stephenipc wrote:
To compute the variance of an N-play version of a game from the
list, just add the base game variance to (N-1) times the covariance.
ok, so using this formula for JoB... I would need 49x10.079% =
493.871%
So the general pratical advice of having 3x to 5x RF as Bankroll
would come out:
RF=$200 (4000 nickles)
5x $200 = $1,000 (Jean Scotts practical advice)
$1,000 x 4.93871 = $4,938.71
Can someone look this over and make sure my reading comprehension,
use of percentages, and multiplication looks good?
Stephen,
I'll toss out a few observations here. There are a couple of things
to clear up first.
There's a certain ambiguity when it comes to the term "bankroll".
It's used in two contexts -- the largest loss you might suffer in
lifetime play (defined under a stated risk tolerance) and,
alternatively, the amount you should take with you for a single
session or trip. I prefer to discuss the latter as a "stake" to avoid
confusion, but prevailing usage calls this a "trip bankroll".
At any rate, JBQ's reply addressed your bankroll question in the
"trip" sense -- how much more you should bring to see you through a
trip of 50-play. However, I don't think play variables were
sufficiently defined to arrive at firm answers.
···
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Touching on the Jazbo article you've found:
http://jazbo.com/videopoker/nplay.html
Jazbo discusses the method by which n-play vp variance can be
calculated. He goes on to suggest if a single line game requires a
lifetime bankroll of x, and an n-play version of the game has a
variance (expressed in bets) that is T% greater, that the bankroll
requirement of the n-play will also be T% greater.
However, in a section addressing "volatility", he goes on to note that
people report a perceived volatility that's greater than what the
preciding would suggest. He suggests this may be the overall higher
volume of play implicit in n-play.
I'd suggest that it's another factor though. The variance
calculations that he performs are valid over the long-term. But
they're poor as a descriptor for what will happen in the shorter run.
In particular, a RF is hit very infrequently but is a very strong
component of the variance value.
Frankly, if the goal is to stake yourself for a losing trip, hitting a
RF isn't exactly a predominent concern. I'd suggest that an
alternative variance comparison, in which rare hands such as a RF are
excluded, would have greater validity. I'd expect that the n-play
values would be considerably higher than single line, under this
calculation, and would prove a more reliable basis for trip stake
(bankroll) determination.
------------
But, all that is by way of saying that for most people the only good
way to get a feel for what they want to bring to the n-play table is a
sense they've developed through their own play over time.
If you want stronger guidance, than give some concrete examples as to
what you'd bring for Jacks play under other scenarios and ask for
suggestions as to what an appropriate amount would by for a given
n-play -- stating clearly how much play you want to be assured of on
your stake.
------------
You dropped a couple of comments along the way which would appear to
be references to lifetime-play bankrolls. You've quoted "Jean Scott's
practical advice" of a 5-RF bankroll requirement.
I see similar statements from time to time by others, made outside of
any specific context. More familiar is guidance to bankroll for the
value of 3-5 RF's.
The statements are made under very clear play circumstances, typcially
play of FPDW with about .25% additional cash. Generally speaking,
we're talking about playing at a 1% advantage on a low variance game.
In that case, a 5-RF bankroll translates to about a 1% ROR; 3-RF to
about 5% ROR.
When you're talking about 9/6 Jacks, unless you're looking at a
minimum of .46% kicker (to error-free play), there's no such thing as
a defined "bankroll". You're playing a negative-expectation game and,
over the horizon of "forever", there's no limit to expected losses.
For a "positive" game, the bankroll concept offsets the risk of
short-term volatility by the fact that you have a winning expectation
in the longer term. The stronger that edge and the lower the game
variance, the smaller the necessary bankroll.
Bottom line, there's no general bankroll "rule of thumb" that can be
applied to all play options. Understand the "5-bankroll" one you've
cited in the context in which it's valid.
- Harry