Variance/co-variance of multiplay vp bears some explanation. I won't
assume any specific understanding of the concepts because it's not
unusual for there to be at least a few gaps in what the average player
does understand.
ยทยทยท
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Let's look at the practical consequences of multiline variance:
Consider single line and multiline play at the identical base
denomination -- say $.25 single line and $.25 3-play.
It's intuitively obvious that in playing several lines at once in
multiline, where the individual hand outcomes are closely related to
each other as a consequence of being formed from the same initial
hand, you bear greater risk of sub par results over a given amount
coin-in compared to single line play for the same coin-in.
For example, for 3 triple line plays vs. 9 single line plays, it's far
more likely that you might have 3 sour multiline outcomes than it is
you'd encounter 9 poor single line hands in a row.
--> Thus, n-play is riskier vs. single line play for a given $
coin-in, assuming both are played at the same denomination.
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Having said this much, typically n-play is considered as an
alternative to single line at a higher denomination. This alters the
situation.
Compare $.25 multiline with $1 single line: For the sake of example
I'd like to keep total wager per play identical, so think in terms of
a (practically extinct) 4-play machine. (Still, 4-play is available
as a partial play on a 50/100-play machine.)
First, compare playing $x coin through on $.25 single line vs. $1
single line, it's likely a no-brainer that we benefit from LOWER risk
in putting that coin through on the quarter play (we just have to work
a lot longer).
If, instead, we play that $x in coin through on a 4-play $.25 machine,
we face HIGHER downside risk than playing it on $.25 single line (as
initially discussed above).
On the other hand, the 4-play $.25 will be subject to lower risk than
single line $1. Again, as discussed above, the 4-play results are
distributed over multiple, independently drawn hands.
--> Thus, in this example, it's more likely that a series of $1 single
line plays will fare poorly than it is that 4 times the draws on
4-play will.
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The simple point of the above discussion is to make crystal clear the
two key relationships between single line and multiline play:
-- At a given denomination, multiline play will INCREASE risk over any
$x coin-in compared to single line.
-- For multiline play, at a lower denom than single, AND where wager
per play is identical, multiline play will DECREASE risk for any $x
coin-in compared to single line.
You'll forgive me if I've belabored the obvious, but a firm grasp of
the above is essential. It's not unusual for a player's understanding
to mesh these multiline characteristics a bit.
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Having said this much, a player is often drawn to multiline play, yet
confronts the uncertainty of the risk involved (vs. their typical
play). The challenge in assessing risk comes from the fact that the
multiline play under consideration generally involves a greater wager
per play than a typical single line wager.
I've noted that when the total wager is constant, multiline will yield
the lower loss risk. As you increase the wager per play, the loss
risk for a given $x coin-in increases as well.
The consequence is that as you add additional lines to play, there
will be a point at which the player exposes themselves to greater risk
than in their single line play.
This appears to be the gist of reboozer's post; and I presume that, in
essence, reb's allusion to a "breakpoint" is a reference to that point
at which n-play presents similar loss risk to a given single play machine.
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I can't say what the basis for reb's "20 to 25" hands is. I will say
that it's difficult to say exactly what the "breakpoint" is for a
given play -- experience may be the best guide.
That said, that experience is best gained through modest increments in
number of lines played. As with any play, what you see in a
particular session may differ sharply from how play generally tends to
proceed.
For a one time proposition, such as DIAD, there's good reason to
proceed with some caution rather than risk "bettor's remorse".
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I hope that satisfies reb's desire for a general understanding. I'm
following with a couple "theoretical" observations that are best
skipped by most (if not all):
I offer up that there is a makeshift means to roughly approximate
reb's "breakpoint" -- you equalize variance between your single line
play and multiline over the course of intended wagers.
Discussing how to do that is outside the scope of this discussion.
While not terribly difficult, it involves something beyond just
seeking out the point at which single line variance is equal to the
multiline variance as calculated above (for which Jazbo provides
necessary covariance values for a number of games).
What must be equalized isn't variance per play (the numbers just
noted) but instead variance over all plays in your intended session(s)
-- where you determine cumulative play variance, accounting for the
number of plays given a different wager per play).
I simply note this as an approach for those determined; it has it's
limitations that make it more an academic exercise than practical.
The variance statistic describes fluctuations in play over the "long
term". Short term behavior differs between single line play vs.
multiline (in other words, if you were to chart loss risk over varying
number of total coin-in, the graphs for each would have differing
shapes). As a consequence, while the approach noted above might be
viable in assessing relative longer term bankroll risk, over the
course of something as abbreviated as DIAD play it'll only roughly
describe how the two compare.
Still, that rough description isn't too bad a place to start if you're
really looking for a quantitative approach (and I have), followed up
with some fine-tuning "in the field".
- Harry