···
------
If you're looking at a trip where you want to allow sufficient trip
stake, the stake is simply:
Expected Coin-in x Worst Case Loss Allowance.
(You wouldn't expect me to turn tail on terminology now and talk
"bankroll", would you? 
But I'll note it's the case that Jazbo does
refer to "ending bankrolls", i.e. trip win/loss, as well as "long term
bankrolls" on his website.)
So, if we're talking 10,000 hands of $.25 vp, and a worst case 10%
loss allowance, then it's $12500 x 10% = $1250.
------------------------
Ok. Let me explore Jazbo's charts on his website to strengthen this
loss allowance. This is going to get a little entailed, but not
overly complicated.
In this discussion I'll reflect that in preparing myself for a trip
I'm comfortable staking myself to see my play through 95% of the time.
I can deal with a short trip 1 out of 20 times.
If we had used that 8% worst case in the calculation above, then the
loss allowance would be $1000. I'm suggesting something less than
this would be appropriate. Let's see how Jazbo's numbers compare.
--> If you don't want to walk through a lengthy dissection of Jazbo's
charts and wish to push right to the answer, skip past the next two
sections (to the next series of x's).
xxxxxxxxxx
Jazbo has does a decent review of VP Probabilities which are a useful
reference. But let me state right off the bat that his charts deal
with the expected ending loss of a trip.
But there's little doubt that at some point in most trips your loss
position will exceed your ending loss. That means that after looking
at Jazbo's work, we'll need to pad any conclusions from his numbers.
Keep this in MIND.
The chart that is of greatest use is the very last one on his
Probabilities page: Cumulative Probabilities - 5000 hands.
That chart shows the distribution of expected Ending Bankroll (i.e.
trip win/loss), expressed as number of bets.
Examination shows that on 5000 hands, there's roughly a 99% certainty
that losses won't exceed 500 bets - in other words a 10% loss. The
exception to this is 10/7 DB, where similar confidence involves a 700
bet loss (14%).
When we pare back the confidence that the trip stake will see us
through 95% of trips of 5000 JB hands, the appropriate loss allowance
looks to be about 300 bets, or a 6% loss. ($375 on a quarter game)
(It's interesting to note that of all the games noted (including the
higher return games of PE, 10/7 DB, & FPDW), at 5000 hands JB permits
for the smallest loss allowance. That's simply because for JB, aside
from the RF, the highest paying hand is a quad, paying 25 bets. The
highest non-RF hands in the other games have much higher pays. This
makes the JB return excluding the RF much less variable.)
------
So, repeating myself for my own sake and others who may be Alheizmer's
impaired, for 5000 hands played it looks like 300 bets will see us
through 95% of our JB play. What does that say about a 10000 hand trip?
Getting a decent guesstimate on this becomes a little more tricky
using the charts on Jazbo's website because he doesn't display 10000
hands in this manner. You'll notice that the 5000 hand chart is
labelled "Cumulative Percentage" (you do have his website open in a
separate window now, right?). Any point on it represents the
probability that the trip loss didn't exceed the corresponding amount.
That chart was built up from data that he plots out on a related chart
labelled "Probability Distribution", which for 5000 hands is the chart
immediately above. This chart displays the probability of any given
single loss.
For example, for JB, we see that the most probable loss is about 125
bets (2.5% loss), with a .26% likelihood. Note that this is the
approximate expected JB loss when you simply subtract out the RF from
the total game ER.
To extrapolate from the 6% loss allowance for 5000 hands to one for
10000 hands, what we might do (and this is very "back of the envelope"
is compare a point on the 5000 hand Prob Dist'n chart to a comparable
point on the 10000 hand chart to see how the chart has shifted. (And
have I confused the hell out of you yet, or do you still have your
bearings?)
I'm not going to walk through the steps of my eyeball comparison
because this post is already becoming unwieldy. But ...
xxxxxxxxxxxx
For 10000 hands the corresponding trip loss on 95% of trips would fall
around 4%, or $500 playing $.25 9/6 JB. But this is the expected
ending loss. Most trips will produce a greater loss somewhere in the
middle than the ending loss.
If we pad this loss accordingly, something more like 5% or 6% would
very likely see a player through the entire planned play 95% of the
time. And this is very consistent with my experience.
I'd say that a player expecting a trip of 10000 9/6 JB hands would be
pretty well prepared on a stake of $700. That's not to say that an 8%
stake ($1000) wouldn't hurt to provide practically complete assurance.
------
Hopefully this work-up serves to give a concrete loss allowance for
play that you can have some confidence in.
Additionally it provides the basis from which, using Jazbo's charts,
you can work up an allowance for a JB trip of another number of
expected hands AND another game as well.
- Harry
