Path: csiph.com!eternal-september.org!feeder.eternal-september.org!nntp.eternal-september.org!.POSTED!not-for-mail From: Tim Rentsch Newsgroups: comp.arch Subject: Re: IA-64 Date: Wed, 18 Mar 2026 01:01:03 -0700 Organization: A noiseless patient Spider Lines: 41 Message-ID: <86zf454lds.fsf@linuxsc.com> References: <10n6ts2$3fjht$1@dont-email.me> <10o9s6b$34qug$1@dont-email.me> <20260304202556.000063d9@yahoo.com> <10oa6tk$38csm$1@dont-email.me> <10onere$3o39t$1@dont-email.me> <86pl5874op.fsf@linuxsc.com> <10p3uoo$bka8$2@dont-email.me> <86y0js6bit.fsf@linuxsc.com> <10p94fc$227s2$1@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Injection-Date: Wed, 18 Mar 2026 08:01:07 +0000 (UTC) Injection-Info: dont-email.me; posting-host="d8ad6cc581418585937912c9311862c5"; logging-data="3810187"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18+jMux4qoiCzKMyEjkq308T9GyMgwxKQk=" User-Agent: Gnus/5.11 (Gnus v5.11) Emacs/22.4 (gnu/linux) Cancel-Lock: sha1:rVW3qEFaHsyiaFNO0BMXO8Stt90= sha1:4a+oOxz0su/srrgw5urymelc124= Xref: csiph.com comp.arch:115413 Terje Mathisen writes: > Tim Rentsch wrote: [...] >> An unrelated item for your reading pleasure... >> >> Take an unbiased coin and start flipping it. Keep flipping until >> the number of heads first exceeds the number of tails. Compute the >> fraction: the number of heads divided by the number of flips (which >> always gives a number between 0.5 and 1.0). >> >> Repeat the above process as many times as desired. Compute the >> average of all the fractions and what do you get? >> >> I heard about this yesterday from a friend. That's a hint, of >> sorts. (It is now Sunday afternoon where I am.) > > So, by definition the list of possible sequences start with > H ; 1/2 of all > THH ; 1/8 > TTHHH ; 1/32 > THTHH ; 1/32 Sum up to here is 22/32 > TTTHHHH ; 1/128 > TTHTHHH > TTHHTHH > THTTHHH > THTHTHH > etc > > Here's a wild-assed guess: sqrt(0.5) = 0.707 That's an interesting idea for how to analyze it. I'm not sure it works. One thing I can say for sure is when I tried to replicate it in a program I got wrong answers, or maybe it converges very slowly. An easy way to get a result that matches the theoretical value is just to simulate the coin flips using a random number generator. To save you the trouble of doing that the ultimate value is pi/4 (and it converges VERY slowly). Incidentally, the hint mentioned above is that I heard about it on pi day, March 14th. :)