With
Keeping your betting equal, using RA indices reduces your EV but reduces variance a worthwhile amount. To figure out your EV gain you would hold variance (the nominal amount) fixed and play at a higher bet to have a higher EV for the risk you take. I'm sure you know this, but just as a quick explanation for anyone who isn't familiar.
To me, more EV is more EV. If I'm paying the same or less in the risk I take I don't see why you wouldn't take it save for the effort. Also, I'd imagine it's more of hassle to general mixed indices (some RA, some EV-max) than generating them all one way or another.
The more general question here is how much added variance would we take in exchange for an increase in EV? I suppose this depends in part on your utility function.
It's a volume business sensitive to margin per transaction. Every business has its mix of products with its varying mix of margins. Blackjack AP is no different. Maximizing your business health means not putting all of your eggs in 1 basket, which means judicious use of the various tools at your disposal.
Some of your product Arsenal will be risk averse, which means high profit per transaction. Other product lines, your bread and butter so to speak, represents the larger volume of transactions, but at lower profit. One line provides a hedge against the other.
I'd say it's not just the gain in EV, but what the EV is for either option (standing/hitting or doubling). One matchup the EV might be $75 or $77 depending on if you hit/stand or double, while another might be $15 or $17 if you hit/stand or double.
Not to mention, the frequency of the match up. You're gonna get a lot more 11's vs T's than you're going to have A9 vs 6 (when the index reaches the point of doubling). I don't know what the EV's are nor their differences, but always hitting 11 vs T (I'd imagine) would be more costly than always standing on A9 vs 6....even if they have the same EV differences.
And even if the difference in EV is the same, I'd also think what the lower-risk EV is. If it's $75 vs $77, I'd say taking the $75 option may be better. But if the EV's are $15 vs $17, then the better option may be to take the riskier decision.
"Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]
Short answer: no. As you mention, there are three critical inputs to determine a RA index, and you're looking to eliminate one of them and get the right answer anyway. No can do!
Reminds me of a joke that you can find somewhere in BJA3: "Here's a partial football score: Notre Dame 21, ..." :-)
You want a RA index, you need to know what you're betting in relation to your bank, the difference in e.v. for the for the two plays AND the difference in variance for the two plays. No shortcuts.
Don
When an index for a Basic Strategy Departure is
exceeded the gail in e.v. increases at different rates.
I believe that soft doubles gain the slowest after
reaching the proper fully-realized (floored) index.
There ought to be a table to reference for each index
~ and how fast it gains e.v. as the index is surpassed.
Anyone ?
This is the closest I have: https://card-counting.com/cvcxonlineviewer3.htm
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
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