Roland Langley wrote:
In the short term, Lady Luck rules; in the long term, the laws of
probability rule. But as Keynes once brilliantly observed, in the
long term, we'll all be dead. Other than that, there seems to be a
large range of opinions of what long term is.
Keynes statement was in direct observation of policies that focused on
long term objectives while ignoring critical immediate needs.
However, he was hardly a fan of a short term approach and abhored
investors in the 30's who speculated in the stock market for short
term gains rather than the objective of long term income.
I have a particular perspective on the "long term" that is a focus
point for my playing strategy. (And I hope you'll indulge me in
straying to make what I consider a critical point.)
I fully accept that over my playing carrer my results will never fully
converge to long term expected values. As "lwluiki" notes in a post,
the "long term" for some infrequently occurring hands with substantial
payouts can run into millions of hands (although the majority are
considerably shorter).
But that is an unlikely justification for varying strategy in most
instances. Typically, strategy adjustments a player favors out of
this truth is to take more long shots at valuable, but less probable
hands. They hold that if they make sufficient long shots, they'll
clearly outweigh any sacrifice from not hitting more likely hands.
Now, it's clear that in deviating from optimal strategy that the "long
term" expectation is that they'll sacrifice greater return from the
otherwise more probable hits than they'll gain in hitting more higher
value hands. These players are betting that during the course of
their play that they'll manage to beat this expectation.
But this is a gamble, nonetheless. And frequently the hands involved
have a relatively short frequency so that the long-term is well within
the stretch of their career play. They're making a bet that they may
win, but odds are clearly against them.
But let's talk about shots for a royal. Clearly this is a hand where
we'd expect that there likely will be a significant variation from
what a player may actually achieve in their play and the expectation.
Whatever that variation may prove to be, these players are again
betting that the revised play strategy will improve their number of
royals to their advantage despite sacrifices in other hands. That may
be the case, but the expectation is that some will and others won't.
The combined play of these players will achieve long term results and
closely approximate long term expectations - in aggregate they will
suffer a shortfall in return from expectation if they stuck to
strategy. To believe otherwise is to reject the whole of statistics.
Do this if you will, but I don't recommend that you go into the life
insurance business.
If you're willing to acknowledge that these players as a whole will
fall short of the EV of "optimal" strategy play, then for any one
player to believe that they'll fare better than expected is to wager
that they're luckier than average.
If a player truly believes that they're lucky in general, then it's
certainly a "rational" decision to vary play from optimal strategy.
However, in the case of my own play I don't believe I possess some
endowment that makes me "luckier" than others (at least with respect
to my vp play :).
So you'll understand if I attempt to adhere strictly to optimum
strategies (although I'll own up to succumbing to the occasional
temptation where I'm counting on a little luck :).
- Harry