At least three different methods of calculating RORBR have been
proposed. How can we determine which (if any) of these methods yields
an exact answer? Allow me to propose a testing procedure.
To make the following discussion easier, I define a new term, ERBR,
as the Expected Return Before Royal. This is computed as the game's
perfect play ER, less the contribution of the royal, plus any slot
club cash rebate.
If the actual frequency of every payoff other than the royal was as
calculated by the game analysis (i.e., a straight occurred every 89th
hand right on schedule), then a situation with ERBR > 100% would have
zero RoR, and we would not need any risk calculations. But that's not
real life. In Jacks or Better with accurate play the probability of a
straight is about 1/89, but the actual occurrence of straights is
random, and that's why we need computations such as these.
Now back to the Risk Of Ruin Before Royal (RORBR). Consider a game
with ERBR = 99.999% (for example, 9/6 JoB played perfectly with
0.455% slot club cash rebate). A viable formula for RORBR should work
and produce a useful result.
Now suppose the slot club rebate is increased by 0.002%. The ERBR is
now 100.001%. Will the formula converge? If so will the result be
very close to the result with ERBR just under 100%? Does it work if
the ERBR is exactly 100%?
If the formula won't converge with ERBR > 100%, then perhaps we could
use the regular Sorokin formula as if the situation sans RF was the
complete game. Would this yield very nearly the same result on a
100.001% situation as RORBR formula on the same game with 0.002% less
slot club rebate?
If we get almost exactly the same RORBR on such a game in all three
cases, and the result decreases almost lineally as the ERBR
increases, that's good evidence that the method is viable, but if the
results differ widely then it's proof that the method is inexact.
A Monte Carlo simulation does NOT assume that the frequency of every
payoff other than the royal will be as calculated by the game
analysis -- only that their probabilities meet that criterion. This
could explain any difference between the formula's results and a
simulation.
Dan
ยทยทยท
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Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com
"Chance favors the prepared mind." -- Louis Pasteur
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