Danton wrote:
I appreciate the software references, but don't want to invest in
them for a one-time calculation. And the risk of ruin calculator
doesnt quite help me.
Perhaps someone can run the numbers for my particulat situation.
Assume $500 bankroll playing a $1 JoB full coin. After 250 hands,
what is my expected loss at the bottom 20% level -- i.e. 1 out of 5
times I should expect to lose $X or more?
The free Lottspiech "Gambler's Ruin" calculator to which Jon referred
you is fine for general use. The commercial products which I
discussed have greater flexibility in a number of aspects, including
the ability to analyze a far greater number of games/paytables.
As far as "investing" in a software tool, I'll note that VP for
Winners is (in most respects) the finest practice tutor available.
Should you decide to go beyond what you currently use, it's a
particularly fine option (I do have some reservations about its
suitability for use on an older computer ... say, one that's 3+ years
old -- minimum stated system speed req is 1 GHz). For an investment
of no more than what you'd pop into a machine to see you through a
half-hour of quarter Jacks play, you can't go wrong.
···
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Concerning the probability distribution that Jon has detailed from the
Lotspiech calculator, I suspect that he's run it with a different game
than 9/6 Jacks, or used parameters other than what you specified. I
received different results.
Because this involves such a limited hand run, I took a few minutes to
run the analysis using all 3 referenced products: Lotspiech, Dunbar's
VP-RA, and VPW. The results are as follows:
Ending
B/R < Lotspich . . . DVP-RA . . . VPW
-500 . . . 0% . . . . . 0% . . . . 0%
-400 . . . 0% . . . . . 0% . . . . 0%
-300 . . . 2% . . . . . 2% . . . . 2%
-200 . . . 10% . . . . . 10% . . . . 10%
-100 . . . 21% . . . . . 22% . . . . 22%
0 . . . 26% . . . . . 26% . . . . 26%
100 . . . 20% . . . . . 20% . . . . 20%
200 . . . 11% . . . . . 12% . . . . 11%
300 . . . 5% . . . . . 5% . . . . 5%
400 . . . 2% . . . . . 2% . . . . 2%
500 . . . 0% . . . . . 1% . . . . 1%
500 . . . 1% . . . . . 0% . . . . 0%
The minor differences in values program to program are largely related
to rounding.
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As a final comment, I note that you provided the basic rationale for
stepping up to $1 play. However, I wonder whether this move will best
serve your overall goals, particularly if you should be make the large
leap from $.25 play to $1.
As jt notes, you want to take careful stock of the potential benefit
form the play and weigh it against the bankroll risk. I'll add that
you might wish to consider whether there are other options that might
meet your needs.
For example, it may be the case that you're drawn to $1 play in this
case because it's the lowest level at which 9/6 Jacks is offered - all
lower denoms being, say, 8/5. However, on such limited coin-in I'll
suggest that running the play through on lower denom 8/5 Jacks might
be a more prudent move (again, depending upon specifics). If you play
out $1250 coin-in on $.25 8/5 Jacks, you give up about $25 in EV but
significantly cut your loss risk on that play.
This is merely offered as something to mull. There's nothing worse in
tackling a "pot shot" than coming away with a loss that, in hindsight,
the benefits of the play didn't warrant. (Although there's every
reason to expect that you'd approach this prudently without any
prompting 
- Harry