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

[Monte Davis]

P. 56:

“But squares that have already* had* several hits, I mean—”

“I’m sorry. That’s the Monte Carlo Fallacy..."


At the wiki, contributor MD defines it as:


The belief that if events have deviated from our expectations of chance in
one direction, they are bound to deviate in the opposite direction soon, as
if to compensate. The name is drawn from a famous event at the Monte Carlo
Casino in 1913, when a roulette ball settled on black 26 times in a row --
and the casino grew richer as more and more patrons bet on red,
anticipating a "rebound." [ https://en.wikipedia.org/wiki/Gambler's_fallacy
 ]

As Roger patiently explains, no rocket is influenced by what previous
rockets have done, any more than the roulette ball was influenced by what
it had done on a previous spin -- or 25 previous spins -- of the wheel. The
Poisson distribution depends on the assumption that events in a data set
are genuinely random and independent -- i.e. that in this case, there is no
systematic "skew" in how the V-2s are aimed and launched, or in the many
manufacturing and environmental variables that affect their trajectory and
scatter their impacts around the target point.


*


Those Monte Carlo bettors may have been misled by their intuition of a
valid statistical principle, the law of large numbers: "The average of the
results obtained from a large number of trials should be close to the
expected value, and will tend to become closer as more trials are
performed." E.g.,  getting tails from a flipped coin six out of ten times
isn't remarkable at all -- but 60 out of 100 is less likely, and 600,000
out of 1,000,000 is vanishingly unlikely.

https://en.wikipedia.org/wiki/Law_of_large_numbers


Where the bettors went wrong was that 26 spins of a roulette wheel simply
isn't that large a number. The brain doesn't store or process quantitative
data well enough to be very good at this kind of thing "on the fly,"
especially when something important is at stake (money at Monte Carlo, life
or death under the scatter of V-2s)... which is why statistics were
developed in the first place.


Note Roger's search for a pen at 56.28: "reaching for pocket after pocket,
why are there never any damned... ah here..." Of course "never" is absurd,
Roger; you're just annoyed. (BTW, have you ever noticed it's always in the
last pocket you check?)


Given GR's association of rockets and death, the Roman sieve and the
supposed healing power of the stalks that grow through it is is a totally
fucking brilliant touch.


"his face often grows chalky and clouded, as behind the smudged glass of a
railway carriage window as vaguely silvered barriers come down, spaces
slide in to separate him that much more, thinning further his loneliness. "


We learned about trains and barriers from the Evacuation nightmare. And
while "thinning his loneliness" might seem ambiguous or imprecise here, it
will be somewhere in the back of our minds when Slothrop is slivered away
into Postwar.
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