Bill Velek wrote:
Anyway, if I understand correctly, the variance is determined by the
paytable, assuming perfect play; this is why WinPoker indicates a
stated value for variance for each game, independent of how many
hands are played.
<snip>
Anyway, given all of that, I have a hard time understanding why the
variance (which is a fixed figure anyway) on a single game of 10 play
is going to be any different than what the variance is on 10
successive games on a single-play machine.
<snip>
Are there _really_ any differences, and does the covariance really
explain this?
Hi Bill,
The key to the puzzle is your fortuitous use of the word "independent"
in the first snippet above. If the hands on a multiplay were
independent of each other then the variance of the machine would be
the same as a single play machine.
However, clearly the hands are linked by the initial deal on which the
resulting three hands are all dependent. That relationship is defined
by the statistic covariance. I won't delve into the specifics of
covariance. There are some rules of thumb that are helpful, however:
The volatility of wins/losses of 3-play (not variance mind you, but
ultimately we use variance and standard deviation to understand the
volatility of a game) is roughly equivlalent to that of single line
play at twice the denomination. In other words, $.25 3-play
wins/losses (as an absolute $ amount) will approximate those of
playing $.50 single line.
The volatility of wins/losses of 10-play will approximate that of
single line at 4x the denomation (wins/losses of $.25 10-play are
roughly those of $1 single line play).
Note, however, that if you look at a single hour of play swings can be
much more severe. Over the course of an extended session, and
especially over several sessions, these relationships between
multiplay and single line play will bear out. I hope this is
sufficiently explanatory.
- Harry
Note to all: For whatever reason, I've been on a bit of a posting
"jag" that I'm sure is getting tiresome to read. I'll cool it for
awhile. At any rate, I'm outta here in 5 days for 11 nights in LV!
- H.