I didn't understand where the arbitrage comes from until I worked out this bet. Indeed, this is a risk-free bet, you win every single time! This is almost disappointing, as the best strategy turns out to be borrowing as much as you can, and betting 100% of your bankroll, on every bet. So much for our initial calculations, where we totally ignored black/green as "no need to bother". This does make me wonder if I can do the same with my portfolio of trading strategies.
What is your strategy?
- Thread starter kut2k2
- Start date
- Status
I didn't understand where the arbitrage comes from until I worked out this bet. Indeed, this is a risk-free bet, you win every single time! This is almost disappointing, as the best strategy turns out to be borrowing as much as you can, and betting 100% of your bankroll, on every bet. So much for our initial calculations, where we totally ignored black/green as "no need to bother". This does make me wonder if I can do the same with my portfolio of trading strategies.
Probably not - it's possible here because the various strategies are
a) complete (you can bet on every possible outcome)
b) net positive expectation
In the real world those two are unlikely to coexist in a portfolio of strategies that aren't specifically the legs of an arb.
There is still an interesting (and difficult to find) answer to the OP if you can't borrow. Maximizing growth might very well choose to blend the arb with the risky play.
I'll see if I can set it up for simulation. Should not be that difficult. Thanks for your participation in this thread, SplawnDarts. I've learned a few good things from you.
Yeah, the more I think about it I think you can bunch the "total amount bet on black/green" into one term since they're obviously symmetrical. It won't be as much of a PITA as I was thinking.
One interesting thought: initially I was very concerned about "what bankroll?" - clearly the first bet of a long string should be sized against what you've got with you, and the last bet against your "life roll". But what about bet N-1? It's somewhere in the middle probably, but that's vague and I can't see how to deal with it. But in this case the arbitrage makes that problem go away. Now I can go to town on all the bets, only concerned with being able to meet margin. The case of an artificial bet size limit and non-infinite N bets when there is no arb but still positive expectation still has me baffled though.
Glad I was helpful. I've learned quite a bit noodling around in this thread as well. Kelly in the context of complicated correlated bets with weird restrictions is a pretty tricky and counterintuitive subject.
Yeah, clearly it is. It got us all fooled for weeks, and we still don't know the answer. Well, it's coming.
Divide your bankroll into 32 equal parts. Place one part on each of the not-red numbers and the remaining 18 parts on Red. This is a guaranteed winner of one eighth of your bankroll on each and every spin. Over ten spins, you have more than tripled your $1000.
Now go play some poker.
Now go play some poker.
I wish. I probably won't play a hand until the July 4th week. I'm hoping to go out to Vegas and play 80/160 LHE or whatever big stud I can find the days leading up to the WSOP main event.
I was referring to the interview question. Good luck on your Vegas trip.
So I think we have The Absolute Best Answer now. And I'm beginning to see why quants are so obsessed with hedging.
The rules as stated in the beginning do not allow borrowing. They clearly say that the maximum bet can't exceed the bankroll. We don't have the solution for this yet.
Where did I say anything about borrowing?
- Status