What is the Probability of Flipping Two Strange Coins?

[micromass]

I'm not discarding anything. I said I don't disagree with your theory, it just doesn't invalidate the other possibilities, only practical experiments can do that.

No, since the theory actually proves the results beyond the shadow of a doubt. If you would study the theory, then you would see actual rigorous proofs of the results.

Besides, what other possibilities? You have the theory of mathematical probability which is so immensely successful that it is used everywhere and gives perfectly accurately results every single time and which all serious scientists accept as true. What other theory is there? You have only presented vague things like "the feeling that we can't get more than 100 sixes in a row". That is not a theory, you can't build on it, you can't deduce other things from it, you can't falsify it, you can't use it to make other predictions, you can't use it in applications, etc.
The mathematical theory of probability is something you can build on, something you can deduce many other things from, something you can falsify, something you can use to make predictions, something that is used in applications. There is no other theory about these matters that does this!

 

[Matterwave]

I'm not discarding anything. I said I don't disagree with your theory, it just doesn't invalidate the other possibilities, only practical experiments can do that.

Sometimes a theory can be counter-intuitive. And indeed, there are aspects of probability theory that are counter-intuitive when you first meet them. This is often why many people fall victim to things such as the Gambler's fallacy ("oh, I'm doing poorly now, my luck must change for the better soon!"). Which is actually, it seems, the exactly fallacy that you are falling victim to. (You can see this article for a summary of this fallacy: http://en.wikipedia.org/wiki/Gambler's_fallacy)

Sometimes, we have to just take the hard evidence into consideration and accept a theory even if it's counter-intuitive. You ask for practical experiments. Well, practical experiments in probability theory are being carried out every single day and every day probability theory is being validated. ALL casinos in this world operate on this theory. If this theory were fundamentally flawed, then casinos could not be successful. In addition, all of quantum mechanics operates based on probability theory. Again, if probability theory were fundamentally flawed, quantum mechanics would be fundamentally flawed. But we know from experience that casinos make money, and quantum mechanics gives you the right physical answers. So this gives us good indication that we should accept this theory to be true.

If your contention is that a DIFFERENT theory will gives us ALL the same results, then it is your duty to produce this theory, as nobody has yet found one. You cannot expect us, who are all content with the current theory, to try to find a whole new set of laws that obey YOUR intuitions and still reproduce all the successes of probability theory. Indeed, no such theory is possible, because it can be shown that your intuition on this matter leads to incorrect conclusions. Conclusions such as "no string of 15 or more of the same number will ever appear" are patently false.

Having said that, building one's intuition is not without benefit. So, I suggest that instead of holding on to your intuitions so tightly, you should try to see things with an open mind.

Let me ask you a question. If I roll a dice, and it's a unweighted dice so it has no biases, and one day I rolled 8 6's in a row and I hold on to this dice in my hand, it seems to me that you think this dice will be somehow UNLIKELY to roll another 6, is that correct?

Now, what happens if I give this dice to you to roll? Do you think that YOU are unlikely to roll a 6? In other words, do you believe this property of "being unlikely to roll a 6 next" is carried with the dice, or with the roller?

What if I never rolled this dice for a year. In the interim, I roll many other dice, but never this one. The next time I roll this dice, do you think I STILL have a less than 1/6 chance of rolling a 6?

What happens if I never roll a dice for a year. Are my chances of a next dice roll affected by what I did a year ago?

Why might this be different if I waited just a second before my next roll?

What do you think?

 

[StrangeCoin]

No, since the theory actually proves the results beyond the shadow of a doubt.

Speaking of results, they are finally in for 94,036,996,915 rolls. It took a while.

4: ++Lucky Streak = 2
10: ++Lucky Streak = 3
118: ++Lucky Streak = 4
502: ++Lucky Streak = 5
2,001: ++Lucky Streak = 6
61,246: ++Lucky Streak = 7
563,660: ++Lucky Streak = 8
563,661: ++Lucky Streak = 9
563,662: ++Lucky Streak = 10
128,971,519: ++Lucky Streak = 11
171,349,947: ++Lucky Streak = 12
443,007,272: ++Lucky Streak = 13
94,036,996,915: DONE!

You said 94,036,996,915 rolls were supposed to produce 15 in a row streak, but 13-streak is still the longest I've seen so far. That number of rolls was actually supposed to produce more than few 14-streaks, but it didn't. Will you please run the test and see if you can get 14 in a row on your computer?

