I wrote:
> (.25 3-play has a higher bankroll requirement than $.25 single
> play strictly as a consequence of covariance, not the fact that
> you wager more per play)
iggy replied:
that's incorrect for the same total wager, multiplays have lower
bankroll requirements multiplays lower the variance of the draw,
dealt variance remains unchanged
No argument with your statement, iggy. But keep in mind that my
comparison was betwen multiplay and single play at the same
denomination ($.25), not "total wager" (here the example was a $3.75
3-play wager and a $1.25 single play wager).
This fragment of my post (which FWIW, didn't reference the deal) was
to illustrate that the reason why when you play multiple hands at a
given denomination in multiplay vs. the same number of hands (not
plays) in single play, variance (and bankroll requirement) increase
strictly as a consequence of covariance, and not the greater wager
each play.
However, as you note, when you increase the denomination of single
play so that the total wager per play is identical (e.g. $.25 4-play
and $1 single play), a second influence on variance kicks in -- the
dispersion of that greater wager over more hands per play. This
variance reducing effect is stronger than the effect of covariance and
thus, as you note, at the same total wager variance is reduced.
- Harry
