Poker Poker Poker!: [vpFREE] Re: Here we go again?

The topic of variance as it applies to multiline play has been rather
comprehensively covered in this thread at this point. Still, I'd like
to offer a "common sense" perspective from which to grasp the concept,
just to make it a little more concrete.

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Think of variance as a measure of play streakiness, i.e. the extremes
to which the peaks and valleys of play might run. Consider play of
$.25 Jacks in two guises, single line play and 4-play. Look at the
expected streakiness of play, one vs. the other.

For any given total $ in total wagers, you have 4x more single line
plays than multiline plays. Each individual single line play is
independent of the next. That independence distributes results fairly
widely and swings tend to be moderate. On the other hand, in 4 play,
each set of 4 individual hands that are completed are all related by a
common deal. If that deal should be particularly strong, then the
resulting completed hands tend to be high paying. Conversely, if the
deal is quite weak, the completed hands will likely be weak as well.

The consequence of 4-play is that return is concentrated in a
considerably fewer number of deals and, due to the relationship
between completed hands from those deal and the initial deals, there's
a much stronger potential for overall play to run negatively or
positively. Simply put, there's a smaller opportunity for results to
even out over the course of play vs. single line play with 4 times the
deals.

This naturally translates to a higher variance for 4-play vs. single
play at the same denomination. Statistically, covariance is the
measure of the variance that is directly related to the added
dimension of multiple hands being derived from a common deal in
multiplay and is additive to single line variance in determining
overall multiplay variance.

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There's another dimension when it comes to considering multiplay
variance -- the relative variance when comparing single line play and
multiline play where the wager per play is a constant. An example is
$1 single line play and $.25 4-play (total wager $5 in each case).

In this instance, the $5 wager in single play yields a single outcome
that determines the payout from the play. In $5 4-play wager has an
outcome that is spread over 4 separate drawn hands. The consequence
is that the 4-play wager has a smaller variance than single play; the
risk is dispersed.

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Depending upon the context in which multiplay variance is considered,
it may be higher or lower than single line play (as was summarized
elsewhere in this thread).

- Harry