 

[micromass]

You said 94,036,996,915 rolls were supposed to produce 15 in a row streak, but 13-streak is still the longest I've seen so far.

How many 13-streaks did you see? Do you have any information on that?

 

[micromass]

Also, I don't know if you can just continue running the program or need to run the program again. But if you run it again, I would be happy if you can save some information for me.

So basically, can you write and run a program (I would do it myself, but your program is apparently much more efficient) that throws a dice a number times and where he records

1) The number of $1$, $2$, $3$, ...
2) The number of streaks of length $2$ formed with $1$ (I do not count 111 as a streak of length $2$), the number of streaks of length $2$ formed with $2$, ...
3) The number of streaks of length $n$ (take $n<20$ to be sure) formed with $1$, ...

Then please run your code for a time of $100,000,000,000$ iterations, and please show all of the above information when you hit the following for the first time: 1000 iterations, 10,000 iterations, 100,000 iterations, etc. I would also appreciate it if you would display all the information whenever a streak of a certain length is first formed, for example, the first time you see a streak of 5.

 

[micromass]

Also, it is possible that the rand() is subpar. For example, see this part of the C/C++ manual: http://man7.org/linux/man-pages/man3/rand.3.html

NOTES
The versions of rand() and srand() in the Linux C Library use the same
random number generator as random(3) and srandom(3), so the lower-order
bits should be as random as the higher-order bits. However, on older
rand() implementations, and on current implementations on different
systems, the lower-order bits are much less random than the higher-
order bits. Do not use this function in applications intended to be
portable when good randomness is needed. (Use random(3) instead.)

So I suggest a few changes to really make sure we randomized everything and that we don't produce a sequence that repeats itself over and over again. First, use the random function instead of rand.

Second, you have used the code "rand()%6;".
Apparently, using "rand()%2" might give problems, a good replacement for that is "random() & (1<<13)".

So please use the "random() & (1 << 13)" to ouput 0 and 1. Using this outputs, you can generate the dice as follows:
1) Draw 3 random numbers $x$, $y$, $z$ using the code above (so three numbers either 0 and 1)
2) Form the number $a = 1 + x + 2y + 4z$
3) If $a\leq 6$, then output $a$ as our random dice roll, in the other case, go to (1) again

This should give a good sequence of random dice rolls. You should test it by generating some 100 values and see if it works.

http://cseweb.ucsd.edu/~dasgupta/103/5a.pdf
http://cseweb.ucsd.edu/~dasgupta/103/5b.pdf

 

[StrangeCoin]

How many 13-streaks did you see? Do you have any information on that?

I didn't count it that time, but I'm counting repeated streaks now in 564,221,981,491 rolls run. 13-streaks are pretty regular at about every 2-3 billion. Here is the output of the run so far, it's taking forever:

