MJ: Question for Don: Insurance

[MJ]

How does buying insurance help to reduce variance?

Is it true that there are certain hands whose variance decreases when you take insurance (totals 18-20, 8-11, blackjack, or any soft hand) so even when the insurance wager has EV of 0% (TC of 2.7) you should still insure these hands in order to reduce variance?

Thanks,
MJ

[Don Schlesinger]

> How does buying insurance help to reduce variance?

It doesn't always. It does sometimes. It depends on the hand. Clearly, if you insure a natural, it decreases variance. Instead of getting no payout 4/13 of the time and a 3:2 payout 9/13 of the time, you get even money 100% of the time. So, while the average squared result of the second scenario (insuring) is 1, the average squared result of the first (no insurance) is 9/4*9/13 = 81/52 = 1.56, which, of course, is larger.

> Is it true that there are certain hands whose variance
> decreases when you take insurance (totals 18-20, 8-11,
> blackjack, or any soft hand) so even when the
> insurance wager has EV of 0% (TC of 2.7)

Not sure where you got 2.7 from. How many decks are we talking about? Not six, for Hi-Lo.

>you should still insure these hands in order to reduce variance?

That depends on whether or not you're interested in risk-averse indices or e.v.-maximizing ones. If the latter, then there are different insurance values depending on the hand in question. In fact, there are different indices even for e.v.-maximizing, so the two are actually separate ideas.

Don

[MJ]

> It doesn't always. It does sometimes. It depends on
> the hand. Clearly, if you insure a natural, it
> decreases variance. Instead of getting no payout 4/13
> of the time and a 3:2 payout 9/13 of the time, you get
> even money 100% of the time. So, while the average
> squared result of the second scenario (insuring) is 1,
> the average squared result of the first (no insurance)
> is 9/4*9/13 = 81/52 = 1.56, which, of course, is
> larger.

Thanks for the response.

The variance calculation confounds me. Suppose BJ paid out at 3:1 instead of 3:2. Does that mean the variance would now be (3/1)^2 * 9/13 = 81/13 = 6.23 if forgoing insurance? In this instance, even though the variance is greater than that for taking even money, I would rather bypass insurance. Variance is suppose to be the enemy. But in this case the higher the payoff for BJ, the greater it becomes. Isn't rising variance suppose to be a bad thing?

Suppose player BJ pays 3:2 if the dealer doesn't have BJ and 1:2 even if the dealer does have BJ. Is the variance now (1/2)^2 * 4/13 + (3/2)^2 * 9/13 ~ 1.63?

> Not sure where you got 2.7 from. How many decks are we
> talking about? Not six, for Hi-Lo.

6-8 decks for Hi-Lo. The goal is to maximize CE, so R-A indices would be best.

> That depends on whether or not you're interested in
> risk-averse indices or e.v.-maximizing ones. If the
> latter, then there are different insurance values
> depending on the hand in question. In fact, there are
> different indices even for e.v.-maximizing, so the two
> are actually separate ideas.

I like a one-size fits all, simple approach. Perhaps I should just use a bare minimum of TC of +3 and be done with it.

MJ

[Don Schlesinger]

> Thanks for the response.

> The variance calculation confounds me. Suppose BJ paid
> out at 3:1 instead of 3:2. Does that mean the variance
> would now be (3/1)^2 * 9/13 = 81/13 = 6.23 if forgoing
> insurance?

Yes, absolutely.

> In this instance, even though the variance
> is greater than that for taking even money, I would
> rather bypass insurance.

But, if BJ paid 3:1, then insurance shouldn't pay 3:2 anymore.

> Variance is suppose to be the
> enemy. But in this case the higher the payoff for BJ,
> the greater it becomes.

Unavoidable. That's the way it is.

> Isn't rising variance suppose
> to be a bad thing?

It's offset by the extra e.v.

> Suppose player BJ pays 3:2 if the dealer doesn't have
> BJ and 1:2 even if the dealer does have BJ. Is the
> variance now (1/2)^2 * 4/13 + (3/2)^2 * 9/13 ~ 1.63?

Yes. But, technically, I'm calculating the average squared result. For the variance, you have to subtract the square of the e.v.

> 6-8 decks for Hi-Lo. The goal is to maximize CE, so
> R-A indices would be best.

> I like a one-size fits all, simple approach. Perhaps I
> should just use a bare minimum of TC of +3 and be done
> with it.

I would.

Don

[MJ]

Regarding the variance for even money, technically shouldn't it be 0 because you are 100% certain to receive a payment of 1:1? Variance implies that there is some uncertainty here.

Why should a hand such as hard 20 (10,10) have reduced variance by taking insurance? With even money on BJ it becomes obvious but in this case not so. As a matter of fact most BJ texts say that you should be less likely to insure a 'good' hand of 20 because of its very composition. The more tens on the felt, the less likely the dealer has a ten in the hole.

MJ

[G Man]

One of the good discussion on the subject is in "Beyond Counting" from James Grosjean. Chapter 5 titled "Expectation Isn't Everything"

[Don Schlesinger]

> Regarding the variance for even money, technically
> shouldn't it be 0 because you are 100% certain to
> receive a payment of 1:1? Variance implies that there
> is some uncertainty here.

As I said, I was really quoting the average squared results in each case, without removing the square of the e.v., which in the case above, is 1.

> Why should a hand such as hard 20 (10,10) have reduced
> variance by taking insurance? With even money on BJ it
> becomes obvious but in this case not so. As a matter
> of fact most BJ texts say that you should be less
> likely to insure a 'good' hand of 20 because of its
> very composition. The more tens on the felt, the less
> likely the dealer has a ten in the hole.

Again, there are precise index values for insurance according to the hand you are holding. Cacarulo published them some time ago on Don's Domain. You might search for them.

To know whether insurance helps or hurts variance, you have to know the e.v. for the hand in question and then work through the extra bet for insurance, the payoffs each way etc.

Don

[Brick]

If remember correctly Cacarulos index numbers are based on adjustments for the number of aces on the flop,which causes the insurance count to significantly change. Is this the index values you are speaking of? Thanks.

[Don Schlesinger]

> If remember correctly Cacarulo's index numbers are
> based on adjustments for the number of aces on the
> flop, which causes the insurance count to significantly
> change. Is this the index values you are speaking of?
> Thanks.

No. His insurance indices are strictly composition-based and reflect the player's two-card holding vs. the dealer's ace.

Don

[Don Schlesinger]

Posted By: Cacarulo
Date: Monday, 3 February 2003, at 9:52 a.m.

Since this question has been asked several times on the free pages I've decided to post the analysis over here.

Let's start with a 6D game and a TC'ed system like Hi-Lo. Normally a "one-fit-all" index is used disregarding the player's hand composition. Let's call this index: Generic Insurance's index (GII).

Of course, it's possible to generate an index for each hand composition as you'll see below.

Generic Index = +3.01 (GII)

Now, let's separate the Hi-Lo tags into four categories:

T = Ten

A = Ace

Z = 7,8,9

L = 2,3,4,5,6

These 4 categories make 10 different indices:

A,A vs A = +2.37

A,Z vs A = +2.57

A,L vs A = +2.73

T,T vs A = +3.28

T,A vs A = +2.82

T,Z vs A = +3.01

T,L vs A = +3.18

Z,Z vs A = +2.76

Z,L vs A = +2.92

L,L vs A = +3.09

Suppose the count is exactly +3 and you're playing heads up: you have 15 and the dealer has an Ace, would you insure? Obviously the answer depends on the composition of the hand. If my hand is 10,5 I won't insure but if it is 9,6 then I will.

Here are the indices for 1D and 2D:

Indices for 1 deck:

Generic Index = +1.41

A,A vs A = -2.42

A,Z vs A = -1.32

A,L vs A = -0.26

T,T vs A = +2.95

T,A vs A = +0.09

T,Z vs A = +1.31

T,L vs A = +2.36

Z,Z vs A = -0.22

Z,L vs A = +0.84

L,L vs A = +1.90

Indices for 2 decks:

Generic Index = +2.38

A,A vs A = +0.46

A,Z vs A = +1.02

A,L vs A = +1.53

T,T vs A = +3.16

T,A vs A = +1.76

T,Z vs A = +2.36

T,L vs A = +2.86

Z,Z vs A = +1.58

Z,L vs A = +2.09

L,L vs A = +2.60

If you're good at memorizing indices then go ahead and learn the above. It's also good cover when you're playing two hands.

Sincerely,

Cacarulo

[Brick]

Thanks Don,yes I vaguely remember when he posted this and payed close attention to the dramatic effect aces can reflect on the ins. count for single deck. Notice how Ace verses Ace-Ace against Ace verses Ten-Ten has over a 5 point swing,this is a huge difference!

[chgobjpro]

> Posted By: Cacarulo
Would it be a fact that using an Ace neutral 2 level count system would probably change all these index numbers?

[Don Schlesinger]

> Would it be a fact that using an Ace neutral 2 level
> count system would probably change all these index
> numbers?

Sure. Cac posted for other counts, as well. Search for them.

Don