Accuracy of the insurance index and insuring for less

[ArcticInferno]

First, let’s return to school for some Blackjack 101.
Insurance, the most important strategy deviation, is a side bet independent of the hand dealt.
For the purposes of this discussion, we will assume that the number of decks is sufficiency large so that the affect of the cards in the initial round is negligible.
4/13 of the cards are tens, so the probability of winning is 4/13, and that of losing is 9/13.
The insurance payout is 2:1, so you will win 2x(4/13) and lose 1x(9/13).
8/13 vs 9/13 can be improved if the remaining deck composition is rich in tens.
Consider a 6-deck shoe depleted of 24 non-tens, so that 4/12 are tens and 8/12 are non-tens.
The true count would be 4 in a hypothetical insurance counting system that compares the tens to non-tens
You will win 2x(4/12) and lose 1x(8/12), so now insurance is a break-even proposition.
At such point, you wouldn’t take insurance because you gain nothing but must weather the variances/fluctuations.
Also, at minimally positive EV, the aggravation may not be worth the negligible gain.
The complication arises from the inherent inaccuracies built into the common counting systems with regards to insurance.
The 8 is never accounted for.
Depending on which system you’re using, the 7 may or may not be accounted for.
Some systems account for the 9 in the wrong direction; the Ace, too.
The 5 is sometimes given a greater weight, again contributing to the inaccuracy.
The insurance wager is obvious at extremes of the true count.
How reliable/accurate is using true count of 3 for the threshold for the insurance wager?
As stated earlier, if the EV is only slightly positive, then the variance/fluctuation associated with the insurance wager isn’t worth the aggravation.
Some of you will argue that insurance reduces the overall variance, but I’m talking about the insurance side bet in isolation.
The hypothetical insurance counting system (described above) has no “gray” area where the probability is uncertain.
However, because of the inherent inaccuracies of all counting systems, there’s a gray area where the accuracy of the count for the insurance wager is uncertain.
In some TC range of, e.g., 2.5 - 3.5 or 3.0 - 3.5, what would be the effect of insuring for less?
Also, is the insurance threshold a function of point in the shoe?
For example, consider the classic Hi-Lo on a 6-deck game. In the beginning, the insurance threshold is TC:3.
However, after half of the shoe has been dealt out, is the insurance threshold less than 3?
I have CVData, but I don’t know how to run the simulations.

 

[zengrifter]

what would be the effect of insuring for less?

ONLY to reduce variance at the expense of EV. At any count it will further decrease the EV of the play.
It can be, however, a nifty little low-cost camouflage move in some (not all) environments.
Can anyone help him with his sin err sim? zg

 

[neversplit5s]

Speaking strictly in terms of EV, insurance is like doubling down (in a non-tournament game): When it's favorable you should do it for the full amount, and when it's not don't do it at all.

 

[jack.jackson]

ONLY to reduce variance at the expense of EV. At any count it will further decrease the EV of the play.
It can be, however, a nifty little low-cost camouflage move in some (not all) environments.
Can anyone help him with his sin err sim? zg

But let us say, you have a $100 bet out and you take insurance@+6(l2) and the count is +5. You mean theres no +EV in even a $5 bet? When you would bet $50@+6.

 

[SystemsTrader]

How reliable/accurate is using true count of 3 for the threshold for the insurance wager?

Its accurate over the long run. In the short run it can be way off but so is any true count. Unless you are using a count specific for insurance with 100% information the true count of 3 will always be an estimate. Maybe the math guys around here will be able to really answer your question properly.

As for insuring for less, in Griffin's "The theory of blackjack" he has a section about how a kelly bettor can insure for less in some situations. I don't have the book in front of me to look up the details.

 

[ArcticInferno]

I think you guys may have misunderstood my post.
Insuring, like doubling, should be done for the full amount if you have the advantage.
However, you must be certain of the advantage.
The hypothetical insurance counting system described in the original post does calculate the probability of a ten being in the hole with absolute certainly.
However, common counting systems don’t calculate the probability of a ten being in the hole with absolute certainty, and therein lies the problem.
Common counting systems don’t account for the 8, which contributes to the uncertainty.
Release of an Ace should increase the probability of a ten being in the hole, but the count would indicate decrease in the probability, again contributing to the uncertainty.
At extremes of the count, the uncertainly is small enough to be negligible, so the insurance wager should be taken for the full amount.
However, there’s a range of counts where the uncertainly of the insurance index is significant enough that the insurance wager becomes a game of pure chance.

 

[ArcticInferno]

Its accurate over the long run. In the short run it can be way off but so is any true count. Unless you are using a count specific for insurance with 100% information the true count of 3 will always be an estimate. Maybe the math guys around here will be able to really answer your question properly.

As for insuring for less, in Griffin's "The theory of blackjack" he has a section about how a kelly bettor can insure for less in some situations. I don't have the book in front of me to look up the details.

Yes, I agree that the insurance index (TC:3) is good enough in the lo-ooo-ng run.
When the count hovers around 3, what would be the effect of insuring for less (e.g. half)?
In the lo-ooo-ng run, how will the outcome be affected?
My speculation is that the winnings from the insurance wager will not be significantly affected, while the variance associated with the insurance wager will be reduced noticeably.

 

[Blue Efficacy]

Easy solution. when you are right around the index, only insure "good" hands. This will first reduce variance somewhat, and secondly will make you look more "normal."

 

[ArcticInferno]

Easy solution. when you are right around the index, only insure "good" hands. This will first reduce variance somewhat, and secondly will make you look more "normal."