4: ++Lucky Streak = 2
7: ++Lucky Streak = 2
23: ++Lucky Streak = 2
34: ++Lucky Streak = 2
35: ++Lucky Streak = 3
52: ++Lucky Streak = 3
81: ++Lucky Streak = 3
84: ++Lucky Streak = 3
90: ++Lucky Streak = 3
143: ++Lucky Streak = 3
156: ++Lucky Streak = 3
196: ++Lucky Streak = 3
202: ++Lucky Streak = 3
203: ++Lucky Streak = 4
620: ++Lucky Streak = 4
639: ++Lucky Streak = 4
741: ++Lucky Streak = 4
746: ++Lucky Streak = 4
747: ++Lucky Streak = 5
748: ++Lucky Streak = 6
2,620: ++Lucky Streak = 6
8,029: ++Lucky Streak = 6
29,488: ++Lucky Streak = 6
36,209: ++Lucky Streak = 6
37,886: ++Lucky Streak = 6
61,193: ++Lucky Streak = 6
63,539: ++Lucky Streak = 6
68,750: ++Lucky Streak = 6
100,251: ++Lucky Streak = 6
100,252: ++Lucky Streak = 7
126,887: ++Lucky Streak = 7
204,030: ++Lucky Streak = 7
332,047: ++Lucky Streak = 7
366,103: ++Lucky Streak = 7
391,031: ++Lucky Streak = 7
396,170: ++Lucky Streak = 7
396,171: ++Lucky Streak = 8
837,998: ++Lucky Streak = 8
1,242,992: ++Lucky Streak = 8
1,334,809: ++Lucky Streak = 8
2,333,617: ++Lucky Streak = 8
2,853,957: ++Lucky Streak = 8
2,853,958: ++Lucky Streak = 9
6,137,019: ++Lucky Streak = 9
7,126,857: ++Lucky Streak = 9
10,186,210: ++Lucky Streak = 9
10,384,535: ++Lucky Streak = 9
10,671,344: ++Lucky Streak = 9
10,671,345: ++Lucky Streak = 10
10,891,052: ++Lucky Streak = 10
15,955,095: ++Lucky Streak = 10
30,630,427: ++Lucky Streak = 10
32,083,312: ++Lucky Streak = 10
42,555,159: ++Lucky Streak = 10
49,257,512: ++Lucky Streak = 10
49,257,513: ++Lucky Streak = 11
258,233,847: ++Lucky Streak = 11
290,135,840: ++Lucky Streak = 11
298,589,987: ++Lucky Streak = 11
311,274,124: ++Lucky Streak = 11
438,644,650: ++Lucky Streak = 11
544,103,963: ++Lucky Streak = 11
582,954,796: ++Lucky Streak = 11
582,954,797: ++Lucky Streak = 12
734,495,721: ++Lucky Streak = 12
926,307,589: ++Lucky Streak = 12
956,678,986: ++Lucky Streak = 12
1,095,259,396: ++Lucky Streak = 12
1,197,964,913: ++Lucky Streak = 12
1,197,964,914: ++Lucky Streak = 13
3,345,448,562: ++Lucky Streak = 13
5,492,932,210: ++Lucky Streak = 13
7,640,415,858: ++Lucky Streak = 13
9,787,899,506: ++Lucky Streak = 13
11,935,383,154: ++Lucky Streak = 13
14,082,866,802: ++Lucky Streak = 13
16,230,350,450: ++Lucky Streak = 13
18,377,834,098: ++Lucky Streak = 13
20,525,317,746: ++Lucky Streak = 13
22,672,801,394: ++Lucky Streak = 13
24,820,285,042: ++Lucky Streak = 13
26,967,768,690: ++Lucky Streak = 13
29,115,252,338: ++Lucky Streak = 13
31,262,735,986: ++Lucky Streak = 13
33,410,219,634: ++Lucky Streak = 13
35,557,703,282: ++Lucky Streak = 13
37,705,186,930: ++Lucky Streak = 13
39,852,670,578: ++Lucky Streak = 13
42,000,154,226: ++Lucky Streak = 13
44,147,637,874: ++Lucky Streak = 13
46,295,121,522: ++Lucky Streak = 13
48,442,605,170: ++Lucky Streak = 13
50,590,088,818: ++Lucky Streak = 13
52,737,572,466: ++Lucky Streak = 13
54,885,056,114: ++Lucky Streak = 13
57,032,539,762: ++Lucky Streak = 13
59,180,023,410: ++Lucky Streak = 13
61,327,507,058: ++Lucky Streak = 13
63,474,990,706: ++Lucky Streak = 13
65,622,474,354: ++Lucky Streak = 13
67,769,958,002: ++Lucky Streak = 13
69,917,441,650: ++Lucky Streak = 13
72,064,925,298: ++Lucky Streak = 13
74,212,408,946: ++Lucky Streak = 13
76,359,892,594: ++Lucky Streak = 13
78,507,376,242: ++Lucky Streak = 13
80,654,859,890: ++Lucky Streak = 13
82,802,343,538: ++Lucky Streak = 13
84,949,827,186: ++Lucky Streak = 13
87,097,310,834: ++Lucky Streak = 13
89,244,794,482: ++Lucky Streak = 13
91,392,278,130: ++Lucky Streak = 13
93,539,761,778: ++Lucky Streak = 13
95,687,245,426: ++Lucky Streak = 13
97,834,729,074: ++Lucky Streak = 13
99,982,212,722: ++Lucky Streak = 13
102,129,696,370: ++Lucky Streak = 13
104,277,180,018: ++Lucky Streak = 13
106,424,663,666: ++Lucky Streak = 13
108,572,147,314: ++Lucky Streak = 13
110,719,630,962: ++Lucky Streak = 13
112,867,114,610: ++Lucky Streak = 13
115,014,598,258: ++Lucky Streak = 13
117,162,081,906: ++Lucky Streak = 13
119,309,565,554: ++Lucky Streak = 13
121,457,049,202: ++Lucky Streak = 13
123,604,532,850: ++Lucky Streak = 13
125,752,016,498: ++Lucky Streak = 13
127,899,500,146: ++Lucky Streak = 13
130,046,983,794: ++Lucky Streak = 13

Pretty sharp cut off, too sharp. I really wanted to see a 14-streak by now, this limit looks too artificial. We need some other RNG to cross examine and verify. We need RNG that is representative of "natural" randomness and free of any artificial limits, if such thing can even exist on a computer. Do you think you can find out about some RNG used in scientific experiments and such settings?

