Should you insure good hands?

Exactly. RA indeces are delayed behind EV maximizing indeces not because we are afraid of losing the bet, but to improve your EV a bit before making a play that has high variance. This is essentially like waiting to play a game with deeper pen than playing the game you are currently scouting. You are waiting for the play to have a higher SCORE before risking money.

Im not sure, but to compare the insurance bet with no insurance. I would think that you just combine the bets. The BJ bet has a expected value X and a variance Y. The insurance bet has a expected value of A and a variance of B. The result of taking insurance would have an expected value of X+A and a variance of (Y+B)/SQRT(2). No insurance would just be the regular BJ bet. To find the CE, you use the expected value, variance, kelly risk factor, bet size, and bankroll for each option (the latter 3 will be the same for both). Then, to find the RA index, you just do the same at various counts and find where insurance > no insurance. This can be done with doubles and splits.

from my understanding of the kelly criterion, it does incorporate the variance of 'the bet' but a kelly bet was originally defined for a bet that either wins or loses (with defined odds on the bet).

of course in blackjack your hand does not simply win or lose because of things like splitting, doubling, blackjacks, insurance, etc. so we may end up with more money on the table or getting paid 3:2 on our blackjacks instead of 1:1 like normal. this extra variance is not accounted for in the bet of '2% of your BR on a 2% edge' and so the 'optimal' bet for a hand of blackjack in the kelly spirit is really some fraction of that "x% of BR for x% edge".

to the subject of RA vs EV play, it is a balance between 2 extremes:
1) very RA plays: lower $/hr, lower variance, but allows for a higher fraction of a full 'kelly bet'
2) EV-maximizing plays: higher $/hr, higher variance, but allows for a smaller fraction of a 'kelly bet'

the key is to find the right balance. the best way to settle this would be with sims..

it all depends

imho insurance or not isn't really the question, it's a sub question.

the real point on this stuff is that math is a tool used by humans.
as such the math is a utility function.
so the real point is utility with respect to the user of the tool, which is the point alluded to by Flash.

you can go broke doing stuff right and you can go broke doing stuff wrong, what ever right or wrong may happen to be.
you can also make one helluva lot of money both ways.
but in reality just exactly what is the correct way to do stuff and just exactly what is the incorrect way to do stuff isn't so clear.
most people want to make money when they gamble, thing is most people don't end up doing so.

it's been shown that having goals can slow down the achievement of advantage. thing is if you think about it that is not necessarily true for the achievement of making money. none the less the desire to make money is a goal. hence not only for the humane spirit but also for one's pocket book we have a dilemma, lol.

point being as a thinking being one is free to transcend theory and still make decisions beyond the effective utility of that theory.
the results will be what they are, question is are you happy with them or not. statistics will not give you the answer.

I do not see why your insurance decision should have anything to do with what your current hand is. Isn't insurance a bet that the dealer's hole card is 10?

my thoughts exactly. I, for one, am not there to bet the 1, or 2 unit plays, I am there for the 10-12 units and PLEASE give me the option to double those!!! - well, I'd take a BJ first, but if not, I'll take a DD:cool2:

Muppet, Kelly criteria takes into account EV/Var, and EV isn't just whether or not you lose the bet, but rather what your expected return is at a particular count, which does take into account doubles, splits, etc.

Muppet, also, regarding RA plays, the goal is to have the Var decrease faster than the EV, so that EV/Var actually increases, and you can safely put more money on the table.

Sage, interesting thoughts! Nothing wrong with trying to find the "correct" play mathematically, because even though we won't ever hit 1 billion hands, you can have a higher chance of being in +EV territory (i.e. winning money while "gambling") by using the correct play. I agree though that the insurance issue can be thought of as a subquestion to a larger question.

Psyduck, my original post proved just that. However, my OP was only taking into account the EV of the hand (which cancelled out). What we are discussing currently is to also take into account variance of a hand. So what it comes down to is that perhaps by insuring certain hands before you're "supposed" to may hurt your EV by -0.0001%, it might decrease your variance by -0.1%, making it a "smart move" for people trying to reduce their RoR. And regarding Sucker's post, I can say from experience that sometimes it isn't easy to have a bankroll in which you are always playing with a very low RoR, and sometimes extra steps must be taken to decrease that RoR if your bankroll is limited.

hmm, well previous post was fairly uninformed. i was basing it mostly on info i read in the wiki, which only showed it's application to a bet with two outcomes.

i've done a lot of reading today on the subject and i believe that i now have a fairly good grasp of the concept as it applies to blackjack.

but one thing i'm confused on is how ev/var came about? in one source it was assumed to be an approximation of the correct kelly bet. i read a different source that instead used ev divided by standard deviation.

Kinda math-y but this post http://bjmath.com/bjmath/Betsize/theory.htm (Archive copy) contains everything you need to know about EV/Var. Brett Harris is a well respected blackjack mathematician. If you need help understanding feel free to start a new thread with some specific questions about it

thanks, i'll take a look at this

A small point here: if you have 10 or 11 vs 4 to 6, you should always double for bs, unless indices indicate otherwise.

Thanks, chessplayer, but in all fairness trust me - Flash is one to know his basic strategy. ! And a small note here: there are many other plays in which the player should double according to basic strategy.