Camoflage aside,...
Blue Efficacy, with all due respect:
Insuring only the “good hands” is a ploppy misconception.
Insurance is a side bet independent of the hand dealt.
By variance, do you mean overall variance or the variance of the insurance side game?
The variance of the insurance side bet can be reduced by playing the insurance side game only at extremely high counts, at the expense of reducing the overall winnings from the insurance side bet.
Insuring only the “good hands” will have zero effect on the outcome,... long-term, short-term, overall, etc.
Insurance is an independent side game, and you must assess the probability of a ten being in the hole. A “good hand” or a “bad hand” won’t change the probability of a ten being in the hole. The ratio of tens to non-tens of the remaining deck composition determines the probability of a ten being in the hole.
Insurance is a strange animal in that even veterans who have written books sometimes misunderstand the mystery of insurance.

 

[zengrifter]

But let us say, you have a $100 bet out and you take insurance@+6(l2) and the count is +5. You mean theres no +EV in even a $5 bet? When you would bet $50@+6.

I said "reduces EV" - but in my mind insurance for less is ONLY
for camo and variance reduction when the bet is NOT +EV. zg

 

[zengrifter]

Insurance is a side bet independent of the hand dealt.

But the point I thought of this thread - and any advanced discussion of Insurance -
- is that its NOT fully independent, notwithstanding what many experts have published. zg

 

[ArcticInferno]

Zengrifter, the sentence that you quote is in the same post as this sentence.
---
A “good hand” or a “bad hand” won’t change the probability of a ten being in the hole.
The ratio of tens to non-tens of the remaining deck composition determines the probability of a ten being in the hole.
---
Insurance is a game that asks you, “Do you think there’s a ten in the hole?”
What determines the probability of a ten being in the hole?
The “goodness” of the hand dealt, or the remaining deck composition?
By the way, the point of the original post was not about the concept behind insurance (or even money).

 

[zengrifter]

Insurance is a game that asks you, “Do you think there’s a ten in the hole?”
What determines the probability of a ten being in the hole?
The “goodness” of the hand dealt, or the remaining deck composition?
By the way, the point of the original post was not about the concept behind insurance (or even money).

Yes, the remaining deck composition, of course.
But the correlation of the two bets make them not as unrelated as earlier experts published.

I guess you could size your I-bets according to your edge, just like the main bets. Nothing wrong with that, but it would only amount to an infrequent insure for less.

On the other hand, insuring certain occasional good hands, for full or less, when the I-bet is not favorable, can be an interesting camo art in some venues.

ExhibitCAA book and BC have some data on this. zg

 

[Automatic Monkey]

If you only insure hands larger than your minimum bet, you might be surprised how little it costs you. Sim it and see.

 

[bj21abc]

That's interesting - never thought to sim that - ins at +1. Will give it a go.

Re insuring good hands - I believe that Grosjean covered this at some point - there is a larger reduction, as I recall, in variance if insuring "good hands" - as if you lose the insurance bet you have a good chance of winning the hand.

If you only insure hands larger than your minimum bet, you might be surprised how little it costs you. Sim it and see.

 

[ArcticInferno]

bj21abc, if you’re going to run some simulations, please do for TC of 2, 3, & 4.
Also, the effect of insuring for less (half) at 2, 3, & 4.
If you know the exactly ratio of tens to non-tens of the remaining deck composition, then you can determine the probability of a ten being in the hole with absolute certainty.
However, if the ratio of tens to non-tens is uncertain, then the probability of a ten being in the hole is also uncertain.
That’s the crux of my original post. What happens when you make a wager with uncertain probability near the threshold? What is the optimal course of action?

 

[ArcticInferno]

Re insuring good hands - I believe that Grosjean covered this at some point - there is a larger reduction, as I recall, in variance if insuring "good hands" - as if you lose the insurance bet you have a good chance of winning the hand.

bj21abc, I’ve heard that argument before, but it’s one of many flawed gamblers superstitions.

You’re due for a win because you lost a lot in a row.
Always play your hand with the assumption that the dealer has a ten in the hole.
Always take even money because that’s the only sure bet in the house.
Etc.

If you insure a bad hand, then you may lose both the insurance and the hand, so you lose twice.
If you insure a good hand, then you may win at least one of them to cancel each other out.
This misconception is an optical illusion.

We’ve already established beyond doubt that the “goodness” of your hand doesn’t determine the probability of a ten being in the hole. The remaining deck composition does.
If you insure a good hand at low counts, then you’re playing the insurance side game with negative EV, which will reduce the overall winnings.
If you not insure a bad hand at high counts, then you miss a valuable opportunity for potential winnings at positive EV, so your expected final overall winnings will be reduced.
The logical strategy is to play the insurance side game (or even money) without considering the hand dealt.

 

[ArcticInferno]

If you only insure hands larger than your minimum bet, you might be surprised how little it costs you. Sim it and see.

If you know that you will lose (albeit little) in the long run, what would be the point?
What do you gain, or hope to accomplish?

 

[johndoe]

bj21abc, I’ve heard that argument before, but it’s one of many flawed gamblers superstitions.

I'm sure I'm not the only one incredibly amused that you'd consider one of JG's analysis as equivalent to common gambler's superstitions!

Read and learn:

http://www.blackjackinfo.com/bb/showthread.php?p=147055#post147055

 

[bj21abc]

"Incredibly amused" may be pushing it a little

To be fair "insuring good hands" is indeed a ploppy strategy which has nothing to do with JG's analysis... Do you find it surprising that only a (small?) minority of posters have read JG or gone into depth on these points ? I would say that you have to be fairly serious about AP and/or interested in fine points of the game, some of which are purely theoretical. I myself don't own BC - just borrowed a copy from a friend