You make an excellent point. I'd never done the math, though it's pretty
simple, and my impression was that the multiplied dealt Royal contribution would
be higher. Until I reviewed the math, of course!
In general, you can figure out the contribution of ANY hand (hand
frequencies don't change, as strategy doesn't change) with any multiplier, by
multiplying the "regular" hand contribution by 4.05 / 15 * 5/6 = .225.
For example, at 9/6 JOB, the Royal contributes 1.98% of the total return. So
multiplying that by .225 gives you .446%, which is the contribution of all
multiplied Royals (including the dealt ones). Since the multiplied Royal will
occur, on average, once in 15 * 40,391 = 606,000 hands, it is quite possible
to play the game pretty heavily and never see ANY multiplied Royal. If that
happens, your total return will be significantly lower than the theoretical
return. I would think that (at least playing JOB) you would see all other
combinations sooner or later, with the possible exception of the multiplied dealt
SF, which contributes only .00156% of the TR. However, if you play the STP
version of a high variance game, there might very well be other multiplied
dealt hands you will never see in a lifetime of play, like dealt
Aces-with-kicker, or a dealt quint in a Joker version. Fortunately, as you point out, the
contribution of these rare dealt and multiplied hands is pretty miniscule.
I happen to find STP a lot of fun to play. For many players, the much higher
variance will (and should) be the biggest deterrent. On the plus side are
the higher EV, the slightly greater coin-in/hour, and the very small chance of
some pretty huge payoffs, up to 6667 times your bet!
Brian
···
===============================================
In a message dated 7/21/2008 7:35:30 A.M. Pacific Daylight Time,
wincerwj@yahoo.com writes:
While that is true, you should still remember that even a hit that
large is an incredibly small percentage of the total payout. Using
the approximate numbers available on the wizard of odds site:
multiplier cycle - 15
10 X came 17 times in 440 multipliers
dealt royal cycle 649740
we get a dealt 10X royal cycle at roughly 252,252,000 hands. Each
dealt 10X royal has a payout of 6666 2/3 credits per credit wagered,
so the dealt 10X royal accounts for .00264% of the total payout.
Of course, that is just the value of the 10X dealt royal and doesn't
include all the other dealt royals with multipliers that you expect
to have received. If we include those using the figures of a 15 hand
cycle for a multiplier and a 4.05 average multiplier, we get a dealt,
multiplied royal every 9,746,100 hands with an average payout of 2700
credits per credit wagered. This translates to dealt, multiplied
royals accounting for .0277% of the total payout.
Now, I'm not arguing with your opinion that the slight increase in ER
that STP provides is not worth the greater risk. I think that is an
assessment that would and should differ from person to person. I am
just pointing out that the statement:
As you know, the game's optimal return INCLUDES 10X with a dealt
royal
(it's baked in); in fact, if you NEVER hit 10X with a dealt royal,
you
will NOT get the optimal return; in fact, your return is a less.
is refering to a much smaller part of the total return than the
average reader would intuit. In fact the error rate of the average
reader likely costs them significantly more of the total return than
they would lose by never hitting a dealt royal with any multiplier.
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