Steve, what paytable did you use? The original poster wrote "The
paytable, for the curious, is (for a five coin bet) 2500, 225, 125,
40, 30, 20, 10, 5." But that's missing a payoff, which I'm guessing
is 15 for trips. Also, did you use the 2500 for RF?
--Dunbar
> Steve, I agree that the answer will depend on the strategy. That
> does not make the question intractable for all strategies. The
> poster did not specify that he wanted to maximize the chance of
> reaching his goal. Many people are content to play a maximum ev
> strategy with both a stop-loss and a goal. I assumed that this
is
> the problem the poster was addressing. For this type of
problem, a
> quite precise answer CAN be achieved.
Agreed. In fact, I think you can get a pretty good approximation
by
computing the risk of the given strategy. For this game, I compute
R = 1.00343744 and the probability of turning 10 units into 30
units
is given approximately by:
p = (R^10 - 1) / (R^30 - 1) = 0.32196
So there is about a 32.2% of turning 10 units into 30 units when
using max-EV strategy. Using min-risk strategy gives R=1.00312174
to give a 32.3% chance of success (not much better).
Reducing the target to 25 units gives:
p = (R^10 - 1) / (R^25 - 1) = 0.3897 (about 39.0% chance).
These estimates are overly optimistic, but I don't know how far off
they are. What does your risk analyzer give?
> Therefore I think your "bottom line" should be changed to "nobody
> knows the exact answer to your question IF THE STRATEGY IS
OPTIMIZED
> TO REACH A SPECIFIED GOAL". For someone happy with the maximum-
ev
> strategy, a precise answer can indeed by found.
>
> --Dunbar
>
> > > Nope, this is not another Rob Singer thread.
> > > It is related to the wacky world of online gambling.
> > >
> > > Anybody know how to solve this puzzle?
> > >
> > > Suppose you are playing dollar 8/6 JOB with $50
> > > You plan to play until you either hit $150 units or
> > > go bust.
> > >
> > > The paytable, for the curious, is (for a five coin bet)
> > > 2500, 225, 125, 40, 30, 20, 10, 5. But obviously the
> > > nunbers for the RF and SF will have little impact upon
> > >
> > > My 2 questions are simple.
> > >
> > > 1. What is the probability that I will quit by reaching
> > > 30 units, instead of busting out?
> >
> > The answer depends on the playing strategy. Do you
> > also want to find the playing strategy which maximizes
> > your probability of success?
> >
> > > 2. Given the same situation, but with a target of only
> > > $125, what is the probability that I would quit by reaching
> > > my target, instead of busting out?
> > >
> > > Also, I'd like to know the general method for calculating
> > > this sort of thing and
> >
> > Finding the optimal strategy for this type of problem is
> > extremely difficult, much harder than finding a max-EV
> > strategy or a min-risk strategy. Why? Because the playing
> > strategy changes as you get closer to the target.
> >
> > For example, suppose your target is 30 units and you've
> > been playing for a while and you're almost there -- you
> > now have 29 units. Hitting any payoff that gives a net gain
> > will reach the target, so you should treat all hands that
> > are better than a high pair as equivalent in value. Then, the
> > optimal playing strategy will maximize the probability of
hitting
> > a winning payoff before losing the 29th unit. An "equivalent
> > game" ends up using a payoff of 1 unit for a high pair and
> > a payoff of 3.2416425 units for all higher payoffs. If you
> > uses these payoffs in your favorite VP analysis program,
> > it will give the optimal playing strategy whenever you are
> > one unit shy of reaching your target. The probability of
> > reaching the goal before losing the 29th unit is 1/3.2416425.
> >
> > The optimal strategies with fewer units are more difficult
> > to compute, and finding the "equivalent value" for each
> > payoff gets complicated. I've only solved a few cases, and
> > each one depends on the numbers for all of the cases that
> > are closer to the target. For a target of 30 units, the
optimal
> > solution will use 29 different playing strategies, one for each
> > distance from the target.
> >
> > As you move further from the target, the
> > playing strategy continues to change until you reach a
> > point "far enough" from the goal so that the strategy
> > becomes uniform. This only happens if your distance from
> > the goal is (much?) more than the number of units paid for a
royal.
> > Out at this distance from the goal, the playing strategy is
> > min-risk, and the probability of reaching the target is
>
> approximately
>
> > equal to the probability of playing forever when starting with
your
> > current bankroll. For negative games such as this one, the
chance
> > for success is very tiny unless you start with a very large
>
> bankroll.
>
> > Bottom line: nobody knows the exact answer to your question.
It
> > is an extremely difficult problem to solve, and I'm quit
confident
> > that nobody has ever produced a precise answer. To solve it
>
> exactly
>
> > would require a very sophisticated program. If anyone tells
you
···
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@...> wrote:
On Saturday 18 March 2006 10:10, dunbar_dra wrote:
> --- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@> wrote:
> > On Friday 17 March 2006 18:30, what7do7you7want wrote:
>
> they
>
> > have an exact answer, I'd be very skeptical.
>
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