mkl54321 wrote:
Additional stat: "The streak" is now at 155, namely, missed one-
card draws to royals. The previous streak ended at 127, so the
aggregate is one royal in 282 tries. Another statistic that is so
far out there, I can't attribute it to simple "bad luck".
Earlier, there was an assertion that mk1's (Kevin) overall RF results
(a success rate of 1 in 155,000 over the course of 2 mil + hands) lay
somewhere in the range of "six sigma".
I'm still curious about that calculation but am willing to accept it,
although that sounds a little extreme. "four sigma" is equivalent to
a record that only 1 out of 30,000 players would see in a given 2+ mil
run of hands. I believe "six sigma" sets the record out in the
stratosphere of only being seen by something like 1 in over 1 million
players. That certainly would set Kevin apart, but it seems a tad high.
···
------
However, what I want to address is the excerpt above and examine just
how far out this stat is. That's one I can handle.
The probability of missing a given one-card draw to a royal is 46/47.
Now, to determine the likelihood of Kevin's one RF in 283 attempts we
look at the probability of one specific sequence in which this is the
success rate (say 1 hit, followed by 282 failures) and then multiply
that result by the total 283 ways in which the attempts can be
sequenced with only 1 success. (I hope it's clear that in a sequence
of 283 attempts with only 1 success, there are 283 possible positions
in that sequence in which that single success can occur.)
Ok, for the first case (1 success, 282 failures), we multiplay out the
individual probabilities of each event. The probability of a success
is 1/47; a failure is 46/47. We multiply the one success by 46
failures. Using an exponential calculation -- allowing us to
calculate this easily with a calculator or spreadsheet using the "^"
function -- the equation is (1/47)*[(46/47}^282].
(I'm stating what is obvious to many for the sake of the statistically
uninitiated who might be drawn to run the calcs. themselves.)
The value of that equation is: .000049433
Multiply this by 283 and we get: .013989
In other words, the likelihood of this streak is 1.4% for each 283
attempts made by a player. A player who runs two such trials of 283
draws will have a probability of 2.8% of managing only one RF on at
least one of those trials.
I'd say that these probabilities give Kevin a reasonable number of
players with similar runs as company in his travels through the
casinos and isn't a result that's "so far out there". Nonetheless,
rest assured that I feel his pain.
My point here isn't to suggest that Kevin is off his rocker. I
imagine all of us, without exception, have aspects of our play that
we're quite confident damn few others experience. It's the nature of
the beast.
However, the reality of the game is that it's almost inevitable that a
player will experience a pretty nasty streak in some element(s) of
their play; ones which bear a sharp cost. The fortunate thing is that
it's very likely that good fortune in some other aspect of play will
balance out that cost to a large extent.
However, when the element involved is RF frequency it's not to be
expected that this cost will be readily covered by luck on other
hands. And Kevin's overall subpar RF results suggests that other RF
draws haven't done the trick.
But again, I'm not sure that even that costly record lies beyond the
realm of imagination, or the future experience of one or more players
here -- provided they have the stamina and bankroll to stick it
through as Kevin has.
- Harry