Quote:
Originally Posted by Aaron W.
In the first case, your goal is ambivalence (finding the intersection of two payout curves). In the second case, it's about minimizing losses (finding the lowest point of a single curve). I don't see any reason why one might intuitively think these would give the same result.
How can you be so certain in the first case (against normal opponent) it's ambivalence that is optimal? What if the graph looked like the following:
The red line represents how much I would have to pay out on average if he bets on red and the blue line represents how much if he bets on blue.
The point of the two lines crossing isn't optimal. There's a point lower down on the graph where the payout is even lower.
It's for this reason that I thought of the first case as trying him picking the line that had the highest profit, so i had find lowest point the curve below.
So from my understanding, both cases are about minimizing losses by finding the lowest point of a curve.
Then again, given the constraints of the problem it may not be possible to have a graph with so many curves in it to make the graph this shape. But in any case I also wanted to know what's the best way to calculate that the best odds to lay against the time traveller are (1.5 , 3.0) to 1? I did end up using the quadratic formula to calculate this but I'm wondering if there's a more efficient way.
Last edited by Karganeth; 01-30-2017 at 11:22 AM.