Partial Insurance with Late Surrender

[Deathclutch]

http://www.bjmath.com/bjmath/playing/insure.htm (Archive copy)

Here's something cool I ran across that I haven't seen discussed here before.

"Note that some partial insurance is always justified. With a late surrender hand, the optimal bet is 1/6. If you had wagered 6 units, you would insure with 1."

If I'm reading this correctly, which I may not be, it says that if you're going to insure a hand that you plan on surrendering you'd optimally insure for 1/6 of your wager.

"If you have a possiblity of taking "half-insurance" (25% of your bet), then your critical value is 1/8. You will always be above this, so half-insurance always decreases variance in borderline cases. If you are playing 2 spots, insure one of them, no matter how bad they are."

I know some people here play a lot of LS games so I thought this may be of interest to them.

 

[Meistro]

How is taking a -EV bet optimal

 

[Nynefingers]

How is taking a -EV bet optimal

It decreases variance. If the decrease in variance is significant compared to the decrease in EV, then this can be an acceptable trade off. The title of the page is "Optimal (RA) Insurance Strategy," so we aren't necessarily talking about maximizing EV. I would view this as somewhat similar to using risk averse indices instead of expectation maximizing indices. The part I'm not sure about is when exactly he is advocating using (partial) insurance. I believe this page is discussing borderline situations with the count near +3.

 

[Meistro]

I see. I wonder if the insurance efficency of your system plays into this at all?

 

[Finn Dog]

"If you are playing 2 spots, insure one of them, no matter how bad they are."[/QUOTE] Deathcluth: are you reading this as: when playing two spots, always insure one hand no matter how bad both hands are (IE. two stiffs), [U]despite[/U] what the TC is? Anyone else? Thanks in advance, FD

 

[Deathclutch]

Deathcluth: are you reading this as: when playing two spots, always insure one hand no matter how bad both hands are (IE. two stiffs), despite what the TC is?

Anyone else?

Thanks in advance,

FD

The first time I read it it seemed to make more sense. Insuring a hand when not being close to the index wouldn't make sense though. Maybe someone else can clear that up that's better with the terminology.

 

[Nynefingers]

I'm still understanding the whole thing to be discussing situations where the count is near the insurance index.

First, that statement, as it stands is not true. If you are in borderline situation (1/3 or remaining cards are 10s) then you should take "All or Nothing Insurance" when your hand has -25% conditional expectation, or better. That is, there are lot of losing hands for which you should still take full insurance.

Mathematically your optimal insurance bet in this situation is


B = (-R+CE)/3

where CE is the conditional expectation of your hand, assuming the dealer does not have blackjack. . R is the result that you will be paid if the dealer does have BJ. R is -1, unless you have a natural in which case R=0.

...

Note that some partial insurance is always justified. With a late surrender hand, the optimal bet is 1/6. If you had wagered 6 units, you would insure with 1.

With a late surrender hand, your conditional expectation CE is -0.5 since you will surrender your bet if the dealer does not have BJ. R is -1, so using the equation given, B = (-(-1)+(-0.5))/3 = (1-0.5)/3 = 1/6. That means the entire article appears to be tied together with regard to the math, so I'm taking that to mean that a roughly neutral EV situation is assumed throughout, and the question is only about how to minimize variance. I can't say for sure, but that's what it looks like to me.