I did not "guarantee anything approaching success". What I stated
was under the assumption of Normally Disrtributed results, one can
be 90% sure that with $1,700 one can _play through_ 20,000 hands of
single line 25c PFDW. In this sense, there is a short term bankroll
requirement, and this is true even for a game with a negative
retrun. Of course, the long term bankroll for a negative return game
is potentially infinte.
True, you didn't guarantee anything. If, however, one were to take the
mathematical models of ER and variance to court, a judge might well rule
that there is an inherent promise of success when the "products" are used
by the consumer as a basis for play. And, in fact, they are designed
specifically as models for how to best achieve success against ER and
variance. So in a very strong sense, there is an implied promise of
success. If not, then why use such models as a strategic tool?
One of the problems is the implications that arise from their use. There
is an underlying assumption of both normal distribution long term and
normal variance long term. But in short term play the models don't hold
up. The question of what defines the differences between long and short
term have been discussed here many times, with varying conclusions (to no
one's satisfaction <g>), so I don't want to get into that.
The point I'm most eager to make is this: many players rely on these
models as a basis for their play, and in most cases that reliance is
beneficial because players extend their time and may benefit from positive
short term variance. But their use as a model for a minimum bankroll
requirement, ROR stats notwithstanding, are virtually nil. Variance is
thoroughly and completely unpredictable, short of long term approximations.
lb