I agree it might be too ambitious to look at all nondominated strategy.
I went for “nondominated” as a condition because it was, in my eyes, the best formal translation of the initial intuitive claim I was trying to test. Besides, that’s what is used in the complete class theorem.
There might be interesting variations of the conjecture with stricter requirements on the strategy. But I also think it would be very hard to give a non-tautological result that uses this notion of “no matter the odds”.
The very notion that there are odds to discuss is what we are trying to prove.
I agree it might be too ambitious to look at all nondominated strategy. I went for “nondominated” as a condition because it was, in my eyes, the best formal translation of the initial intuitive claim I was trying to test. Besides, that’s what is used in the complete class theorem.
There might be interesting variations of the conjecture with stricter requirements on the strategy. But I also think it would be very hard to give a non-tautological result that uses this notion of “no matter the odds”. The very notion that there are odds to discuss is what we are trying to prove.