Steve, several days ago I indicated that I'd have some brief follow-up
questions in this thread; sorry for the delay, but I'm in the midst of
some extra reserve duty. I've been trying to keep up with this thread
as much as possible, and have noted some very interesting things. I'm
pretty weak on Kelly betting, although I think I managed to grasp much
of that discussion, so I've saved all of those posts and I intend to
review the info I've collected on Kelly, revisiting web-sites, etc. Any
way, my additional comments and questions appear below:
Steve Jacobs wrote:
Perhaps my quibble is with the word "appropriate".
I want to move onto technical questions, so let's just say that I took
liberty in my choice of wording that I shouldn't have, and based it on
what I thought were somewhat reasonable assumptions that I still think
would apply to the vast majority of vp players, and therefore merely
meant that I though max-ER would, for various practical reasons, appeal
to most vp players more than would the various alternative strategies
that we have also discussed. That was presumptuous and perhaps very wrong.
snip
... However, it
is possible to take a standard issue WinPoker or FrugalVP
and trick it into computing/using strategies that are min-cost or
min-risk.
If the program can be configured with user specified payoff values,
then the concept I call "virtual payoffs"
snipped some additional description/explanation of virtual payoffs
Yes, Steve, I'm familiar with how WinPoker and Frugal can be
manipulated, such as can be done with the roughly +6/+4/+2 adjustments
for Multi Strike. My comment, essentially, that there are no programs
available to practice alternative strategies was meant more along the
lines of not being able to _fully_utilize_ the programs after you have
loaded a virtual table that, and by this I mean, for example, playing
and saving games which track your actual credits, with payments being
made according to the paytable that you would see in a casino, rather
than according to the 'virtual' paytable that must be kept loaded in
order for the game to recognize strategy errors. In other words, I want
my game to look like a JoB-9/6 paytable, with a 4000-coin Royal, 45-coin
Full-House and 30-coin Flush, and to be paid accordingly, but I would
like the game to tell me when I've made an error while using the min-RoR
strategy, or the min-cost strategy, etc, and to then record my errors
for review later, etc. I might want to look at some graphs in Frugal,
too. Since we can have only one table ... or the other ... loaded at a
time, it is impossible for these programs to do everything for a
strategy _other_ than max-ER that they are designed to do when the
strategy is _for_ max-ER and is therefore using the same paytable as
that which is displayed (i.e., there is no virtual paytable).
Virtual payoffs
are determined by scaling the actual payoffs according to a
scaling policy that is consistent with your objective. Max-EV
uses no scaling at all, just the actual payoffs. Min-cost uses
a linear scaling policy, but excludes one unit of each payoff
from the scaling process.
Do you mean that you are adjusting each hand to account for the fact
that one betting unit for each hand is merely a return of your bet?
I.e., Jacks+ is really a push, so you make it '0', and with two-pair,
we're really only 'winning' one betting unit, so you change it from '2'
to '1'? I assume that the reason why you are not having to include a
line for a negative one (-1) for losing hands is because it would just
reproduce the identical max-ER strategy; this is why we don't need to
include any per-line adjustments for coin-in cash-back, although
whatever difference that factor might make would probably be so slight
as to still never make any discernable difference in choices anyway.
Min-risk uses a non-linear scaling
policy, scaling a payoff of N units to a value of (1-R^N)/(1-R),
for a risk parameter of R.
Are you saying that you use the above formula to compute a necessarily
different factor for each different hand in a paytable? ... and could
you give an example -- at least of a value for R and what that
represents? I'm having a little difficulty here because I thought I
understood the min-risk (and I assume that is just a shortened name for
min-RoR, right?) ... to be completely independent of either
bankroll/stake and goals, as well as duration of play (number of games),
but rather that it just generated the absolutely optimal strategy for
playing as long as possible, and that there is not really a particular
risk level that has anything to do with the strategy (other than just an
incidental result). In trying to grasp this, I keep leaning toward
imagining that the risk parameter is some sort of acceptable risk level,
such as 10% risk of ruin, for which the R value would be .1 -- but I
can't seem to substitute any values into your formula to produce
anything that resembles the values in your table, below.
Thanks again for your help with all of this.
Bill Velek
The virtual payoffs are then plugged
into the VP program, and the cost or risk parameter is adjusted
until the program gives a breakeven game. This generally
takes a few iterations.
Here are the virtual payoffs that give min-cost and min-risk
strategies for 9/6 JoB:
Max-EV min-cost min-risk min_cost_royal
---------------------------------------------------------------
800 806.7376 947.8674 975.9932
50 50.4132 50.5096 50.0000
25 25.2024 25.1244 25.0000
9 9.0675 9.0149 9.0000
6 6.0422 6.0062 6.0000
4 4.5202 4.0025 4.0000
3 3.0169 3.0012 3.0000
2 2.0084 2.0004 2.0000
1 1.0000 1.0000 1.0000
---------------------------------------------------------------
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