vp_player wrote:
This is why the question was asked about given just a single data
point, how many standard deviations away from the mean would it
need to be before one would wonder about a machine being "gaffed".
My orignal response was 6 SD, but now, after having actually done
the math and graphed the curve, I wouldn't argue with a case being
made for 4 SD (only 1 or 2 RFs in 20.7 cycles) to make one wonder
about the fairness.
The "single data point" is extraordinarily unusual.
I see an alternate question being that given observation over the last
year, what is the probability of some even of similar rarity and
negative consequence being observed (and, as a result, give rise to a
post of similar nature to the original). Obviously that probability
is much higher.
In that context, does this event still raise concern of a "gaffe".
For that matter, might it not be reasonable to suggest that the
appropriate measurement period would be over the player's lifetime
play, for certainly had it occurred at any time during that period it
might give rise to similar question with equal concern.
I won't argue that this experience doesn't give cause to ask the
question about fairness. After all, it's a certainty that the
postulated gaffe (double royal cycle extension) would give rise to
such an event with a decent probability (other potential gaffes that
would also be to the advantage of the casino, such as restricting the
probability of a quad, wouldn't).
As such, it gives space to question existance of a RF gaffe. However,
if you closely evaluate any short-term run of play it's likely that
you'll find some aberration in play results (flushes, quads, dealt 3
card SF's, whatever) that could prompt you to speculate on a specific
possible machine gaffe.
Given this big picture, I find it difficult to class this particular
observation as "very disturbing" (aside from the fact that the related
consequence of the hand shortfall in $ terms might be larger than
other possible scenarios not involving a RF ... though not necessarily
so, given higher win frequencies involved in other cases that amplify
their consequence).
I see only one significance: This frames a specific possible gaffe
that can not newly be tested in a fixed trial that will give rise to a
valid probability that this gaffe "hypothesis" can't be rejected on
the basis of the statistics -- hard evidence to submit to the casinos
gaming authorities. (And this is as good as it gets with any
statistical test.)
- H.