Maybe Kramnik is onto something

In addition as the streak is more than 50% of the total tosses the 3rd toss is actually the most important one for a streak where if it falls on tails a streak is impossible. For example if we get Heads per toss in valid streaks you get that are HHHHH HTHHH THHHH TTHHH HHHHT THHHT HHHTH HHHTT

Toss 1 = 5/8 or 5/12
Toss 2 = 6/8 or 7/12
Toss 3 = 8/8 or 12/12
Toss 4 = 6/8 or 7/12
Toss 5 = 5/8 or 5/12

So you can see that with streaks middle values get much higher probabilities of being within it since the 3rd toss can be the 1st, 2nd or 3rd value in a streak.

woah... first time i can't nerd out :(

@kindaspongey said in #66:

That strikes me as a very difficult sort of calculation. Just for fun, I decided to do a brute force simpler calculation. Suppose that one only tosses the coin 5 times. Assuming that I did not goof it up, the probability of 3 or more consecutive "heads" is 25%.
For the experiment that I was considering ("one ... tosses the coin 5 times"), there are 32 equally likely outcomes:
@V1g1yy said in #70:
... HHHHH HTHHH THHHH TTHHH
HHHHT HTHHT THHHT TTHHT
HHHTH HTHTH THHTH TTHTH
HHHTT HTHTT THHTT TTHTT
HHTHH HTTHH THTHH TTTHH
HHTHT HTTHT THTHT TTTHT
HHTTH HTTTH THTTH TTTTH
HHTTT HTTTT THTTT TTTTT ...
Of those possibilities, I only see 8 (HHHHH HTHHH THHHH TTHHH HHHHT THHHT HHHTH HHHTT) that have "3 or more consecutive 'heads'". So, for the question that I was considering, the answer would seem to be 8/32=0.25 .
"12" is not the answer to a probability question where the answer must be somewhere in the range from 0 to 1.
I suppose that one could ask some sort of expectation question where the answer would be:
3(1/32) + 1(5/32) + 2(2/32) + 0(24/32) = 12/32 = 3/8 = 0.375,
but that would not be a question asking for a probability.

@kindaspongey said in #73:

Of those possibilities, I only see 8 (HHHHH HTHHH THHHH TTHHH HHHHT THHHT HHHTH HHHTT) that have "3 or more consecutive 'heads'". So, for the question that I was considering, the answer would seem to be 8/32=0.25 .
"12" is not the answer to a probability question where the answer must be somewhere in the range from 0 to 1.

Well "8" isn't then either but you just said it. I never said 12 as having anything to do with a probability, did I?

Please troll someone else.

@kindaspongey said in #66:

... Just for fun, I decided to do a brute force simpler calculation. Suppose that one only tosses the coin 5 times. Assuming that I did not goof it up, the probability of 3 or more consecutive "heads" is 25%.
@KMcGeoch said in #67:
... These are the following permutations that work: ...
@V1g1yy said in #70:
... for the first permutation above, HHHHH, for your count of possibilities, is that considered 1 possible 3-in-a-row, or is that considered 3 3-in-a-rows? If counted as 1, then yes there are 8 which have a string of 3 H. But if counted in aggregate, there's 12 ...
@kindaspongey said in #73:
For the experiment that I was considering ("one ... tosses the coin 5 times"), there are 32 equally likely outcomes ...
Of those possibilities, I only see 8 ... that have "3 or more consecutive 'heads'". So, for the question that I was considering, the answer would seem to be 8/32=0.25 .
"12" is not the answer to a probability question where the answer must be somewhere in the range from 0 to 1.
I suppose that one could ask some sort of expectation question where the answer would be:
3(1/32) + 1(5/32) + 2(2/32) + 0(24/32) = 12/32 = 3/8 = 0.375,
but that would not be a question asking for a probability.
@V1g1yy said in #74 (~34 minutes ago):
... Well "8" isn't then either ...
That is why I gave the answer to the probability question as "8/32=0.25".
@V1g1yy said in #74:
... I never said 12 as having anything to do with a probability, did I?
I was not aware of you identifying 12 as the answer to any specific statistical question, but you DID ask:
"... HHHHH, ... is that considered 1 possible 3-in-a-row, or is that considered 3 3-in-a-rows? ..."
Consequently, it did seem appropriate to me to react by pointing out that 8 was the correct number to use as part of my answer to the probability question.
@V1g1yy said in #74:
Please troll someone else.
I am sorry that you regard it as "troll"ing that I tried to react to your question. I did try to identify a statistical question where 12 could arise as part of the answer.
By the way, this discussion seems to be well past the 50 post limit and has been sinking for ~5 days. As I write this, there seem to be about 90 topics above this one at "General Chess Discussion".

https://imgs.xkcd.com/comics/significant.png