My Monte-Carlo simulation agrees. Here are the top 10 strategies, if betting on Red is not allowed: Code: R16 R14 Score 8.4 5.7 8.009759 8.5 5.7 8.009752 8.4 5.8 8.009728 8.5 5.8 8.009715 8.3 5.7 8.009667 8.4 5.6 8.009662 8.5 5.6 8.009660 8.6 5.7 8.009647 8.3 5.8 8.009641 8.6 5.8 8.009606
My 2 wheel analogy isn't correct. With 2 wheels, you could win on both wheels, with one wheel you can only win one bet and lose the other. NeverthelessI just did a monte carlo sim, definitely better by miles to do both bets.
The reason is quite simple. The edge for betting on r16 is 289%. For betting on both r16 and r14 (8.26% and 5.48%, respectively) the edge is 250% i.e. lower. From this you might conclude that r16 on itself has a higher edge and so just bet on that. But you have to take into account you are wagering much more on the combined total and so the actual expected value overall will be greater even though the percentage edge is lower. To illustrate, say u had two trading strategies, one that has a 5% edge but which can be applied to a $1 million worth of trades and another which has a 10% edge but can only be applied to $100,000 worth of trades. If you could only pick one, the 5% edge strategy would be better because the total ev is $50k as opposed to only $10k from the higher edge strategy.
Nope, not even close. For {R-14, R-16}, k*E == (36z + 71)(36z + 71)/(37(47952zz - 47952z +1295)). where z is the fraction of a unit bet that is placed on R-16, 1-z is the fraction of a unit bet that is placed on R-14. k*E is only positive when z > 35/36 or z < 1/36. k*E clearly reaches its maximum at z == 1, i.e., when a pure R-16 bet is made.
We'll have to disagree then. My sim shows massive out performance when combined and i have provided the rationale why that is so. Will leave it there, spending far too much time on this.
Can you try to maximize the Ln(k*E), instead of (k*E)? I think you'll have the same results as Visaria and myself with Ln(k*E). K*E maximizes the bankroll, while Ln(k*E) maximizes the rate of growth.
I think there is an error some place in your derivation of k*E. Based on your formula, my results indicate that there are only 2 combos which are profitable, at z=0, and at z=1. So, it says that all combination bets are losers. This is clearly not right.
I think you are correct. I have faith in the numerator but there is something wrong with the denominator. I didn't expect Visaria to give up so easily. I'll work on this problem later when I have more time.