I think I know why you think there is equivalency here. There are 16 red singles, not 18. So, placing 1/16th of the unit on the 16 red singles wins 1.25 units (35*(1/16)-15/16 = 1.25), not 1 unit. Thus, there is no sense in betting on red color. Agreed?
What is your strategy?
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I think I know why you think there is equivalency here. There are 16 red singles, not 18. So, placing 1/16th of the unit on the 16 red singles wins 1.25 units (35*(1/16)-15/16 = 1.25), not 1 unit. Thus, there is no sense in betting on red color. Agreed?
Disagree. R-14 and R-16 are potential red bets too. Not singles, but they have to be covered to synthesize Red.
107/37 is the expected return of betting on R-16 alone.
71/37 is the expected return of betting on R-14 alone.
-1/37 is the expected return of betting on any other single number alone.
I was wrong. A bug in my code led me to believe in the red numbers "superiority". I am re-running the sim, and will post the results shortly.
Okay, here are the top 20, with all bets accounted for correctly:
R16: bet on R16
R14: bet on R14
RC: bet on red color
RN: bet on all individual red numbers (other than R16 and R14), equally distributed
BC: bet on black color
BN: bet on all individual black numbers (including Green-0), equally distributed
Code:
R16 R14 RC RN BC BN F(R16,R14,RC,RN,BC,BN)
8.2 5.5 47.1 1.4 0.0 37.8 0.2115470448
8.3 5.6 45.3 3.0 0.0 37.8 0.2115470448
8.4 5.7 43.5 4.6 0.0 37.8 0.2115470448
8.5 5.8 41.7 6.2 0.0 37.8 0.2115470448
8.2 5.5 47.0 1.5 0.0 37.8 0.2115470258
8.3 5.6 45.2 3.1 0.0 37.8 0.2115470258
8.4 5.7 43.4 4.7 0.0 37.8 0.2115470258
8.5 5.8 41.6 6.3 0.0 37.8 0.2115470258
8.3 5.6 45.4 2.9 0.0 37.8 0.2115469688
8.4 5.7 43.6 4.5 0.0 37.8 0.2115469688
8.5 5.8 41.8 6.1 0.0 37.8 0.2115469688
8.2 5.5 47.2 1.3 0.0 37.8 0.2115469688
8.6 5.9 40.0 7.7 0.0 37.8 0.2115469688
8.1 5.4 48.7 0.0 0.0 37.8 0.2115469117
8.2 5.5 46.9 1.6 0.0 37.8 0.2115469117
8.3 5.6 45.1 3.2 0.0 37.8 0.2115469117
8.4 5.7 43.3 4.8 0.0 37.8 0.2115469117
8.5 5.8 41.5 6.4 0.0 37.8 0.2115469117
8.2 5.5 47.3 1.2 0.0 37.8 0.2115467978
8.3 5.6 45.5 2.8 0.0 37.8 0.2115467978R16: bet on R16
R14: bet on R14
RC: bet on red color
RN: bet on all individual red numbers (other than R16 and R14), equally distributed
BC: bet on black color
BN: bet on all individual black numbers (including Green-0), equally distributed
That looks like what I expected - our old solution, plus a bunch of what appear to be equivalent ones all with the same score.
And I think that concludes that - thanks for what's probably the most interesting thread I've seen on ET, well, ever.
And I think that concludes that - thanks for what's probably the most interesting thread I've seen on ET, well, ever.
Yeah, it's been fun. kut2k2, feel free to start a new thread to see if k*E is a good performance measure.
Thanks for all your contributions to the thread.
Thanks for your inputs, it wouldn't have been as much fun without them.
I still prefer the strategy that bets equally on all slots. It's pure elegance. Very appealing, and easier to analyze than most strategies.
Only had time to browse a few pages, but what struck me was that everyone seemed to assume the optimal strategy does not change with spin number.
If we assume the goal is to maximize the expected value of terminal wealth after 10 spins, the optimal bet changes with each spin. In particular, on the final spin, the optimal strategy is to bet everything on R-16. You have to work backwards to identify the optimal strategy at each spin. In other words, having a positive expectation on the 10th spin creates something like risk aversion on the 9th spin. Note that risk aversion doesn't exist on the terminal spin if the goal is to maximize expected terminal wealth.
I agree that the problem takes the character of optimal portfolio allocation, particularly on the early spins.
It is a very challenging, interesting problem.
If we assume the goal is to maximize the expected value of terminal wealth after 10 spins, the optimal bet changes with each spin. In particular, on the final spin, the optimal strategy is to bet everything on R-16. You have to work backwards to identify the optimal strategy at each spin. In other words, having a positive expectation on the 10th spin creates something like risk aversion on the 9th spin. Note that risk aversion doesn't exist on the terminal spin if the goal is to maximize expected terminal wealth.
I agree that the problem takes the character of optimal portfolio allocation, particularly on the early spins.
It is a very challenging, interesting problem.
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