 

[micromass]

I didn't count it that time, but I'm counting repeated streaks now in 564,221,981,491 rolls run. 13-streaks are pretty regular at about every 2-3 billion. Here is the output of the run so far, it's taking forever:

4: ++Lucky Streak = 2
7: ++Lucky Streak = 2
23: ++Lucky Streak = 2
34: ++Lucky Streak = 2
35: ++Lucky Streak = 3
52: ++Lucky Streak = 3
81: ++Lucky Streak = 3
84: ++Lucky Streak = 3
90: ++Lucky Streak = 3
143: ++Lucky Streak = 3
156: ++Lucky Streak = 3
196: ++Lucky Streak = 3
202: ++Lucky Streak = 3
203: ++Lucky Streak = 4
620: ++Lucky Streak = 4
639: ++Lucky Streak = 4
741: ++Lucky Streak = 4
746: ++Lucky Streak = 4
747: ++Lucky Streak = 5
748: ++Lucky Streak = 6
2,620: ++Lucky Streak = 6
8,029: ++Lucky Streak = 6
29,488: ++Lucky Streak = 6
36,209: ++Lucky Streak = 6
37,886: ++Lucky Streak = 6
61,193: ++Lucky Streak = 6
63,539: ++Lucky Streak = 6
68,750: ++Lucky Streak = 6
100,251: ++Lucky Streak = 6
100,252: ++Lucky Streak = 7
126,887: ++Lucky Streak = 7
204,030: ++Lucky Streak = 7
332,047: ++Lucky Streak = 7
366,103: ++Lucky Streak = 7
391,031: ++Lucky Streak = 7
396,170: ++Lucky Streak = 7
396,171: ++Lucky Streak = 8
837,998: ++Lucky Streak = 8
1,242,992: ++Lucky Streak = 8
1,334,809: ++Lucky Streak = 8
2,333,617: ++Lucky Streak = 8
2,853,957: ++Lucky Streak = 8
2,853,958: ++Lucky Streak = 9
6,137,019: ++Lucky Streak = 9
7,126,857: ++Lucky Streak = 9
10,186,210: ++Lucky Streak = 9
10,384,535: ++Lucky Streak = 9
10,671,344: ++Lucky Streak = 9
10,671,345: ++Lucky Streak = 10
10,891,052: ++Lucky Streak = 10
15,955,095: ++Lucky Streak = 10
30,630,427: ++Lucky Streak = 10
32,083,312: ++Lucky Streak = 10
42,555,159: ++Lucky Streak = 10
49,257,512: ++Lucky Streak = 10
49,257,513: ++Lucky Streak = 11
258,233,847: ++Lucky Streak = 11
290,135,840: ++Lucky Streak = 11
298,589,987: ++Lucky Streak = 11
311,274,124: ++Lucky Streak = 11
438,644,650: ++Lucky Streak = 11
544,103,963: ++Lucky Streak = 11
582,954,796: ++Lucky Streak = 11
582,954,797: ++Lucky Streak = 12
734,495,721: ++Lucky Streak = 12
926,307,589: ++Lucky Streak = 12
956,678,986: ++Lucky Streak = 12
1,095,259,396: ++Lucky Streak = 12
1,197,964,913: ++Lucky Streak = 12
1,197,964,914: ++Lucky Streak = 13
3,345,448,562: ++Lucky Streak = 13
5,492,932,210: ++Lucky Streak = 13
7,640,415,858: ++Lucky Streak = 13
9,787,899,506: ++Lucky Streak = 13
11,935,383,154: ++Lucky Streak = 13
14,082,866,802: ++Lucky Streak = 13
16,230,350,450: ++Lucky Streak = 13
18,377,834,098: ++Lucky Streak = 13
20,525,317,746: ++Lucky Streak = 13
22,672,801,394: ++Lucky Streak = 13
24,820,285,042: ++Lucky Streak = 13
26,967,768,690: ++Lucky Streak = 13
29,115,252,338: ++Lucky Streak = 13
31,262,735,986: ++Lucky Streak = 13
33,410,219,634: ++Lucky Streak = 13
35,557,703,282: ++Lucky Streak = 13
37,705,186,930: ++Lucky Streak = 13
39,852,670,578: ++Lucky Streak = 13
42,000,154,226: ++Lucky Streak = 13
44,147,637,874: ++Lucky Streak = 13
46,295,121,522: ++Lucky Streak = 13
48,442,605,170: ++Lucky Streak = 13
50,590,088,818: ++Lucky Streak = 13
52,737,572,466: ++Lucky Streak = 13
54,885,056,114: ++Lucky Streak = 13
57,032,539,762: ++Lucky Streak = 13
59,180,023,410: ++Lucky Streak = 13
61,327,507,058: ++Lucky Streak = 13
63,474,990,706: ++Lucky Streak = 13
65,622,474,354: ++Lucky Streak = 13
67,769,958,002: ++Lucky Streak = 13
69,917,441,650: ++Lucky Streak = 13
72,064,925,298: ++Lucky Streak = 13
74,212,408,946: ++Lucky Streak = 13
76,359,892,594: ++Lucky Streak = 13
78,507,376,242: ++Lucky Streak = 13
80,654,859,890: ++Lucky Streak = 13
82,802,343,538: ++Lucky Streak = 13
84,949,827,186: ++Lucky Streak = 13
87,097,310,834: ++Lucky Streak = 13
89,244,794,482: ++Lucky Streak = 13
91,392,278,130: ++Lucky Streak = 13
93,539,761,778: ++Lucky Streak = 13
95,687,245,426: ++Lucky Streak = 13
97,834,729,074: ++Lucky Streak = 13
99,982,212,722: ++Lucky Streak = 13
102,129,696,370: ++Lucky Streak = 13
104,277,180,018: ++Lucky Streak = 13
106,424,663,666: ++Lucky Streak = 13
108,572,147,314: ++Lucky Streak = 13
110,719,630,962: ++Lucky Streak = 13
112,867,114,610: ++Lucky Streak = 13
115,014,598,258: ++Lucky Streak = 13
117,162,081,906: ++Lucky Streak = 13
119,309,565,554: ++Lucky Streak = 13
121,457,049,202: ++Lucky Streak = 13
123,604,532,850: ++Lucky Streak = 13
125,752,016,498: ++Lucky Streak = 13
127,899,500,146: ++Lucky Streak = 13
130,046,983,794: ++Lucky Streak = 13

