...and for your kind words. You, DD and John May each contributed significantly to the thinking on this thread, and I appreciate the ideas and concepts that were shared.
One advantage of simulations is that you don't need to intuitively understand a problem to find the answer. In fact, the process sometimes works in reverse, with the sim refocusing one's intuitive understanding. That's what happened for me in this case.
I've begun thinking about how to do a more rigorous analysis/simulation of the Loss-Rebate problem. The easy part is to say:
(1) If the Rebate > -2 x EV, then the game can be profitable.
(more precisely: R> 1-((1+EV)/(1-EV)), but this is very close to R>-2(EV) for typical EV values)
(2) If your bankroll does not support betting above the table limit, then the optimum strategy is to make a single win-or-lose bet during each rebate period.
(3) The single bet strategy has an EVS (EV of Strategy) of
EVS = ((1+EV)/2) - ((1-R)(1-EV)/2)
Where:
EV = Expected Value of the base game (-0.6% in our example)
R = Rebate (10% in our example)
The hard part is to determine the optimum strategy when your bankroll allows you to exceed the table limit during each betting period. It appears the optimum strategy is approximately "+3/-3" for the example we have been using, and this strategy has an EVS of about 3.7%. It would be interesting to determine the optimum strategy and EVS for games with other EV and rebate values. I would prefer to do this with a more realistic distribution of bet outcomes (-2, -1, -0.5, 0, +1, +1.5 +2), as opposed to the simplifying assumption (-1 or +1) we have been using. This probably would require a special purpose sim, and I have started thinking how to build it. Any ideas or suggestions would be welcome and appreciated.
