thanks for the well-written reply, toonces and Harry Porter, for
politely telling me the correct logic in plain english.
If I can make another observation without going thru the numbers,
this will be a good exchange.
I think your math is off, toonces. You certainly don't lose a dollar
99.91% of the time.
By Keeping the 3-part Royal, there are scenarios other than the Royal
that hit that are impossible when the high pair is kept: XX% of the
time the straight(4to1) or the flush(6to1) comes in. XX% of the time
trips (3to1) comes in (of a different rank).
of course XX% of the time you bust and lose the high pair (-1to1).
And there's a loss of trip or quads improvement to the tossed pair
card (-25to1 + 3to1) and (-3to1 + 1to1)(your drawn hand still pays
trips or high pair). And lost two pairs (-2to1) if the 2nd pair is a
low pair.
Etcetera. I think we are all talking the same story.
A proper EV calc for each holding takes all this into account.
It amounts to 5 cents or less per occurrence at the dollar level I
think. An occurrence is dealt high pair with 3 card Royal in 9/6 JoB.
Tom Ski's EV tables are linked from this website. Maybe I should try
my hand at the numbers.
I'm guessing you see this scenario 5 times max per 500 hands. Let's
say that's a quarter loss per hour for you or me at 500 hands per
hour. Whatever level of play we're talking just one Royal hit makes
up for 4000+ hours of lost payoff from tossing the high pair. Even
more-so when playing Progressive Royal jackpot machines.
I'm pretty sure both of us have errors in our numbers, but even if we
get this hand 5 times an hour I can't believe the small difference in
EV could drain anyone.
hold high pair: draw no Royals ever
hold 3-card Royal: draw just ONE royal and you won't even bother
calculating EVs. you'll be busy enjoying the money.
You know, we all understand the math, but to me, when two hands are
close, I like to pick the one that doesn't shut-out the lucky jackpot
draw. Close to half the folks who play it this way will come out
ahead in the long run whether or not they hit the Royal and WAY ahead
in the short run if they do.
And for all the folks who don't hold the 3 card Royal, I hope that
you live long enough to play the extra hands that holding the high
pair buys you. We are replying to two folks who admitted bankroll
hurt due to (they say) lack of jackpots. I think they should try this
low-risk change to "perfect" strategy.
~Mark
--- In vpFREE@yahoogroups.com, "tooncesthecatwhocoulddriveacar
<tooncessnl@h...>" <tooncessnl@h...> wrote:
--- "Mark P. wrote:
> You guys should try holding the 3-card Royal instead of High
pairs
> for a few months
> ~Mark Time
Not here. Take, for example, Jacks or Better, and a hand like
KhQhJhJd3c.
The problem is that combining two concepts clouds your reasoning.
You say that going for the royal costs you a few cents, but gives
you
a chance at the royal, therefore, it's worth it. However, it only
costs you a few cents assuming you get exactly .0009 royals each
time
(i.e. your expected value). In reality, 99.91% of the time that
you
drop the pair to try for the royal, you won't get the royal and it
will cost you $1 (even more, when you hold hands like AJTs) in EV.
If this happens twice per hour, someone who plays 20 hours a week
will lose $40/week or $2080/year. Now, on average, this person
will
hit 1.92 extra royal flushes a year, for $1920, but that doesn't
make
up for the $2080 it cost you to try for it. In addition, every
year,
there is a 1 in 7 chance (14%) that you will miss the royal every
time you try for it, and your strategy will cost you $2080, as well
as an additional 2 in 7 chance (28%) that you get only 1 royal and
lose $1080. In the other hand, every year, there is only a 30%
chance that your strategy produced at least 3 royals, making your
strategy change profitable.
If you play less than this, the same concept applies, but the
numbers
···
will vary.