Pretty sharp cut off, too sharp. I really wanted to see a 14-streak by now, this limit looks too artificial. We need some other RNG to cross examine and verify. We need RNG that is representative of "natural" randomness and free of any artificial limits, if such thing can even exist on a computer. Do you think you can find out about some RNG used in scientific experiments and such settings?

Yes, your random number generator is broken. You clearly see that you get a 13-streak exactly every $2,147,483,648$ iterations in the last few lucky streaks:

582,954,797: ++Lucky Streak = 12
734,495,721: ++Lucky Streak = 12
926,307,589: ++Lucky Streak = 12
956,678,986: ++Lucky Streak = 12
1,095,259,396: ++Lucky Streak = 12
1,197,964,913: ++Lucky Streak = 12
1,197,964,914: ++Lucky Streak = 13  <--- This is the only 13-streak, all the others below are merely repetition of this one
3,345,448,562: ++Lucky Streak = 13
5,492,932,210: ++Lucky Streak = 13
7,640,415,858: ++Lucky Streak = 13
9,787,899,506: ++Lucky Streak = 13
11,935,383,154: ++Lucky Streak = 13
14,082,866,802: ++Lucky Streak = 13
16,230,350,450: ++Lucky Streak = 13
18,377,834,098: ++Lucky Streak = 13
20,525,317,746: ++Lucky Streak = 13
22,672,801,394: ++Lucky Streak = 13
24,820,285,042: ++Lucky Streak = 13
26,967,768,690: ++Lucky Streak = 13
29,115,252,338: ++Lucky Streak = 13
31,262,735,986: ++Lucky Streak = 13
33,410,219,634: ++Lucky Streak = 13
35,557,703,282: ++Lucky Streak = 13
37,705,186,930: ++Lucky Streak = 13
39,852,670,578: ++Lucky Streak = 13
42,000,154,226: ++Lucky Streak = 13
44,147,637,874: ++Lucky Streak = 13
46,295,121,522: ++Lucky Streak = 13
48,442,605,170: ++Lucky Streak = 13
50,590,088,818: ++Lucky Streak = 13
52,737,572,466: ++Lucky Streak = 13
54,885,056,114: ++Lucky Streak = 13
57,032,539,762: ++Lucky Streak = 13
59,180,023,410: ++Lucky Streak = 13
61,327,507,058: ++Lucky Streak = 13
63,474,990,706: ++Lucky Streak = 13
65,622,474,354: ++Lucky Streak = 13
67,769,958,002: ++Lucky Streak = 13
69,917,441,650: ++Lucky Streak = 13
72,064,925,298: ++Lucky Streak = 13
74,212,408,946: ++Lucky Streak = 13
76,359,892,594: ++Lucky Streak = 13
78,507,376,242: ++Lucky Streak = 13
80,654,859,890: ++Lucky Streak = 13
82,802,343,538: ++Lucky Streak = 13
84,949,827,186: ++Lucky Streak = 13
87,097,310,834: ++Lucky Streak = 13
89,244,794,482: ++Lucky Streak = 13
91,392,278,130: ++Lucky Streak = 13
93,539,761,778: ++Lucky Streak = 13
95,687,245,426: ++Lucky Streak = 13
97,834,729,074: ++Lucky Streak = 13
99,982,212,722: ++Lucky Streak = 13
102,129,696,370: ++Lucky Streak = 13
104,277,180,018: ++Lucky Streak = 13
106,424,663,666: ++Lucky Streak = 13
108,572,147,314: ++Lucky Streak = 13
110,719,630,962: ++Lucky Streak = 13
112,867,114,610: ++Lucky Streak = 13
115,014,598,258: ++Lucky Streak = 13
117,162,081,906: ++Lucky Streak = 13
119,309,565,554: ++Lucky Streak = 13
121,457,049,202: ++Lucky Streak = 13
123,604,532,850: ++Lucky Streak = 13
125,752,016,498: ++Lucky Streak = 13
127,899,500,146: ++Lucky Streak = 13
130,046,983,794: ++Lucky Streak = 13

For example
127,899,500,146+2,147,483,648 = 130,046,983,794
