particularly good one. Whether its biases would have a noticeable impact on this kind of simulation, I don't know.

I don't see how this simulation addresses the question of how many tosses are needed to see twenty heads in a row.

Your inner most loop counts the number of tails in 14 tosses.

Your simulation also treats each set of 14 tosses as separate, so you might have the last 9 tosses of one set of 14 be all heads and the first 11 tosses of the next set of 14 tosses be all heads, making 20 heads in a row, and you would miss it.
 

Deleted member 115935

Joined Dec 31, 1969
0
Fine. Let's stipulate that this "memory" is provided by the observer.

Will you NOW describe how this observer's memory somehow influences the outcome of future coin flips based on what they have observed in prior coin flips?

Or will you continue to duck the question?

I refer to my previous posts,

I have found your answers insulting, for instance implying that I think coins have memory

and then it takes you a number of posts for you to even answer the question can we agree that the memory is with the observer.

And now you start shouting " Will you NOW describe "
and being aggressive " will you continue to duck the question "

as such ,as per my previous post, I can see no further reason to continue this "discussion".

Again ,

thank you for your time,
it has been very informative ,

have a good day,
 

402DF855

Joined Feb 9, 2013
271
You're moving the goal posts.
No I'm not. Rather, people are discussing two distinct but related issues. Your issue is that the odds of flipping heads is 1/2. This is obvious and no one is arguing otherwise. My issue is that when flipping the coin more than once, we are likely to see approximately the same number of heads and tails. (See graph below.) Joed999 stated that seeing 8 tails in 14 flips is 1 in 16384, which is ludicrous. (Sorry Joey!) Not only is it about 1/6 the odds of seing 6, 7, or 8 are what 60%+. So if you all tails, or even mostly tails, this would be a remarkable outcome. Not impossible, but unlikely.
1607970583879.png
 

WBahn

Joined Mar 31, 2012
29,976
I refer to my previous posts,

I have found your answers insulting, for instance implying that I think coins have memory

and then it takes you a number of posts for you to even answer the question can we agree that the memory is with the observer.

And now you start shouting " Will you NOW describe "
and being aggressive " will you continue to duck the question "

as such ,as per my previous post, I can see no further reason to continue this "discussion".

Again ,

thank you for your time,
it has been very informative ,

have a good day,
In other words, you will continue to duck the question.

You are correct, there's no point continuing this part of the discussion when that's the case.
 

WBahn

Joined Mar 31, 2012
29,976
No I'm not. Rather, people are discussing two distinct but related issues. Your issue is that the odds of flipping heads is 1/2. This is obvious and no one is arguing otherwise. My issue is that when flipping the coin more than once, we are likely to see approximately the same number of heads and tails. (See graph below.) Joed999 stated that seeing 8 tails in 14 flips is 1 in 16384, which is ludicrous. (Sorry Joey!) Not only is it about 1/6 the odds of seing 6, 7, or 8 are what 60%+. So if you all tails, or even mostly tails, this would be a remarkable outcome. Not impossible, but unlikely.
View attachment 224866
Joey was referring, somewhat tongue in cheek, to the specific sequence that was observed, not the collective description consisting solely of the total number of heads and the total number of tails.

What do YOU say that the odds are of seeing exactly 7 heads and 7 tails in a set of 14 tosses?

Is it more or less than the odds of seeing exactly 5 heads and 5 tails in a set of 10 tosses?

Is it more or less than the odds of seeing exactly 10 heads and 10 tails in a set of 20 tosses?

What happens to the odds of seeing exactly N heads and N tails in a set of 2N tosses as N increases?
 

402DF855

Joined Feb 9, 2013
271
"That sequence": i.e. the particular sequence you drew that resulted in 6 heads and 8 tails.
I didn't specify the sequence, you dreamt that up. I just said total tails was 8 out of 14.
The rand() function from the C library isn't a particularly good one.
Of course. I have my own proprietary random number generator; it gives about the same result as rand(). The fact that it appears to show that at large flip counts # of heads equals # of tails seems to suggest it is good enough for these simulations.
 

joeyd999

Joined Jun 6, 2011
5,234
I didn't specify the sequence, you dreamt that up. I just said total tails was 8 out of 14.
measured that I can flip a coin about 14 times a minute, therefore to see 20 tails in a sequence you'd likely have to flip a coin constantly for between 6 and 64 days. During my minute test, there were 8 tails and 6 heads. A very unremarkable and predictable outcome.
During that minute test, you either flipped one coin 14 times, 14 coins once, or some combination of coins such that the total of distinct flips equaled 14.

