(In fact, that's a
little over-simplified but the bottom line is more ER = more royals
in the long run, assuming losing massive amounts of money would make
you play less - otherwise you should simply go for the royal on every
hand.)
I'm sorry, but the equation "more ER = more royals" is simply not true.
The max-EV strategy focuses intensely on squeezing the last drop
of EV from the game without any regard whatsoever for the impact
on frequency of royals.
Now let me ask you this -- how do you define "more royals"? Here
are some possible ways:
1) Most royals per game played. This is an extremely expensive
way to play, but increases your probability of hitting a royal on the
next play by roughly a factor of two.
2) Most royals per dollars consumed through losses. I call this
the min_cost(royal) strategy. It is much different than max-EV
strategy, but is still positive EV whenever the max-EV strategy
is favorable to the player.
3) Maximum likelihood of surviving until hitting a royal. I call this
the best_shot(royal) strategy. For a given starting bankroll, this
strategy gives you the maximum probability of having your bankroll
survive until you hit a royal. This strategy is slightly different
than the min_cost(royal) strategy, but again it is much different
than max-EV strategy. This strategy tends to be very close to
the strategy which minimizes risk-of-ruin.
Further, I would argue that, NO MATTER WHAT YOUR OBJECTIVE, this is
the wrong move (assuming that there are other VP games available with
higher variances and higher ERs, which is usually the case). Even if
your objective is to score more jackpots and even if you're willing
to give up ER to do it, this is the wrong way to achieve that goal.
Not necessarily. If your objective truly is a higher frequency of royals,
then playing more agressively is the only way to achieve that objective.
Paradoxically, if your objective is to have your bankroll survive longer
in order to increase your chances of (eventually) hitting a royal,
then the optimal strategy is best_shot(royal), which tries for royals
less often compared to the max-EV strategy.
So, if your objective is to go after more jackpots, what you should
do is to play this hand by the book.
Sorry, but the max-EV "book" is the wrong book to read if your
objective is anything other than "maximize EV". Different objectives
almost always lead to a different form of optimal strategy.
···
On Wednesday 20 October 2004 07:31 pm, blaw57 wrote: