Did I miss something?
I read thru Blackjack Attack, and Don S presents RA indices for a bunch of plays, but I didn't see anything for surrender. I googled this and didn't find anything either.
Surrender can go a long way to reducing vol. Where are the RA surrender indices?
There's no such thing as a risk-averse surrender index!
The concept behind R-A indices is that you give up a little e.v. in exchange for reducing s.d. by waiting longer, in most cases, to double or to split. No such concept can exist for surrender, because a) the e.v. is always -50% no matter when you make the play, and b) the s.d. is always the same, because there can be no other outcome except -50%, so there is no variation on the theme.
Clear?
Don
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?
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?
Hey Don, while you're on here, do you want to chime in on risk-averse insurance indices?
Thanks. It's awesome to get a reply from you.
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
"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."
Great. Does anyone have links to these?
Let me know what you figure out, Don. Thanks for taking my question seriously.
I asked a few people about this, and Norm has come back with some preliminary work indicating that both 16 v. 8 and 14 v. 9 might have R-A surrender indices that are one less than the EV-maximizing ones. There may be other plays, as well. Answers depend, of course, on bet schemes, rules, etc.
You can calculate these yourself by using the methodology outlined in BJA3, pp. 371-374, but you will need to know the expectations at the various true counts. Simulators such as CV index generator will provide that information. You also need to know the difference in variances for the plays being compared, which is approximately, but not exactly, 0.75 for most of the cases, in that we are usually considering surrendering (average squared result = 0.25 squared units) vs. hitting, where the average squared result is a little less than 1.0, because of pushes.
In any event, I thank you for an interesting question, because, truth be told, I have never considered the idea of R-A surrender indices, and I have never seen anything written about them anywhere in the literature. It's rather refreshing to get a "new" question to which we might provide answers that don't exist anywhere else that I know of.
Don
But, I have started to accumulate some more material, so you never know. :-)
Don
