The risk-averse indices for this play (to surrender) are virtually identical to the e.v.-maximizing ones. I don't know why people don't understand that. By definition, to use the r-a index, you would have a minimum bet out on a shoe game. That being the case, risk-aversion almost never enters into the equation.
In any event, CVData tells us that the +2 and +1 e.v.-maximizing indices are each reduced one to r-a indices of +1 and 0.
Don
I assumed I wouldn't have to explain the increased value of reducing the variance from 2x to 1x is useful for some doubling indices as that is pretty much understood. That cuts the variance in half by reducing by 50% and the variance by x to about 50% of what it was. If that is truly understood I shouldn't have to explain why it is even stronger to reduce the money at risk by 50% and the variance by x to 0% is stronger. One reduces variance by 50% making the long run that much closer, the other reduces variance to 0 which makes the long run 1 hand. Plus it makes you look like an idiot rather than a counter. Only for ace reckoned counts are your Betting Count is your Playing Count. With an ace neutral counts your Playing Count doesn't indicate the bet you will make. You use the Betting Count for that. I guess since Hilo is an ace reckoned count we should look at it as if you see what the counter bets you already know what the index for playing the hand.
I'm glad you explained that three. It's perfectly clear now.
Play within your bankroll, pick your games with care and learn everything you can about the game. The winning will come. It has to. It's in the cards. -- Bryce Carlson
First you have to understand my comments in this thread about RA surrender were not specific to the hand being discussed but general comments on RA surrender aimed at someone worried that applying the index for surrender 1 TC early was costing him a lot. Don is correct that for an ace reckoned count that the bet size will be small but this individual at some point indicated a flat bet max bet strategy while backcounting which would mean he would have his max bet out when he employed the index early if he was using that strategy. Bet size compared to f is the deciding factor for risk aversion so RA plays would need a bet size that exceeded f, the critical fraction of the Kelly BR. I recommend reading pp 370-378 in Don's book, Blackjack Attack edition 3, for those that are interested. I get criticized for long posts and Don took 9 pages in explaining this topic. Obviously brevity and commenting as an aside to the thread causes a lot of misunderstandings. It really helps to look at the quote to get context on what people are responding to.
The formula for the critical fraction of Kelly f for risk aversion is:
f = 2*(E1 -E2)/(V1 - V2)
Where E is the EV for plays 1 and 2 and V is the variance for play 1 and play 2.
When I tried to bring RA surrender up nobody was interested so I looked into it myself for myself.
Lower f favors Play1 more while a higher f favors Play2 more.
If we accept the assumption we can approximate V1-V2 as cutting variance in half for doubling due to the doubled bet size, it is the same change in variance as going to 0 variance. The mathematical caveat is funny things can happen when you deal with a 0 in math. Of course when we start looking at specific matchups V is not a global constant. Plus you are never going to surrender a hand you might double. So the initial idea of equating the delta V's doesn't actually apply to any specific situation. It just illustrates that RA surrender could have the variance change to be considered as a possible RA play.
Risk aversion is about maximizing the certainty of BR growth. It is affected by your wonging style, what you cap your max bet at and the number of spots you play as well as some other things. Few plays qualify as RA and what the RA index actually is depends on many factors that preclude RA indices from being universal. If I got into all the ins and outs of RA play on this forum it would be an order of magnitude or 2 longer than my longest post. I would take any post on RA strategy by anyone including me with a grain of salt. Too many variables exist in the way different people play to talk about RA without the context of how they play. Like I said read Don's fine work on the subject in the pages listed above in his book BJA3.
For those that don't understand my comments on 0 variance is a wonderful thing, which I think is obvious. SCORE loses meaning when talking about 0 variance as variance is in the denominator. But N-zero is proportional to variance divided by EV squared. Obviously changing a play to 0 variance without affecting EV will decrease n0 (and make n0 for the play itself 0). So when not reducing EV 0 variance is a wonderful thing. To a point you can lose EV on the play while still decreasing n0 but EV is an exponential in the denominator so that point is limited. For most surrender plays it is probably limited to no change in the index. When I looked into RA surrender I did not use Hilo and the viability of an RA index is also count dependent.
If I have to explain things that Don took 9 pages to explain in his book and probably still lost a lot of people before making comments, my posts will need to be very, very long. When brevity is specified it assumes a certain degree of BJ intelligence so long explanations are not required. Perhaps this was not a good choice for brevity but I am trying. Before considering anything written on RA indices read and try to understand what I sighted as reference material in Don's book.
Having read the last paragraph of T3's post, putting RA indices into simple terms is best defined as usually max bet situations where count justifies splits and doubles. Some examples
10 v 10 double at +4
99 v 7 split at +3
Double or splitting above hands at exact TC indicated captures a sliver over half of long term EV. In other words, variance increases, EV maximizes and fair to say SCORE suffers. Each increase in TC increases Success rates - so, waiting for, let's say +7 and +5 respectively in hands noted above captures a far higher percentage of total EV. Having said that, I recently doubled 10 v 10 at +12, only to snag a stiff - not pretty.
Other examples would be splitting 10's v 4,5 or 6.
Using a risk averse index, though not for RA reasons would be 8v6. I usually wait till plus 3 as gain us far to much to ignore. To many 8v6 hands to do at +1 and to many hands below index not to double. Easy for the pit to pick you off.
In a sense, quite true. The occasional 8 v 6 double will slip through nicely. However the frequency of this hand is high enough that the pit and eye will get a real good look at you. They will wonder why you double half the time and not the other half. In addition, my prior comments of high variance, maximizing EV and reducing SCORE come into play.Originally Posted by Tthree
The other interesting hands are 11 v 10 and 10 v 9. I always double, except when the count tells me not to. Here, when right at index, I am maximizing EV.
So, if someone wants to thread on the topic of heat averse doubles, might turn into something interesting.
As a humor addon, I recall a couple if hands of 7 v 6, with super max bets where double was warranted. I had the gastric fortitude of doubling one if them. To bad I didn't have the gastric fortitude of doubling both.
I've seen 7 v 6 hand doubled in negative counts, of course with the expected negative results. Oh shit, I'm sure we've all seen crazy stuff.
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