A
noteworthy observation is that, if the ace is to be
counted zero, improvement in the second decimal cannot
be achieved beyond level three. Also, bigger is not
necessarily better; the level four system narrowly
edges the level five system. For the evaluated systems
all decisions are made on the basis of a single parameter,
the average number of points remaining in the deck.
Evidently the maximum efficiency possible for strategic
variation with a single parameter system is of the
order of 70% and one can come quite close to that
without going beyond the third level.
Some
other interesting evaluations follow. Considering
the difficulty and likelihood of error in, for instance,
trying to associate four points with five spots on
the card and one point with seven spots on the card,
it is extremely questionable whether a price tag of
$200 for a less than optimal level four system is
a bargain. Although the Ten Count, when parameterized
as a point count, uses the numbers 4 and 9, it is
certainly not at the 9th level of mental gymnasticsone
keeps track of the proportion of tens by counting
off the tens and nontens as they leave the deck.
Two other methods of evaluation, based on the mysterious
infinite deck, included pair splitting and doubling
down on any two cards as options. They gave very similar
relative results for all the systems' strategy gains
reported here, with only an occasional interchange
of the order of two systems whose efficiencies differ
only in the third digit after the decimal point.

Before
changing stakes, make sure that everyone in the group
is comfortable with the change and doesn't feel trapped
by peer pressure. If Fred is already losing enough
each week to jeopardize his home situation and the
game changes from $510 to $1020, Fred may need to
drop out even if he doesn't want to say so in front
of everyone. But if the game just seems no fun because
the stakes are too low for everyone but Fred, talk
it over as a group and, if appropriate, take a vote.
It doesn't
have to be unanimous, but seriously consider how much
the lone objector contributes to the ambience and
dynamic of the game. If everyone really likes Fred,
or if Fred is the game's biggest regular loser and
doubling the stakes will mean Fred will drop out,
raising the stakes could prove much costlier to the
remaining players than it initially appears. Instead
of winning twice as much, good players may actually
win less.
Discussions about permanent stake changes don't happen
too often in a poker game: Once a year is a lot. The
second kind of stakechanging happens quite often
in private games, though.
