Steve Jacobs wrote:
> I'll respond for a more general audience, and try to explain MCR in
> more detail ...
Steve, that's an admirable discussion. All the basics are well
covered. You've detailed the most appealing aspect of MCR -- when
everything is said and done, it yields the greatest expected profit
per royal hit. If this is a primary objective, the strategy is
attractive.
Right.
I think it begs the question of what circumstances might logically
lend themselves to such an objective.
There is no requirement for any special circumstances. If a player
want the most dollars returned per royal, then MCR is simply the
best strategy for achieving that particular result.
------
For the sake of clarity, understand MCR doesn't yield the greatest
expected profit for any given number of hands or period of play --
max-ER (MER) is the strategy for that. I'm not attempting to diminish
MCR inherent value ... it's only that this result might be
misperceived as a consequence of MCR.
That is correct. MER returns the most dollars per hand played. MCR
returns the most dollars per royal. These are two distinctly different
ways to measure performance.
Inasmuch as MCR reduces the expected loss per hand between royals (vs
MER) for a positive play, it has particular appeal for those who are
concerned about the downside of play during a royal drought.
Agreed.
It should be noted that MCR is applicable to any play and not just
progressives. However, because the amount of return tied up in the
royal for a progressive is particularly high, MCR's objective is most
notably achieved in progressive play.
I'm not sure what "most notably" means. MCR's objective is achieved
simply by virtue of playing MCR strategy. It loses the least average
amount between royals, without regard to how large the payoff is for
a royal.
Perhaps the greatest consideration with MCR is "opportunity cost" --
i.e. what do you give up in playing longer for the royal. In wighing
MCR vs MER strategy, by definition MER's more frequent RF occurance
more than compensates for the added drain per hand. That's simply to
say that competing goals are at work and need to be weighed (but,
that's a given).
Different strategies are geared for different objectives. In my mind this
is no different than comparing apples and oranges. Which is best is
a matter of personal preference, and there is no "right" or "wrong"
answer.
I think you have a natural tendency to say "but I have to give up EV
to play MCR strategy." The problem with that door is that it swings
both ways. A person who has only learned MCR strategy, and who
has been told by many experts that MCR is the "only" way to play,
would have a tough time accepting MER as an alternative strategy,
because they would think "... but I'd get fewer dollars per royal
if I played MER strategy."
Similarly, if you have other attractive opportunities that you might
wish to move on to once you've hit a royal (say that you're pursuing a
"royal doubler" promo that is collectable just once), then you might
want to weigh the value of that next play against the added expected
time spent on the current promotion under MCR.
One circumstance where MCR is clearly a disadvantageous strategy would
be a promotion in which a 2nd royal within a day is doubled. The
reduced expected profit for the promotion should outweigh the basic
MCR benefit for those who find the promo desirable.
I personally doubt that "should" is truly meaningful except to inject bias
into the discussion (however unintentional). If a player wants to
pay the least amount per royal, then it doesn't matter whether some
promotion doubles the payout for a second royal.
If a player want to maximize the number of dollars return per promotion,
then a "best at profiting from doubled royals" strategy becomes more
appropriate than MCR. Note that this is a player choice -- the presence
of a promotion clearly isn't a mandate to play that promotion in any
particular way.
------
It should be apparent that MER works best in a situation where time is
not a factor, nor is your principal concern the expected profit for a
given period of play.
I think you have that exactly backwards. MER cares about time, very
much. It squeezes out profit as quickly as possible. As a result, it
tends to have a higher probability of going broke compared to
min-risk strategy. MER is exactly the strategy you want if your
principal concern is expected profit for a given perion of play.
Did you mean to say MCR instead of MER above?
Likewise, circumstances in which you aren't
looking at alternate desirable plays would best support a rationale
for this play.
Translation: "If you don't want to do something other than maximize ER,
the max-ER is best". That's certainly true, but it seem tautological to me.
