assuming the strategy generated with quad=44:
er=.995936
correct for quad=25:
.995936-.002296(44-25)=.952312
add bonus:
.952312+.002296x(1-(1-.002296)^10)x(800-25)=.992747
additional variance:
.002296x(1-(1-.002296)^10)x(800-25-.992747)^2=31
It does bump it up but only very slightly. If you run the base game
with 4K worth 25, you get 99.58% and a 4K cycle of 438 hands. Using
what I think is the appropriate 4K value, 44, the cycle is 435
hands
and the ER 99.59%.
Looking at the resultant strategy sheets, I think, shows why. In
this
range (25 to 44) of 4K values, the only change you make is hold a
few
more high pairs against some penalized 3RFs. Only a few plays
change,
so your cycle shortens by only 3 hands. Low pairs and 3K have a big
enough cushion between them and the next best hand that almost
doubling the 4K value doesn't move them in hand order, and single
cards are too long a shot to have much added value.
On the appropriate value for 4Ks in determining strategy: Here's a
very simple approach that has no flaws I can see. Hitting a 4K has
only one result, allowing you to play 10 hands at 290% ER. So 10
bets
times 290% minus 10 bets coin-in produces a net benefit of 19
coins.
you don't get to play 10 hands at 290%, what you get is 10 hands or
one bonus quad, whichever comes first
Add 1% cashback and the benefit is 19.1 coins.
On variance, I calculated it at 62.6 under my original mistaken
estimate of 99.83% ER. I think it will be close to that under the
right numbers, but I haven't yet redone the math. BTW, the way I do
it is to lay out one RF cycle of hand-by-hand values in Excel.
Where
you have fractional expected hands, I put in one result at the
fractions (i.e., 2857.7 3Ks get 2857 entries of 3 and one entry of
2.1). I then average all the values to make sure I'm on the nose of
the ER, and if not I adjust the fractional hands accordingly. Then
I
use the excel function to figure the SD, and square it. I've tested
this method against several known variances and it is very close.
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
>
> nightoftheiguana2000 writes:
> > if i remember correctly, you had a run in with variance? in an
attempt
> > at an underbankrolled potshot at dollar doublebonus?
>
> Not exactly ... in fact, I could consistently rely upon a trip
loss
> from one trip to the next ;(
>
> In all truthfulness, what I suffered was an immediate royal
drought
in
> that play of 4 to 5 cycles, plus a moderate shortfall on quad
Aces.
> Granted, these are the greater elements of DB variance but it's
even
> more unlikely that you'll overcome a royal drought in a low
variance
> game like Jacks.
in jacks you only have to worry about a royal drought, in db you have
to also worry about an aces drought, in deuces you have to also worry
about a deuces drought (one of the reasons the 3-5 royal bankroll
approximation begins to fail)
jacks-royal=97.5% (2.5% loss)
db-royal-aces=95% (5% loss)
fpdw-royal-deuces=95% (5% loss)
>
> As far as bankroll, with available cb/bonus, technically I wasn't
> pushing the bankroll excessively in terms of actual ROR. But as
Jean
> notes, psychological bankroll is key. When you're bleeding out
your
> a** on a given game, shifting risk to other games (even if at
lesser
> ER) becomes attractive 
>
> - Harry
yes, bankroll is psychological
if it's all possible funds you can get your hands on, you have a
potential gambling addiction
bankroll is the sustained (net) loss at which point you would quit for
good or at least for a few years
you can either determine it beforehand or you can wing it and discover
it on the fly, but either way there is some sustained net loss that
will cause you to quit, and that is your bankroll, and there is always
some risk (risk of ruin) that you will in fact see that net sustained
loss
···
--- In vpFREE@yahoogroups.com, "blaw57" <blaw57@y...> wrote: