You raised so many aspects that go into this decision, some of which
I was unaware of, some of which I don't understand, and some that I
have been spared(!) thus far.
But to me, it all boils down to this question. You are staring at a
dealt hand of KQJ9,x. The choice is to hold KQJ or KQJ9. The Straight
Flush payout is 250. The Royal Flush payout is more than 10000. There
is a fork in the road.
At that point, apart from the overall strategy of the game, what is
the immediate preferred strategy? The answer for that, it seems to
me, is to hold KQJ is the RF is valued > 11040, and KQJ9 if it is
less. Obviously I am not taking into account all the other factors
into account. I have to admit that I don't know the full import of
some of the factors you mentioned; one in particular that if you draw
to a Royal Flush (of 11040), it will be immediately reset to 4000.
--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@...>
wrote:
>--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@>
>wrote:
>>
>> I (confidently) get $11,040, also. As a practical matter,
though,
>> there are at least 2 reasons to wait until much higher than that
to
>> draw to the royal.
>
>Such as what?
>
>Does one of them has to do with tipping?
Tipping and the time associated with hand-pays would go into the "at
least" category, not being the two primary reasons. The least
important of the two primary reasons, neither of which I know how to
calculate, may not often qualify as making it better to wait until
"much" higher than $11,040, as often does the most important. It's
that there is a higher variance to the royal draw, and thus
requires a
bigger bankroll. All else being equal, besides all the other
reasons
to not draw to the royal, if the progressive, which I assume is the
context, were exactly at $11,040 and I were dealt this hand, I would
unhesitatingly draw to the straight flush, and only at some point
higher than that would I start drawing to the royal. But mainly,
and
in addition, I've never heard of a 10/7 progressive as high as
$11,040. I would value it greatly. Assuming hitting the jackpot
would make it reset to $4000, I would count that as a significant
cost
of hitting it, and would incorporate my best estimate of that cost
into my strategy. The very fact that one is playing a progressive
means that hitting the jackpot will incur this cost. Only if there
are infinitely many 10/7 progressives at $11,040, or anything
equivalent, that one can play immediately after hitting the first
one,
is there no such cost. Calculating it is impossible. Opportunity
cost is relevant. How many machines are on the progressive is
relevant. A machine being broken down, and when it might be fixed,
is
relevant. Meter movement is relevant. At what point one plans to
next play the progressive after this one is hit is relevant. How
long
one plans to play is relevant, which makes the speed of the machines
relevant. How fast other people are playing is relevant, etc. As
opposed to the underlying math, which shows that a royal of $11,040
is
where these two draws are of equal value, this cost changes
constantly, since so many non-mathematical factors go into it.
When I
···
hear anyone say that they play "perfectly" on a progressive, I know
that they aren't incorporating the effect of this cost, as they must
to have any chance of playing "perfectly," on their strategy. The
impossibility of calculating it has simplified my approach. Just as
there's no point in getting, say, the third decimal place of one
number accurate if it will be added to a number which is known to be
accurate to only one decimal place, there's no point in nitpicking
over accuracy of when to start drawing to the royal on a progressive
if one significant factor in that determination is so full of
uncertainty.