It is interesting that the differences of opinion on this topic do
not have to do with math, but with psychology. Some of us give more
importance to a jackpot than others. The degree of importance we give
the different aspects of the game will determine a great variety of
styles.
Take this situation again. You are playing a $25 9/6 non progressive
Jacks or Better machine and you get 5h Tc Th Qh Ah. There are people
that will play the four card flush and not bat an eye if they get a
fourth card to a Royal. I just could not in this example, even if it
is the correct play, hold the four flush and maybe get $750 and pass
a one in a thousand chance for $100,000. The knowledge that if I play
this hand correctly on the $25 machine many, many thousands of times
I would be making money is not pertinent to me. I hardly ever play
$25 machines, and the long term in this situation will never happen
in my lifetime, unless I win Megabucks, LOL.
The concept of the short term is sort of elusive. The shortest short
term is one play, and it is impossible to get back 99.54% of your
money there, even if you play a $1,000 machine, should there be one.
You get back absolutely nothing with a probability higher than 1/2.
If one were to play an expensive machine just once and one really
wants some money back, the best strategy would be to maximize the
probability of winning something, and I believe in the above hand one
would agree that this is met by holding the four flush. This is the
shortest of the short term and I can't imagine anyone playing this
but, who knows?, maybe a homeless person collects enough cans, trades
them for $500 and decides to play a $100 VP machine just for one game
one time in his life. It can work. Isn't there a homeless person that
won Megabucks just this way? What would this homeless person do in
this situation? I think, again, it depends on the individual homeless
person.
We know what the long term is. Strictly speaking it is infinite. In
practical terms, playing a few million hands one can be reasonably
confident to get a return near 99.54% in JB, but there are no
assurances.
What then can be considered the short term in the hunt for a Royal?
To me a few days trip to Las Vegas is the short term. Roughly, one is
dealt three cards to a Royal every 100 hands. Let us assume on a few
days trip one plays 20,000 hands. This means one expects to be dealt
three to a Royal roughly some 200 times. When one holds three to a
Royal, one has roughly a one in a thousand chance to complete the
sought after hand. The above numbers are not too bad. For 200
opportunities to have a one in a thousand chance to get a Royal, I'm
willing to give up 0.07% in return. 20,000 hands is not the shortest
of the short term, but it is short, and I'm willing to sacrifice some
long term return for that Royal and hence play the three to a Royal
all the time.
The problem of not getting Royals can affect even a player playing
millions of hands, as I have read happens in practice. Playing x
millions of hands is no guarantee for hitting x two-dozen Royals.
I wish there was a secret to make sure one gets a Royal in a
reasonable situation, but I don't know any.
E