Cacarulo: Composition-dependent indices for Insurance

[Cacarulo]

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

[Don Schlesinger]

I consider this post so informative that I have actually printed it out -- something I do maybe twice a year!!

Viktor, please archive it immediately!

Nice work, Cac!

Don

[Cacarulo]

> I consider this post so informative that I
> have actually printed it out -- something I
> do maybe twice a year!!

> Viktor, please archive it immediately!

> Nice work, Cac!

Thanks Don!

Sincerely,
Cacarulo

[Viktor Nacht]

[Norm Wattenberger]

Had no idea the differences would be so large. Now I'm going to have to add this to CV.

Great study.

[Cacarulo]

> Had no idea the differences would be so
> large. Now I'm going to have to add this to
> CV.

That would be great.

> Great study.

Thank you!

Sincerely,
Cacarulo

[phantom007]

Thanks for the good info. Would these indicies be "transferrable" to other counting systems? Especially AOII and Revere Systemic?

If not, how could the computer illiterate (me) make adjustments?

Thanks again.

phantom007

[Don Schlesinger]

> Thanks for the good info. Would these
> indicies be "transferrable" to
> other counting systems? Especially AOII and
> Revere Systemic?

They're not "transferable," per se. But, they can be calculated for any count.

Of course, you'd have to tell us what the "Revere Systemic" is, since there is no such count. :-)

Don

[phantom007]

RSC is listed among many others in Mr. Schoblette's book "Best Blackjack".

Quite simple...2-7 = +1, 8 = 0, 9-A = -1. From memory, betting correl. 95%, and play about 56%.

I recently switched to RSC for 6D, and on a recent Tunica trip used it for DD with Satisfactory results. Certainly simple to use. On face-up games, can "count" the table in seconds.

Again, would appreciate info. of this "Composition Dependent Insurance", as to adjusted to RSC and AOII.

Thanks

phantom007.

[Cacarulo]

> Quite simple...2-7 = +1, 8 = 0, 9-A = -1.
> From memory, betting correl. 95%, and play
> about 56%.

I think you are talking about the Silver-Fox system here.

> I recently switched to RSC for 6D, and on a
> recent Tunica trip used it for DD with
> Satisfactory results. Certainly simple to
> use. On face-up games, can "count"
> the table in seconds.

Silver-Fox is not a good system for 6D. Hi-Lo does much better and you don't need to count 7's and 9's. KO is even better.

> Again, would appreciate info. of this
> "Composition Dependent Insurance",
> as to adjusted to RSC and AOII.

It's possible to generate insurance indices for AO2 but a level-2 system needs more indices than a level-1 system. Note tha Hi-Lo uses 10 extra indices and that's already hard to learn.
Now, if you still want the AO2 indices just let me know the number of decks.

Sincerely,
Cacarulo

[Igor]

Can you point me in the right direction? If I wanted to calculate the ten insurance break-even true counts for the above count, how would I?

I've never been happy about being an idiot and my resignation to this fact has led to some lazy habits. I only know, which isn't much at all, that insurance has a zero expectation at a composition where Q(T) = Q(NT)/2, or the NT/T ratio is exactly 2. Uncounted ranks should be assumed to consist of 1/13 per rank of the total cards in the undealt subset. The problem comes in the two tags that share the low half. A high count can presume an undealt subset that holds fewer Fours and Fives among the low cards, raising the NT/T ratio. I trust departure determination algorithms based upon simulation of the undealt subset (meaning SBA) more than algorithms assuming composition of the undealt subset (meaning BCA and PBA) for this reason.

Is there a quick and dirty approach to this? Accuracy two places to the right of the decimal is unnecessary. Even one place would be overkill; I would be ecstatic with accuracy to a fifth, a third or even a half of a point.

Thanks in advance and, although I have always been impressed with your work, I am literally astounded by this development.

Congratulations on your insight.

[Cacarulo]

> Can you point me in the right direction? If
> I wanted to calculate the ten insurance
> break-even true counts for the above count,
> how would I?

It's not that simple. You can find some info on bjmath where Pete Moss developed an algebraic formula for determining indices based on EORs.

> I've never been happy about being an idiot
> and my resignation to this fact has led to
> some lazy habits. I only know, which isn't
> much at all, that insurance has a zero
> expectation at a composition where Q(T) =
> Q(NT)/2, or the NT/T ratio is exactly 2.
> Uncounted ranks should be assumed to consist
> of 1/13 per rank of the total cards in the
> undealt subset. The problem comes in the two
> tags that share the low half. A high count
> can presume an undealt subset that holds
> fewer Fours and Fives among the low cards,
> raising the NT/T ratio.

> I trust departure
> determination algorithms based upon
> simulation of the undealt subset (meaning
> SBA) more than algorithms assuming
> composition of the undealt subset (meaning
> BCA and PBA) for this reason.

You're right here although for insurance, which is a linear function, this is not a problem.

> Is there a quick and dirty approach to this?
> Accuracy two places to the right of the
> decimal is unnecessary. Even one place would
> be overkill; I would be ecstatic with
> accuracy to a fifth, a third or even a half
> of a point.

See Bjmath.

> Thanks in advance and, although I have
> always been impressed with your work, I am
> literally astounded by this development.

You're welcome.

> Congratulations on your insight.

Thank you!

Sincerely,
Cacarulo

[Don Schlesinger]

> RSC is listed among many others in Mr.
> Schoblette's [Scoblete's] book "Best
> Blackjack".

> Quite simple...2-7 = +1, 8 = 0, 9-A = -1.
> From memory, betting correl. 95%, and play
> about 56%.

A friendly word of advice: you would do well, in general, to not quote Frank Scoblete on anything, and, in specific, to even mention his name on this site! ;-

As Cacarulo mentions, the count in question is Ralph Stricker's "Silver Fox." He, in turn, adapted it from Koko Ita's "Green Fountain Count," which uses the identical card tags. Revere had nothing whatsoever to do with this count.

Don