125,752,016,498 + 2,147,483,648 = 127,899,500,146
123,604,532,850+2,147,483,648 = 125,752,016,498
121,457,049,202 +2,147,483,648=123,604,532,850

This indicates that your random number generator repeats itself every $2,147,483,648$ iterations. Isn't it fun how the deviation of your experiment in post 33 from my theory could have been used to predict this?

Anyway, my previous post outlined a way to get a better random number generator. Please implement that in your code. I think that will work better. Could you also implement the other suggestions?

 

[StrangeCoin]

This indicates that your random number generator repeats itself every $2,147,483,648$ iterations. Isn't it fun how the deviation of your experiment in post 33 from my theory could have been used to predict this?

Maybe a little. And how funny is it that my "feeling" was actually correct? Even if only true for standard/casual RNGs, you have to admit it was pretty wild thing to guess.

Anyway, my previous post outlined a way to get a better random number generator. Please implement that in your code. I think that will work better. Could you also implement the other suggestions?

I don't think it's fixable, I shall simply use the best RNG there is:

- "It passes numerous tests for statistical randomness, including the Diehard tests."
http://en.wikipedia.org/wiki/Mersenne_twister

That's the one the scientists use. Are you going to accept the results it is going to produce?

 

[micromass]

Maybe a little. And how funny is it that my "feeling" was actually correct? Even if only true for standard/casual RNGs, you have to admit it was pretty wild thing to guess.

How was your feeling correct? The only reason you couldn't go above 15 was because the random number generator started repeating way too soon.

I don't think it's fixable,

OK, but you haven't even tried my suggestions. I put a lot of effort in these posts, I don't really enjoy that my posts are being ignored.

I shall simply use the best RNG there is:

- "It passes numerous tests for statistical randomness, including the Diehard tests."
http://en.wikipedia.org/wiki/Mersenne_twister

That's the one the scientists use. Are you going to accept the results it is going to produce?

Sure.

 

[StrangeCoin]

OK, but you haven't even tried my suggestions. I put a lot of effort in these posts, I don't really enjoy that my posts are being ignored.

Trying means several hours of waiting, and I would not accept results from a flawed RNG anyway. It would be just more waste of time, so instead I'll have this Mersenne twister RNG ready, in about few hours.

 

[micromass]

Trying means several hours of waiting, and I would not accept results from a flawed RNG anyway. It would be just more waste of time, so instead I'll have this Mersenne twister RNG ready, in about few hours.

OK, but you also ignored some other things like the really good post by matterwave: #32.
Did you at least implement my suggestions of post #35?

 

[StrangeCoin]

OK, but you also ignored some other things like the really good post by matterwave: #32.

