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.
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.