All of this said, there's no question that if a player's strongest
motivation is to reap the greatest expected profit out of each royal,
MCR best achieves that objective.
Precisely.
------
What follows is a more subjective evaluation of the prospects of MCR
as a strategy. Admittedly, this reflects personal biases that may not
hold for the next person:
I have two qualms with MCR. The first is that when the specific
numbers are spelled out, I don't see a notable advantage in what MCR
achieves in added win.
For 9/6 Job, MER players pay $100.84 for the same number of royals that
cost $100.00 for MCR players. That is a difference of 0.84%, and if
we were comparing EV then a strategy change that got you 0.84% would
be something you'd drool over.
When the MCR objective is weighed against other favorable goals (and
not simply as an absolute), I find the circumstances that make MCR
strategy more desirable to be sparse at best.
It isn't a question of circumstances. It is a personal choice as to how
to measure performance. In my view, a player would be perfectly
justified to adopt MCR strategy for every day play. If a player prefers
to view the game by chopping up the stream of hands into segments
than each end in a royal, and want to pay the least in "overhead" for
each of those royals, then MCR will best achieve that objective.
Those who prefer the most payback per hand should use MER. It
isn't a question of circumstance.
Let me ask you this -- do you _ever_ keep track of the actual number
of hands you play during a session, and compute the exact ER that
you achieved for that session? I'll bet you don't, and I'll bet there are
very few player who do (I'm tempted to claim "none" here, but then
I think of Monk...). Why? Because players don't REALLY care about
about the number of hands they've played and how that relates to
their performance.
MCR does reduce risk-of-ruin bankroll requirement vs many other
strategies (including MER). However, I expect most won't consider the
magnitude of that advantage significant when it comes to greater
comfort with play risk.
Same comment as above -- numbers that you'd drool over if we were
talking about EV are numbers that you find insignificant in other contexts.
That is what I mean when I claim that you have a natural bias for EV.
The offset to these considerations is that the tradeoffs vs MER are
fairly slight. Nominal ER is sacrificed (.03% in Steve's recent
example). It's fair to say that someone adopting MCR won't suffer
calamity as a consequence :).
For this reason, if someone is inclined toward MCR, I can't say that
they're making a significant error in judgement. However, MCR is
outside of the mainstream body of discussion.
Practically everything that isn't about maximizing EV is "outside the
mainstream body of discussion." I'm trying to change that, because
viewing the world through EV tinted glasses is kind of like the "good
old days" of black-and-white TV. Having the option to watch TV in
color and/or in HDTV opens up a whole new world of possibilities.
While that, in itself, isn't a crime, my second qualm is that I find
it necessarily distracts play focus (it's unlikely a player will tune
out the predominant MER bias in discussion -- you can consider MER a
distraction from MCR if you wish ... it still introduces an element of
distraction).
By "distraction" I think you really mean to imply "sin". The religious
undertones are starting to come through. We're straying from the
path of righteousness by talking about such blasphemies as MCR
and min-risk.
Because I consider the body of vp knowledge to be mastered in order to
be a skilled player quite challenging, I have a strong inclination to
simplify things as much as possible. For that reason, if no other,
I'm biased against MER in absence of marked advantages.
I think you meant "biased against MCR" here.
I find it rather hilarious that you speak of mastering the body of VP
knowledge while claiming that alternate strategies are a "distraction."
It is really simple. You can use EV tinted glasses and avoid "distractions",
or you can master the body of VP knowledge by exploring alternate
strategies in addition to the max-EV mainstream. Those who choose to
never look beyond EV are choosing to concentrate on one knot-hole of
a single tree rather than explore many forests of different trees.
(No need to dispute that statement or others in this last section ...
they're unquestioningly based on personal bias more than the facts.)
At least you're not in denial about the bias. That's progress! 
···
On Saturday 05 August 2006 2:37 pm, Harry Porter wrote:
