For the mathematically inclined 
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Theory:NightStalker said:PS: I would not bet my whole bankroll on 1% edge, because of high variance.
Don't worry assume_R, ill be bringing my copy of ECAAFLASH1296 said:There is much to be said re: taking insurance (for variance-reduction purposes)
against a BJ (or even a hand of 20) by respected sources, e.g. J. Grosjean.
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I agree with FLASH about the RoR involved with doubles/splits, which is why I always prefer using RA indeces, which take into account the CE (which some of you know is my preferred method of comparison) of the play rather than the EV. Because CE is adjusted depending on my personal RoR, I can feel more comfortable making higher variance plays.FLASH1296 said:When looking at Risk Aversion vis a vis variance reduction — look at it this way:
Let’s say you have a hand where you have a small advantage. The opportunity
to split or double is present. You have an advantage so you need to press that advantage
by doubling your bet. So far so good. Now lets imagine that you
have a nice little advantage — lets say 2%. So you double.
Now lets look at that hand again. IF the hand matchup is to your advantage, then it is
always MORE advantageous (in terms of winning the hand) to refrain from doubling.
We can hit, retaining the right to draw further cards.
What if by doubling (a one card draw) ?
Your advantage drops from 2% to 1.25% ? So … If you double you gain 1.5% of two units,
which is more (by 0.5%) than 2.0% of one unit. SO … Why not double ?
Because you are risking twice as much for a modest increase in profit.
Now where/when/how does this make sense.
The answer resides within your Risk of Ruin.
If your risk is high (whatever that means to you), e.g.> 13%,
every time you have extra money at risk, your bankroll may
get seriously dented. You may soon have to resize your betting ramp.
If your risk of ruin is very low, e.g. < 1.0% than this issue of “money at risk” is hardly even an issue at all.
In my experience training Card Counters, (as “lone wolf“ players),
R I S K should be the paramount concern, when all too often it isn’t.
RA plays are ALL about CE. Instead of making the most +EV play, you make the most +CE play.assume_R said:Makes sense.
So how do you decide that threshold, of how much +EV you'd need to double that bet and bet more money on the table? I guess a more generalized question would be specifically how does one generate risk averse indices? And as a corollary could you say that RA indices are somewhat dependent on your bankroll then? Because I was always under the impression there is a "hard threshold" for what a risk-averse index is (maybe pertaining to C.E.??) which isn't dependent on your bankroll.
And pertaining to some comments on my original post, a question could be what should one take into account when deciding whether or not to insure a good hand (such as a blackjack) if one wants to take into account variance reduction? Is it EV/Var or something else such as how much $$ you have on the table versus your bankroll?
This is a gamblers' fallacy. You are NOT risking two bets. The first bet was already risked; before the hand started. When this situation arises, your decision is NOW whether or not to risk ONE (more) bet in order to gain 0.5%.FLASH1296 said:Your advantage drops from 2% to 1.25% ? So … If you double you gain 1.5% of two units,
which is more (by 0.5%) than 2.0% of one unit. SO … Why not double ?
Because you are risking twice as much for a modest increase in profit.
I guess that's kinda like "Sceered money don't win!" :laugh:Sucker said:.
Jimmy Piersall said it best: "Fear strikes out!".
Can you elaborate what you mean by betting full Kelly is incorrect? Is it because full kelly gives you a 13.5% RoR?Sucker said:This is the whole reason why betting full Kelly is incorrect in blackjack. If you can't afford to make the proper plays, you're overbetting your BR. It's as simple as that.
I believe what you said here and what you meant are not the same, although correct me if I'm wrong. I think what you mean is you should not bet, for example, 2% of your BR on a 2% edge. If that's what you mean, then I don't think that's what Kelly betting would suggest that you do. Kelly betting incorporates the variance of the bet into the optimal bet calculation, hence the advice to bet 73% (I think...going by memory on the %) of your edge. I see this concept misstated frequently. People often say something like "the optimal bet is .75 Kelly, and full Kelly is overbetting", etc. I think these statements stem from a misunderstanding of exactly what Kelly betting means. Of course, I'm no authority on the subject myself. Sucker, if you were referring to another factor that makes traditional Kelly betting suboptimal, I'd be interested to hear your thoughts.Sucker said:This is the whole reason why betting full Kelly is incorrect in blackjack.
Hmm what I would say is that the question isn't whether or not to double/split when a max bet is out, but rather to wait for one more true count. For example, the EV-maximizing index for 9v2 for zen is TC +7 but the RA index is +8.psyduck said:Interesting discussion!
I think if one hesitates to double and/or split when his max bet is out, it only means one thing - the max bet is too large for his bank. My understanding is that doubling down and splitting contribute a lot to our win and we have to use them to the full extent.