As you mentioned only "a coin" twice in the first -- related -- sentence, I made the stupid assumption that you tossed the same single coin 14 times to generate the 8 tails and 6 heads.

The implication is that you generated a sequence of flips, the particular sequence of which had a likely outcome of 1 in 16,384 14 flip trials, regardless of the actual sequence generated.

Thus my comment that you were lucky to have arrived at that particular sequence -- which is highly unlikely.

It was a joke! But it's not funny any more.
 

joeyd999

Joined Jun 6, 2011
5,234
You're moving the goal posts. There are a little more than 3,000 different sequences of 14 flips with 8 tails in them, so the chance of flipping any one of them is about 18%. What is the probability of flipping precisely one of those? 1 in 16384.

Note that you can apply your argument in the original context of the lotto. We (presumably) know that the probability of drawing (5,6,7,8,9,10) is the same as any other sequence. But if we consider the set of all recognizable drawings, then the probabilities increase significantly. One pattern of recognizable drawings includes:

(1,2,3,...) or
(2,3,4,...) or
(3,4,5,...) or
...
(20,21,23,..) or
(21,22, 23,..) or
...
(..., 48,49,50)

Another pattern includes:

(1,3,5,...) or
(3,5,7,..) or
...

Yet another:

(2,4,6,...) or
(4,6,8,...) or
...

Taking the union of all such sets, the probability of drawing a recognizable ("suspicious") sequence of balls is still low, but significantly higher than one might think.
I'd like to know: how many sequences don't "look" random? I wonder if there is a way to determine this by some kind of "randomness" test -- on only 6 numbers.

Edit: For example: would 5, 8, 13, 21, 34, 55 look random to a human? How about to an algorithm?
 

WBahn

Joined Mar 31, 2012
29,976
I'd like to know: how many sequences don't "look" random? I wonder if there is a way to determine this by some kind of "randomness" test -- on only 6 numbers.

Edit: For example: would 5, 8, 13, 21, 34, 55 look random to a human? How about to an algorithm?
While highly subjective, my gut feel is that the sequence would need to be pretty simple in order to be viewed as "non random" by most humans. Few people have even heard of the Fibonacci sequence, let alone would recognize a subsequence from it. Similarly for a sequence consisting of all prime numbers or all perfect squares (though, hopefully, most people have at least heard of those). Most noticed sequences would likely be simple arithmetic sequences and even then the constant between members would probably have to be pretty small -- and with no wraparound. But there would be other sequences that would almost certainly be seen as "non random" by many humans, such as 2, 3, 17, 18, 35, 36 (though most humans probably wouldn't bat an eye).

I think that's what it really comes down to -- it has to be a sequence that somehow "catches the eye". the sequence 10,20,30,40,50,60 would get noticed by a huge fraction of humans, but the sequence 3,13,23,33,43,53 would get noticed by a significant number of people, but not nearly as many, while 5,15,25,35,45,55 would probably ne noticed by some fraction that was in between the other two.

As was pointed out by someone else earlier in the thread (bogosort or xox?), the question of whether a given sequence is random is a largely meaningless question. The relevant questions are about the process that produced the sequence and whether or not the sequence is consistent with that process being random. A single, short sequence almost never sheds any light on that question. Sufficiently long sequences can and, more often, ensembles of many sequences drawn from the same process.
 

bogosort

Joined Sep 24, 2011
696
I'd like to know: how many sequences don't "look" random? I wonder if there is a way to determine this by some kind of "randomness" test -- on only 6 numbers.
It's an interesting question. If we were dealing with long strings instead of short sequences of numbers, a simple test would be to run a few compression algorithms on all the strings and count those that were successfully compressed (an automatic indication of low K-complexity, i.e., K(s) < |s|).

For lotto drawings, we could use the online-encyclopedia of integer sequences (http://oeis.org/) and write a program to iterate through the (ordered) 14 million possible lotto sequences against the database, counting those that return a match. This would likely overestimate the number of "suspicious looking" sequences, as it will include sequences that most people won't recognize. But I don't think it would be too far off.

If someone has the time and inclination, the entire OEIS database can be downloaded as a 25 MB gzip'ed text file (https://oeis.org/stripped.gz). If I can make the time, I'll do it.
 
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