I'm going to condense the past conversation a bit as follows:
HP: Under a 10% ror ... <snip> ... that's not sufficient reduced risk
to bother.
SJ: How much reduced risk would make it worth the bother? ... <snip>
... If you don't have any criteria for how much ER you are willing to
give up in exchange for some a given reduction in risk, then it seems to
me that you don't really know if it would be worth the bother or not.
ME: Doesn't the answer fall within a gray area that is likely to vary
day by day, according to a person's whims?
SJ: If one goes by whims, then sure. If one goes by math, then the
decision might be quite consistent.
My current reply: Well, it seems to me that the weighing of the two
alternatives is a personal value-judgment that has no right or wrong
answer, and therefore probably doesn't have what anyone could say is a
'mathematically correct' answer, despite that the values that are being
considered are derived via math. I don't think the human brain
functions like that for most of us. If I showed you a gray panel that
was very close to midway between black and white, today you might say
that it is closest to white, but then think about it as you lay in bed
and the next morning decide that its actually closest to black. To me,
an initial decision upon a question such as the one at hand involving
Risk of Ruin, amidst the constantly changing status of bankroll, seems
even more likely to be subject to constant second guessing if it
happened to be a very close call to begin with. And that's what I think
we might be dealing with here. For instance, it is obviously a 'no
brainer' if your math reveals that your alternative strategy will cut my
risk in half in exchange for a reduction in ER on only .1% in a game
where I have a .5% edge; it is likewise a 'no brainer' if your figures
indicate that I'd need to surrender virtually my entire edge for a
modest 10% reduction in my risk.
Things don't need to be that glaringly obvious in order to be a no
brainer. If you care _at_all_ about risk, then if two choices have
identical ER and different risk, the choice with lower risk is better,
even if the difference in risk is miniscule. Similarly, if two choices
have identical risk but different ER, then the choice with higher
ER is better, even if the ER difference is miniscule.
The only choices that aren't so simple are when a true tradeoff
occurs and one is better from an ER perspective while the other
is better from a risk perspective.
The problem, as I said, comes in where
the decision is perhaps a very difficult one, and is based on more than
just math. How does it involve more than math? Well, ruin can mean
something more to one person than another, especially if my ruin is the
complete loss of a session-stake that will be replenished with more
disposable income next week and I happen to be a local who can just
drive over to the casino, and your ruin might happen to mean much more.
Then you'll have to resort to tea leaves and chicken entrails. If you can't
quantify the decision precisely, then math may be powerless to help you.
But that doesn't convince me that everyone is so wishy-washy in their
objectives.
It just seems to me that when you add to the equation other
considerations which are difficult or impossible to quantitate, then
you'll find people "going by whims" more often than "going by math" for
this sort of a decision.
Agreed. However, I think we've only scratched the surface in terms
of what can and can't be quantified. For example, it was only a day
or two ago that I figured out how to compute the exact probability of
having a bankroll last until hitting a royal. The same approach can
be applied to any final hand, or even a group of final hands. If
someone wanted to play to maximize the chance of lasting until
hitting "quads or better" then an optimal strategy can be devised
for that goal.
However, I'd like to ask you if you could
perhaps explain your earlier statement to Harry, which was:
"If you don't have any criteria for how much ER you are willing to give
up in exchange for some a given reduction in risk, then it seems to me
that you don't really know if it would be worth the bother or not."
Have you personally established such "criteria", are they mathematically
precise, and can you give us an example or two?
All I'm saying is that if you don't have some criteria for making the choice,
then talking about it being "not worth the bother" is meaningless. Further,
that is in some degree the same as saying "I just don't care about anything
but ER," which I seriously question. Players who only care about ER play
very strangely, betting their entire bankroll on any favorable proposition no
matter how tiny the ER. I've never seen anyone who truly plays that way,
so I take that as evidence that _nobody_ truly believes "ER is everything."
OK, there's that guy who bet it all on Roulette the other day, and won,
but that seems clearly a case of someone who doesn't even care about
ER -- he would have had a better shot by betting it all on the pass line
at the craps table.
And if you just mean
that you have decided that it is "worth the bother" whenever RoR= x at
the same time that sacrificed ER= y ... could you explain what value you
gave to "bother", or how your threshold was determined by anything other
than a non-mathematical and arbitrary choice on your part?
Usually it is a choice and a matter of personal taste. Math can't tell you
what your preferences "should" be, and neither can someone else. When
someone comes to me and says "what is the best way to play" I would
say "that depends on what you are trying to accomplish". Do you want
to win as quickly as possible, or would you prefer to win more slowly
but with greater certainty? Do you have a specific objective in mind, such
as a specific target bankroll or playing to hit a juicy progressive jackpot?
Best is _always_ relative to the particular desires of the individual player.
People who repeatedly play negative games must care about something
other than ER -- probably they want entertainment value or maybe they
would like to have the best possible shot at hitting a royal based on the
limited funds they are willing to risk.
Above I said "usually it is a choice." Sometime you are faced with a
situation where outside constraints narrow down the possibilities that
make sense. If you are compelled to play games that you wouldn't
normally play, or to accept wagers that you would normally pass up,
then you have fewer options. This falls under the general heading
of "constrained optimization problems." Tournaments are one example
where max-ER play is almost certainly the wrong strategy, because the
real cost is the entry fee and the real payback is prize money instead
of payoffs from the machine. Bonus situations such as online matching
funds that must be "earned" are another example. I can easily imagine
players wanting to exploit such offers by playing not to maximize ER
but to maximize the probability of having their bankroll survive until
the requirements are met to qualify for the "free" money.
I hope that has clarified things a bit. Math can't make choices for
you, but that doesn't imply that the choices are arbitrary. They
are usually a reflection of what you "value" whether that is based
on a dollar value or some other kind of value.
···
On Tuesday 13 April 2004 10:27 am, Bill Velek wrote:
