And Bob wrote in his CasinoGaming Column, tiltle "Short-Run Bankroll Calculations" on
Nov 28,
"As a measure of streakiness, we use the standard deviation, which has a mathematically
precise definition that we don't need to go into here. Some programs use the variance,
which is the square of the standard deviation. Both the standard deviation and the variance
correctly rank which game is streakier than the other, but the standard deviation better
indicates how much streakier one game is than another. "
And Bob is plain wrong and misleading on many levels. Let's try to clear it up:
1) VP isn't "streaky". "Streakiness" is a measure of the correlation of outcomes of a
random process. VP results are uncorrelated. Each hand you are dealt has no
relationship to any prior hand you may have been delat or any future hand you may be
delt. Correlation is not directly proportional to the variance or for that matter standard
deviation. No way (correlation and co-variance are related however).
2) VP players often use the word "streak" to describe a series of outcomes that seems to
them to be related-- or correlated. For example, a long series of winning hands might be
called a "winning streak". Some folks use the term "streak" to imply just a series of
similiar results regardless of whether or not they have any determinisitic mathematical
relationship (average correlation; sampled correlation of the randomn process). In other
words they are describing a characteristic common to a series of events (as in "these last
10 hands were all winners") and NOT of the game itself (random process) itself (as NOT in
"these last 10 hands were all winners, therefore this GAME is streaky). In either case the
player is noting that "the game is clearly capable of producing series of 10 hands that are
all winners". For many folks a "streak" is something thay experience rathar than a
"mathematical concept"-- yet if we are going to campare "streakiness" and standard
deviation we will need to bring in some more mathematics.
3) VP players often call one game more "streaky" than another game. Often they do this
when they mean to say "I feel that this game is more volatile than another game" are
saying nothing per say about "streakiness" but instead misusing the word. Other times
they really mean to say that they feel that this game produced outcomes that are more
correlated than the other game. In other words, when someone says "this game is more
streaky than that game" they are often saying that "I observe longer or more streaks with
this game than I do with that game", where a "streak" was defined above. Given what we
already know (about "streaks" and VP), we know this is an erroneous statement. So, when
a player talks about the "streakiness" of a game, he or she is somewhat misusing the word
"streakiness" (creating a new meaning to "streakiness" via the implyed equality streakiness
= function(volatility)) or is making an error. That is, a VP player has the "perception"
that a game is more streaky than another game-- but the mathematical facts are different.
4) Bob claims that "Both the standard deviation and the variance correctly rank which
game is streakier than the other". How could this statement be true? If streakiness is a
measure of how long a streak might be or how likely a streak is, then he must be saying
that a larger variance means a longer streak, more streaks, or more longer streaks (or
something like that). But, "streaks" in VP are all to do with human perception.
Mathematically, we know that video poker is uncorrelated hand-to-hand. So Mathematical
"streaks" don't exist.. if we compare the mathematical concepts/quantities of "Variance" or
"Standard deviation" to a mathematical "streakiness" (such a mathematical comparison
seems justified given Bob's use of the phrase " correctly rank" rathar that "give me the
feeling") we find that BOB IS WRONG unless of coarse "streakiness" itself has some other
definition. (Bob, what is your definition of "streakiness"? Don't say the "percaption of
variance." LOL)
5) Bob claims "the standard deviation better indicates [than the variance] how much
streakier one game is than another." Even if we excepted is earlier erroneous claim, how
can this be? Is a square root or square somehow better than a linear relationship ? Is the
number 2 better than the number 4? Did Bob mean to say that the the standardard
deviation is linearly proportional to streakiness while the variance is proportional to the
square of the streakiness (or that the square root of the variance is lineary proportional to
the streakiness? Perhaps, but probably not. But it doesn't matter. Bob is wrong. [Aside:
The idea of "linearity" is artifical. I used it to keep the discussion simple. Streakiness isn't
linearly related to anything observeable or measureable in VP (except hand-to-hand deal
correlation which is always zero for the game itself). In general if you had to pick some
arbitray relationship between 2 quantities, you ought not to pick linear. Most of the time
you will be wrong. So, Bob, if you want to pick l, you ought to first spend your time show
your work]
6) Bob says: " the variance, which is the square of the standard deviation." Bob statement
is misleading. The fundemental statistical quantity is the variance not the standard
deviation. He should have written "the standard deviation is the (positive) square root of
the variance." When I read Bob's statement I thought "Does he have a unjustified bias
towards the standard deviation?" Then I chuckled "who cares?"
I'm tired of typing... (which is a good thing since I could otherwise go on for a long time
and this post is already incredibly boring, so much so I won't dare read it over to check for
errors, mistatements... lol)
That is a good "rule" for good communication!