Sorry for the triple post.
I found an interesting 2010 paper about "mean time" and "waiting time"
and using it to detect changes in underlying behavior (e.g. a gaffed
game).
http://ff.im/USw3M
So what are the "mean time" and "waiting time" to see a bad streak of
23/200 flushes?
How many hands?
If we have seen 23/200 flushes way too soon, maybe the underlying
machine is "gaffed".
Mitchell
The authors of the papers say "The statistics of waiting time may not
justify the prediction by the gambler's fallacy, but paying
attention to streaks in the hot hand belief appears to be meaningful
in detecting the changes in the underlying process."
The debate over the statistical validity of the hot hand belief has
lasted more than twenty years (e.g., Bar-Eli et al., 2006), and it
is not likely to be ended by simply introducing a new set of
statistics. However, pattern time statistics do seem to support some
of the existing theories.
In particular, it has been suggested that the hot hand belief arises
when people are evaluating human performance, and people pay
particular attention to streak patterns in order to detect a change in
the performance, for example, fluctuations in
the shooting accuracy of basketball players (e.g., Ayton & Fischer,
2004; Burns, 2004; Burns & Corpus, 2004; Sun, 2004).
By such account, the prediction to continue a streak is actually valid
on the basis of a higher probability
of a single outcome (e.g., a higher shooting accuracy, a higher
probability of heads in case of a biased coin).
It can be shown that by the measure of either mean time or waiting
time, streak patterns are indeed a good indicator
for detecting the changes in the probability of single outcomes.
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