BtZ42 Section 9 (pp 53-60): the sieve of chance

[Monte Davis]

>But once it *has* settled...
That's the crux, and a starting point for a fascinating (some other time)
excursus into Bayesian probability. We do much more anthropomorphizing and
projection than we know, and a some level we'll always feel that the
roulette ball has a memory and "knows" it should start evening things out
by settling on red. That feeling grows much faster than the unlikelihood of
any given run of black does -- which is why more players flocked to make
ever larger bets on red, and overall the casino did very well that night.

> It would have been the same probability even if the ball at that point
had settled on black for a few million times in a row, no?

Yes -- aside from the likelihood that you would long since have concluded
the wheel must be rigged :-)


On Fri, May 13, 2016 at 9:32 AM, Thomas Eckhardt <
thomas.eckhardt at uni-bonn.de> wrote:

>  Monte Davis <montedavis49 at gmail.com> wrote:
>
>> P. 56:
>>
>> “But squares that have already* had* several hits, I mean—”
>>
>> “I’m sorry. That’s the Monte Carlo Fallacy..."
>>
>
> I look at it like this: It is highly unlikely that the roulette ball
> settles on black for 26 times in a row. But once it *has* settled on black
> for 26 times in a row, the probability for it to do so again with the next
> spin of the wheel is the same as before (48.6 per cent, that is).
>
> At least that's how I explain it to the kids...
>
> Where the bettors went wrong was that 26 spins of a roulette wheel simply
>> isn't that large a number.
>>
>
> Hmmm. It would have been the same probability even if the ball at that
> point had settled on black for a few million times in a row, no?
>
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