I'm not interested to argue about any of that, yet again. Everyone has their opinion and we all know what everyone thinks. Enough said. Soon the results will come out and then maybe we'll have something new or more to talk about.

Did you at least implement my suggestions of post #35?

I'm exactly testing specific claim I made and what we were talking about all along. You can analyze it, you can predict it, and you can understand it. It's simple and straight forward, and it is testing for all 6 sides at once, which gives better chances for your theory to be proven correct, sooner rather than later. I'm not sure what is it you are actually suggesting or why would you even want to change anything.

 

[StrangeCoin]

If you go up to 18,446,744,073,709,551,615 you can expect a streak of 25.

That number looks like it would take centuries to finish, and only for 25 streaks. We need something better, to somehow test for the same kind of probability we are testing now, but with many less number of loops. Is this possible? Maybe increase the number of sides and/or number of dice rolled in each loop, then we could compare combinations across multiple dice as well as streaks for each dice individually, or something. Does that make sense?

 

[micromass]

That number looks like it would take centuries to finish, and only for 25 streaks. We need something better, to somehow test for the same kind of probability we are testing now, but with many less number of loops. Is this possible? Maybe increase the number of sides and/or number of dice rolled in each loop, then we could compare combinations across multiple dice as well as streaks for each dice individually, or something. Does that make sense?

You could do the test for coins instead of dice and see the longest run of heads versus the longest run of tails. Running it for 10,000,000,000 iterations would get you a 33 streak.

You could also bias the coin such that getting head is twice more likely than getting tails. Running this for 10,000,000,000 iterations would get you a 54 streak.

You could also do things with dice and record the longest streak of not getting a 6. So in 1 3 6 3 1 3 2 6 6 we would have a streak 4 with 3 1 3 2. Doing it this way will get you a 116 streak for 10,000,000,000 iterations.

 

[micromass]

Another idea for a test.

Your claim relies on the following: if we take a fair coin, then if we throw head 15 times, then throwing a head for the 16th time is less likely than throwing a tail? Right?

Well, then why not test this. You could make a program that tosses a coin automatically. Then whenever you see a 15 streak, record whether the next toss is a head or a tail. I claim that the number of heads will be roughly the same as the number of tails. Your claim is that the number of tails is significantly larger, right? Let's put it up for a test then!

 

[StrangeCoin]

You could do the test for coins instead of dice and see the longest run of heads versus the longest run of tails. Running it for 10,000,000,000 iterations would get you a 33 streak.

That doesn't seem to be proportional to 30 sixes in a row. By the way that new Twister RNG rolled 16-strike after 96 billion turns, so I aborted as testing for higher rolls is not practical, but at least we know this indeed looks like proper RNG, whatever that means. Twos got quite a few streaks, and those streaks are in a row too, as a streak of streaks. Cute.

3,152,061,076: [5]x 12
4,902,379,296: [5]x 12
5,118,113,156: [5]x 12
5,204,487,757: [3]x 12
5,310,748,076: [6]x 12
6,553,758,633: [3]x 12
7,548,077,078: [1]x 12
8,297,018,198: [5]x 12
8,719,467,869: [5]x 12
9,244,157,268: [3]x 12
10,135,793,395: [4]x 12
10,308,842,249: [4]x 12
10,436,285,611: [2]x 12
10,436,285,612: [2]x 13
10,575,566,218: [2]x 13
11,978,651,701: [2]x 13
11,978,651,702: [2]x 14
74,568,933,186: [6]x 14
82,054,242,241: [4]x 14
87,237,983,158: [5]x 14
87,640,454,393: [4]x 14
87,640,454,394: [4]x 15
96,050,499,093: [2]x 15
96,050,499,094: [2]x 16

You could also do things with dice and record the longest streak of not getting a 6. So in 1 3 6 3 1 3 2 6 6 we would have a streak 4 with 3 1 3 2. Doing it this way will get you a 116 streak for 10,000,000,000 iterations.

That sounds exactly like my second claim, I'll do this. If it gets over 100-streak, you win. Please place your bets...

 

[micromass]

That sounds exactly like my second claim, I'll do this. If it gets over 100-streak, you win. Please place your bets...

You are expected to iterate around 500 million times to get a 100-streak.

