>Steve Jacobs wrote:
>> Harry, I think you're always inclined to stick with max-EV, and your
>> analysis here is to rationalize that choice. But really, there isn't
>> a need to rationalize. If you prefer to maximize net dollars per
>> hand played, then max-EV is the correct choice FOR YOU. If a player
>> decides they would rather maximize net dollars per royal flush, then
>> min-cost(royal) is a better strategy FOR THEM.
I have a philosophical nit to pick with this, Steve. It still doesn't
address what strategy is best for them, but only what strategy they
perceive as being best for them.
Then I ask you this: who is a better judge of what is "best" for any
given player? My answer: the players themselves. I think it is
presumptuous for _anyone_ to foist their personal choices onto
others, and that applies as much to VP strategies as to anything
else.
You could just as easily say that
playing to minimize EV would be the correct choice for those who
prefer to lose as much money as they can.
Yes, you could, and it is their money to play as they see fit.
Goals aren't always clear
or even known. I've never had a definite goal in mind. "Win as much
money as I can over the next 20 years as safely as possible"
approximates my approach, but definite goals have some arbitrariness
to them, anyway, and aren't necessarily completely correlated with
what's best for the player.
Nobody can help a player who doesn't know what they want to achieve
by their play. Nobody can give proper directions (or draw a map) for
someone who doesn't have a destination in mind.
I agree that goals often have arbitrariness to them, but many goals are
specific and non-arbitrary. If a casino offers a VP promotion that gives
the player a special opportunity, it isn't too hard to come up with a
specific goal to take advantage of that opportunity.
I don't expect a mathematical analysis to
ever solve these problems.
Math cannot solve problems that boil down to human whims.
It's entirely possible to play for 20
years and then realize that one hardly went about accomplishing what
one really wanted to in the best way, even if one strictly followed
the mathematical approach that was optimal for one's explicitly
defined goal. I have yet to come up with a way to strictly quantify
how much to adjust my strategy to balance risk and EV, and, 10 years
from now, I may decide that I adjusted it way too much or too little
the whole time.
I don't claim that anyone should make a final choice and never change
it. Different strategies are best for different situations, there certainly
isn't any "one fits all" strategy.
>Steve, first, thanks for correcting some of my math. I resorted to a
>little back of the envelope calculation that didn't serve me well,
>although the general relationships held true.
>
>Concerning the preference alternatives above, it's notable that most
>players will find both desirable. I expect that no player seeks one
>goal at the absolute expense of all others. The inquiring player who
>is considering an alternative strategy likely looks to evaluate the
>tradeoffs involved. That was the focus of my post, which identified
>those for the case of min-cost(royal) vs. max-EV.
>
>I don't think the situation is best expressed as a strict preference
>for one vs. the other. A discerning player will make a decision,
>balancing the tradeoffs.
>
>- Harry
Exactly, Harry. Where to draw the line is a guessing game, which
implies that there is an unknowable ideal that is being guessed at.
Establishing definite goals and applying strictly mathematically
correct approaches for those goals hardly solves the problem.
Well, I happen to think that the math approach works a lot better than
wild guessing and consulting horoscopes, but perhaps that's just me.
Math is a tool. Those who take advantage of it can better focus their
energy.
Maybe
the best way to look at what approaches mathematical analyses come up
with is as limits. Maybe max-EV shows the limit that there should be
to one's aggression and min-cost(royal) shows the limit to how
conservatively one should play, in between which it's anybody's guess.
That's a tempting thought, and one that I've played with a lot. I've come
to the conclusion that the strategies that are most familiar tend to be
far from being limiting cases. The real extremes are things like playing
to hit a royal, right now, at all costs. Or playing to minimize the chance
of losing, without any regard to payoffs. Both of these extremes play a
part in certain types of optimal strategies.
I feel that studying alternate strategies opens up new ways of thinking
about the game. My method of "virtual payoffs" provides a concrete
means for judging how aggressive one strategy is compared to another,
in terms of how hard the strategy "tries" to hit royals or 4/kind or
whatever. Of course, communicating that is extremely difficult, and
a constant source of frustration for me.
···
On Sunday 30 July 2006 11:35 am, Tom Robertson wrote:
