What is your strategy?

Your strategy has an off-the-chart k*E of almost 0.446. :eek:

Congrats! You've beaten a holy grail (a strategy that never loses).

 

Yeah, I got that wrong, thanks. Should be:

EXP(0.3279876)^10 = 26.57

The difference with your 26.63 is probably due to rounding errors.

 

What's the k*E of your holy grail?

 

I got roughly 1.446^10 ~ 40, so we're close.

 

0.125 without borrowing, infinity with borrowing.

 

Okay, yeah, that makes sense.

 

Another weird observation: the Kelly de-rating process (where you divide all bets by a factor in the 1-10 range to smooth out the equity curve) is clearly wrong when there's an arb in the mix. Then you should reduce only the risky part and then buy MORE arb with the money freed up.

I wonder how you get the effect of de-rating (smoother equity curve) while still maximizing growth within that constraint in the general multi-variable case.

 

You know, as I was coding this, it occurred to me that we are still not doing it quite right. Specifically, we are not considering the bets on Black (the bets on black color, that is), and the bets on any red numbers other than R16 and R14.

 

I THINK we will see both of those at zero.

Betting on each black # is strictly cheaper than bettering 1 unit on black and gives the same effect. So that's a strictly better-than expectation wise thing.

I think a similar but more complicated argument can be constructed for the individual red #s.

But probably worth checking - this is a goldmine of weird effects.

 

A question about risk ...

Every spin you're betting your entire bankroll. But you can only lose 2.7% for any given spin. So what is the "risk", the 100% you're betting or the max 2.7% you stand to lose?