Need to think
Before I came back here to read, I was already considering that something may not be right with how I answered.
"If you're dealt a lousy hand and you consider you are deciding whether to hit or surrender. Here are your choices:
"1. Surrender. EV = -0.5 * x (x = bet size), SD = 0
"2. Hit. EV = some negative number * x, SD = some positive number * x
"Let's assume that your EV for hitting is better than -0.5x (say -0.45x).
"Whether or not you prefer (1) over (2) depends on the size of your bet and the size of your bankroll, right?"
Yes, but I don't think there are any examples where surrendering earlier than usual would make any sense. I may be wrong, but I don't think so.
"If you're betting a tiny amount of money, you hit b/c you just want the better EV. If you're betting a ton of money, you might prefer surrender b/c the sigma is zero. Right?"
Not sure. Have to give it some thought. But, there's a reason why no one ever discusses R-A surrender indices.
"Hey Don, while you're on here, do you want to chime in on risk-averse insurance indices?"
Cacarulo has a very scholarly post on the subject over at Don's Domain, and MathProf has written extensively on the subject, as well. Not much I can add.
"Thanks. It's awesome to get a reply from you."
But not if it's not the right one! :-) Let me get back to you.
Don