Have abusive deranged flametrolls like the former campus
dishwasher Ludwig Hansen nee Poehlmann or Kessler, 72,
born in Arschlick in the Reich, a lunatic who somehow
eluded the police all these years, driven all the
competent ones away?

The problem recited below is an interesting one, but not
one of those replying in the thread "A simple coin-toss
problem that no one can solve" seems to have even
understood it, and their comments are either correct but
irrelevant (eg Sergi o's "dont play roulette! Just send
the Casino a check and save on the airplane and hotel,
save the time, go fishing...") or wrong / absurd /
nonsensical.

Is sci.math a mathematician free zone? Can anyone else
have a go?

THE PROBLEM

Introduction/Background

Trivially, when a fair coin is tossed, ad infinitum:

a) Any arbitrarily-long sequence of consecutive heads
will occur, eventually.
So, for example, the probability that a googolplex-long
sequence of consecutive heads will occur is 1.

b) The sequence will occur infinitely often.

a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.

And here is the simple coin-toss problem that no one, to
date, can solve.

The Challenge

The coin starts off being fair, i.e. p_1 = 0.5

Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
So:
p_2 = 0.5 / B
p_3 = 0.5 / B^2
..
p_n = 0.5 / B^(n-1)

Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.

QUESTION:
Find the range of values (B,k) for which P_B,k = 1

HINT
P_k = 1 for all B>1, k>0 is not the answer.

Perrti Lounesto comes to sci.math with a dufus brain teaser, where the fool has "hints" at the end. Why ask the question in the first place--you crazy fool, if you think you already know the answer.

But the idiot Perrti Lunatic, of the far side of the Moon, cannot even admit slant cut of cone is a Oval, never the ellipse.

It is exactly, math trash like Perrti, that sci.math should be "clear and free of"

Perrti, is the slant cut in cylinder, is that a rhombus, you fool.

On Monday, October 17, 2022 at 2:21:26 AM UTC-5, Perrti Lounesto Jr. wrote:
> Have abusive deranged flametrolls like the former campus
> dishwasher Ludwig Hansen nee Poehlmann or Kessler, 72,
> born in Arschlick in the Reich, a lunatic who somehow
> eluded the police all these years, driven all the
> competent ones away?
>
> The problem recited below is an interesting one, but not
> one of those replying in the thread "A simple coin-toss
> problem that no one can solve" seems to have even
> understood it, and their comments are either correct but
> irrelevant (eg Sergi o's "dont play roulette! Just send
> the Casino a check and save on the airplane and hotel,
> save the time, go fishing...") or wrong / absurd /
> nonsensical.
>
> Is sci.math a mathematician free zone? Can anyone else
> have a go?
>
>
> THE PROBLEM
>
>
> Introduction/Background
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.
>
> b) The sequence will occur infinitely often.
>
> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>
> And here is the simple coin-toss problem that no one, to
> date, can solve.
>
>
>
> The Challenge
>
> The coin starts off being fair, i.e. p_1 = 0.5
>
> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> So:
> p_2 = 0.5 / B
> p_3 = 0.5 / B^2
> ..
> p_n = 0.5 / B^(n-1)
>
> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>
> QUESTION:
> Find the range of values (B,k) for which P_B,k = 1
>
> HINT
> P_k = 1 for all B>1, k>0 is not the answer.

you were already given the answer.

you coin toss problem is simple, for n zeros in a row just p_2*p_3*p_4*...p_n

(identically the same as a given pattern n long)

On 10/17/2022 2:17 AM, Perrti Lounesto Jr. wrote:
> Have abusive deranged flametrolls like the former campus
> dishwasher Ludwig Hansen nee Poehlmann or Kessler, 72,
> born in Arschlick in the Reich, a lunatic who somehow
> eluded the police all these years, driven all the
> competent ones away?
>
> The problem recited below is an interesting one, but not
> one of those replying in the thread "A simple coin-toss
> problem that no one can solve" seems to have even
> understood it, and their comments are either correct but
> irrelevant (eg Sergi o's "dont play roulette! Just send
> the Casino a check and save on the airplane and hotel,
> save the time, go fishing...") or wrong / absurd /
> nonsensical.
>
> Is sci.math a mathematician free zone? Can anyone else
> have a go?
>
>
> THE PROBLEM
>
>
> Introduction/Background
>
> Trivially, when a fair coin is tossed, ad infinitum:
>
> a) Any arbitrarily-long sequence of consecutive heads
> will occur, eventually.
> So, for example, the probability that a googolplex-long
> sequence of consecutive heads will occur is 1.
>
> b) The sequence will occur infinitely often.
>
> a) and b) remain true even if the coin is non-fatally loaded/biased, i.e., for any probability p > 0 of a toss resulting in a head.
>
> And here is the simple coin-toss problem that no one, to
> date, can solve.
>
>
>
> The Challenge
>
> The coin starts off being fair, i.e. p_1 = 0.5
>
> Then, for each successive toss, the coin is progressively biased against heads by a constant factor B > 1
> So:
> p_2 = 0.5 / B
> p_3 = 0.5 / B^2
> ..
> p_n = 0.5 / B^(n-1)
>
> Let P_B,k = Probability that somewhere within the infinite sequence of toss results there will be at least one occurrence of k > 0 consecutive heads.
>
> QUESTION:
> Find the range of values (B,k) for which P_B,k = 1
>
> HINT
> P_k = 1 for all B>1, k>0 is not the answer.
>