How to calculate RA indices from EV,SD at each TC?

duanedibley

Well-Known Member
#1
OK, let's say I have something like this for a particular play (eg. 11 v. 10):

HIT:
TC -3: EV = he-3, SD = hs-3
TC -2: EV = he-2, SD = hs-2
TC -1: EV = he-1, SD = hs-1
TC 0: EV = he0, SD = hs0
TC +1: EV = he+1, SD = hs+1
TC +2: EV = he+2, SD = hs+2
TC +3: EV = he+3, SD = hs+3

DOUBLE:
TC -3: EV = de-3, SD = ds-3
...
TC +3: EV = de+3, SD = ds+3

Where TC = True Count, EV = Expected Value, and SD = Standard Deviation.

Obviously the Expectation-Maximization index is the first i for which dei > hei. But what is the formula for the Risk Averse Index? Is EV and SD of hitting and doubling at each True Count enough information?

Bonus question: Should I make any adjustments to my Basic Strategy given EV and SD data for each play (ignoring the count)? For example say I found the EV of hitting 11 v. 10 for my particular game to be 0.10 and the EV of doubling the be 0.11, but the SD of hitting to be half that of doubling. Should I go with the lower EV play here in light of the SD's? Or is there some EV,SD criterion that would ever warrant adjusting basic strategy?

Thanks.
 

Sonny

Well-Known Member
#2
duanedibley said:
But what is the formula for the Risk Averse Index? Is EV and SD of hitting and doubling at each True Count enough information?
You also need to know your certainty equivalent. Different players might have different tolerances for risky plays than others. The formula is in Blackjack Attack along with some examples of how to use it. As long as the CE for the index play is within the threshold of your personal CE, you make the play. As soon as the play becomes too risky (not valuable enough) you don't make it.

duanedibley said:
Bonus question: Should I make any adjustments to my Basic Strategy given EV and SD data for each play (ignoring the count)?
I wouldn’t bother. If you’re just playing BS then you want to reduce the house edge as much as possible. You can control your risk by adjusting your bet size.

-Sonny-
 
#3
A common way of doing it is to make the advantage of playing the index the same as the advantage of the initial bet at a particular count.

E.g.- at a true count of +4, the advantage of doubling over standing is 0.5%. But the advantage of playing a hand at +4 is 1.0%. So if your initial bet at such a count requires a 1.0% advantage to justify it, it isn't worthwhile to put that same amount as an additional bet at a 0.5% advantage. Now let's say the advantage of the double is 1.2% at +5, then you'd wait until +5 to play it. That would be a risk-averse index.

Hope that was clear!
 
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