Author: fca
Date: 18:48:40 08/14/98
Go up one level in this thread
I view this post as a Troll Directed At Me. ;-)
I even hunted for a #69!
On August 12, 1998 at 22:08:51, Danniel Corbit wrote:
>I agree and I disagree. A ten-zero match will quite likely mean the 10 point
>winner is superior. But the certainty of the result can be measured. Math does
>funny things, and we equate common sense to reality, but it does not always
>work. For instance, flipping a fair coin:
Huh. And when it lands on the edge its a draw, eh? ;-))
>1. h-t-h-t-h-t-h-t-h-t
>2. h-h-h-h-h-h-h-h-h-h
>These two exact outcomes are equally probable. I am not talking about totals,
>but about sequences. The probability of sequence (1) is identical to the
>probability of sequence (2), both of which are precisely 1/(2^10) =
>0.0009765625.
Most here have mastered the binomial theorem.
Note three sided coin required, as all modern coins I've encountered (no holes
in the middle) are anyway, to be similar to chess. If the program A beats
program B x% of the time and draws y% of the time, we need a coin whose
side-landing probabilities are x%, y% and 100-x-y %.
>People think that things are deterministic, but they are not. Everything is a
>probability function.
Ouch. But I shall not rise... Be calm, I say... God is a,,,
>For instance, you may think when you flip on the light
>switch, the light comes on. But it does not work that way. There is a
>probability that:
>1. The light fails (perhaps the bulb is .999 reliable)
>2. The switch fails (perhaps the switch is .999 reliable)
>3. The circuit breaker may be open or the internal wiring may be faulty
>(perhaps .9999 reliable)
>4. The power from the city grid may be down (happened for two days about a year
>ago) (Maybe .9999 reliable over a long period).
>5. Misc other failures are possible, switch not fully engaged, airplane hits
>house, I write void main(){} and Scott Nudds flies out of my nose, etc. (.99999
>reliable)
>So the switch only turn on 998 times out of 1000 in this scenario.
Calculation please, bearing in mind some of the events you have quoted are not
mutually exclusive (naturally) and some are not independent (i.e. internal
wiring fault may already have prejudiced switch operation).
I think you need to introduce a few more numbers to help... ;-)
>A fair coin can and will do silly things. Things very contrary to your
>imagination. If you flip it long enough, you will get 20 heads in a row. We
>could even estimate how many times you would have to flip it to probably get
>this outcome. In about a million trials, one person would get 20 heads in a
>row.
Highly misleading statement. I have no idea what it means, but it is surely
wrong!
Now, Dann, come waltzin' with me.... and let us not count those edge terrace
landings, and let's hypothesise the coin is fair.
Just fill in the blanks for me. It gets better as it goes along. All are of
course "answerable". And all are welcome to reply. Dan, Bruce and Dann
especially.
(a) In 1048576 trials (each of 20 throws) the probability of one or more "20 in
a row"s occurring is ________ .
(b) In order for there to be at least a 99.9% probability of getting at least
one "20 in a row", the minimum number of such trials that can be a priori
expected to be needed is _______________ .
(c) In 1048576 such trials, where exactly 4 "20 in a row"s were observed, there
is a _______ % chance that this result does not contradict the "fair coin"
hypothesis.
(d) "20 in a row" has been just been thrown for the first time in the
experiment. The best guess of the trial number on which this happened is
_____________ .
>The same thing is true of chess games, running contests, and just about every
>other thing we see and do. They are all probability functions. The fastest guy
>does not always win the race. That's what makes it interesting, and that is why
>we bother to run them.
I read about hedgehogs and rabbits and am confused...
>I can effect the outcome of a coin also.
I read "affect". How? Pyramids? Sticky fingers? Jam on one side?
Differential accln due to gravity in the field? Coriolis effect? Chess?
> But even if we are talking about fair
>experiments, at least one hundred trials are going to be needed to make a
>sensible judgement. That is one reason why the approach of bodies like FIDE and
>others make sense. It takes a long time to make a real determination of
>strength.
>I will even go so far as to say that the WMCCC or the WCCC do not necessarily
>determine the strongest program in the world. But they do describe the outcome
>of a very interesting experiment.
I will review the above bearing in mind the numbers that appear in the blanks.
;-)
In stats
Kind regards
fca
*=========================================================*
| 1. Thirteen thirteens are one hundred and seventy nine. |
| 2. Thirteen thirteens is one hundred and seventy nine. |
| 3. None of the above two statements are correct. |
| |
| Q: Are any of the above three statements correct? |
| A: No. Maths is bad in 1 & 2, and "None" is singular. |
*=========================================================*
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