 

[StrangeCoin]

That was quick. Numbers in brackets are not relevant here, this is "not six"-in a row:

20,028,868: [2]x 83
20,028,869: [4]x 84
20,028,870: [1]x 85
20,028,871: [4]x 86
20,028,872: [5]x 87
20,028,873: [1]x 88
20,028,874: [4]x 89
20,028,875: [4]x 90
20,028,876: [4]x 91
20,028,877: [3]x 92
20,028,878: [3]x 93
20,028,879: [2]x 94
20,028,880: [5]x 95
188,496,298: [2]x 95
188,496,299: [2]x 96
215,155,368: [2]x 96
215,155,369: [3]x 97
215,155,370: [1]x 98
215,155,371: [1]x 99
215,155,372: [5]x 100
215,155,373: [4]x 101
552,460,788: [2]x 101
552,460,789: [2]x 102
676,840,973: [4]x 102
676,840,974: [2]x 103
683,592,390: [5]x 103
683,592,391: [1]x 104
683,592,392: [2]x 105
3,561,898,318: [3]x 105
3,561,898,319: [2]x 106
3,561,898,320: [4]x 107
3,561,898,321: [1]x 108
3,561,898,322: [1]x 109
3,561,898,323: [1]x 110
4,747,969,561: [4]x 110
4,747,969,562: [1]x 111
4,747,969,563: [1]x 112
4,747,969,564: [4]x 113
4,747,969,565: [4]x 114
4,747,969,566: [3]x 115
4,747,969,567: [3]x 116
4,747,969,568: [2]x 117
4,747,969,569: [4]x 118
4,747,969,570: [5]x 119
4,747,969,571: [3]x 120
4,747,969,572: [5]x 121
4,747,969,573: [2]x 122
4,747,969,574: [5]x 123
4,747,969,575: [3]x 124
4,747,969,576: [5]x 125
4,747,969,577: [1]x 126
4,747,969,578: [4]x 127
4,747,969,579: [5]x 128
4,747,969,580: [1]x 129
4,747,969,581: [5]x 130
4,747,969,582: [2]x 131
4,747,969,583: [2]x 132

Congratulations. Your prophecy has been fulfilled and the universe hasn't fallen apart. And so it is true, as they say, luck comes in streaks.

- "The fascinating study looked at 565,915 sports bets made by 776 online gamblers in Europe and the United States, and found that, all things being equal, you're likely to win or lose 48 percent of the time (draws presumably account for the remaining 4 percent). After a single winning bid, the chance of winning a second goes up ever so slightly to 49 percent. But here's where things get interesting. After the second win, the chance of winning a third time increases to 57 percent. After that: 67 percent. Following a four-bet winning streak, the chances of scoring a fifth haul increase to 72 percent. The probability of a sixth win is then 75 percent, and finally, after six wins, bettors had a 76 percent chance of notching lucky No. 7."

http://www.popsci.com/article/science/are-lucky-streaks-real-science-says-yes

True?

 

[micromass]

- "The fascinating study looked at 565,915 sports bets made by 776 online gamblers in Europe and the United States, and found that, all things being equal, you're likely to win or lose 48 percent of the time (draws presumably account for the remaining 4 percent). After a single winning bid, the chance of winning a second goes up ever so slightly to 49 percent. But here's where things get interesting. After the second win, the chance of winning a third time increases to 57 percent. After that: 67 percent. Following a four-bet winning streak, the chances of scoring a fifth haul increase to 72 percent. The probability of a sixth win is then 75 percent, and finally, after six wins, bettors had a 76 percent chance of notching lucky No. 7."

http://www.popsci.com/article/science/are-lucky-streaks-real-science-says-yes

True?

I don't know about that. The mathematical theory does not say anything about this situation. The way they obtained this numbers was purely empirical, there is no theory that accompagnies it. So I can't do calculations (like I did in the dice and coin case) and say what the chances are. All we can do here is look at previous data and interpret that.

It's difficult to obtain a working theory for this since it involves human behavior and this is very difficult to impossible to model. Coin tosses and dice rolls are very easy objects from the math point of view.

So in this case, it's just that the previous data has these properties listed in the article. This is true if the researchers did their work well. The question is then to what extent you can draw inference from this data. This is a difficult problem. There are so many variables. Maybe you have a lot of people who only bet on the "easy games" which have a relatively sure winner. That would explain the lucky streaks. A lot depends on what kind of gambler you are and what kind of risks you are willing to take. If you bet truly at random, then you shouldn't be getting such lucky streaks. But nobody bets truly at random on sports: if Brazil plays a football game with Vatican city, then nobody is going to bet that Brazil loses.

 

[StrangeCoin]

Interesting. And nice thread, this, a little bit of everything.