Fuzzy Math: Cacarulo

[Fuzzy Math]

I have a question regarding your "Composition-Dependent Insurance Indices" which are posted in the archives. As we all know, the proper times to insure is simply a relation of what percent of the remaining cards are 10-value. Your indices attempt to correct for the fact that hi-lo counts aces and tens together. I don't question the validity of your calculations.

However, at the end you state: "It's also good cover when you're playing two hands." I take this to mean that you may insure one hand but not the other. Since insurance is a side bet unrelated to the play of the hand, I don't see the benefit in using your new indices to insure one hand but not the other. (I could get the same cover by simply insuring one hand at random any time the decision is borderline.) Your remark seemed to imply that it would be *correct* in some situations to just insure one of your hands, with cover being a side benefit. On the contrary, if I were using your indices I would simply average together the index for each of my hands and use that to determine my decision for both hands. I would appreciate some clarification as to what exactly you meant, as it has struck me as being rather odd each time that I read the post.

[Cacarulo]

> However, at the end you state: "It's
> also good cover when you're playing two
> hands." I take this to mean that you
> may insure one hand but not the other.

> Your
> remark seemed to imply that it would be
> *correct* in some situations to just insure
> one of your hands, with cover being a side
> benefit.

Correct.

> On the contrary, if I were using
> your indices I would simply average together
> the index for each of my hands and use that
> to determine my decision for both hands.

Why would you do that?

> I
> would appreciate some clarification as to
> what exactly you meant, as it has struck me
> as being rather odd each time that I read
> the post.

I'll give you the same example I used in my post. Say you're playing two hands in a 6D game and the count is say +2.95. The dealer has an Ace and your hands are comprised as follow:

1) T,5
2) 9,6

If you were using the generic index (+3.01 in this case) you wouldn't insure any of the hands. Correct?
But, if you were using CD indices instead, you would like to insure 9,6 but not T,5!
The reason is simply that T,5 has an index of +3.18 and 9,6 has an index of +2.92.

Of course, cover is a side effect. You have 15 in both hands but you only insure one. It won't make sense for the dealer although you'll be maximizing your EV.

OTOH, if you average both indices (+3.18 and +2.92) you'll get an average index of +3.05 so you will not insure any of your hands.

Hope this helps.

Sincerely,
Cacarulo

[Fuzzy Math]

> I'll give you the same example I used in my
> post. Say you're playing two hands in a 6D
> game and the count is say +2.95. The dealer
> has an Ace and your hands are comprised as
> follow:

> 1) T,5
> 2) 9,6

> If you were using the generic index (+3.01
> in this case) you wouldn't insure any of the
> hands. Correct?
> But, if you were using CD indices instead,
> you would like to insure 9,6 but not T,5!
> The reason is simply that T,5 has an index
> of +3.18 and 9,6 has an index of +2.92.

Insurance is simply a side bet that the dealer will have a ten. It's either a good bet to take, or its not. Regardless of how many hands I am playing, the dealer only has one hole card, and there can be only one probability of what that card will be. In your example, what if I were to insure T5 but not 96? I would still have the same result as if I insured 96 but not T5. You are merely advocating that I take half as much insurance as I am allowed to bet -- how it is divided between the two hands does not change the payout!

Just to be sure we are on the same page, this is intended to maximize EV, correct? You also had posts on Risk-Averse Insurance (where I can understand why you would insure some hands but not others), but this in particular didn't mention RI.

[Cacarulo]

> Insurance is simply a side bet that the
> dealer will have a ten. It's either a good
> bet to take, or its not. Regardless of how
> many hands I am playing, the dealer only has
> one hole card, and there can be only one
> probability of what that card will be. In
> your example, what if I were to insure T5
> but not 96? I would still have the same
> result as if I insured 96 but not T5. You
> are merely advocating that I take half as
> much insurance as I am allowed to bet -- how
> it is divided between the two hands does not
> change the payout!

Ok. Let me see if I can give you a better explanation. When a CD-index is generated it only takes into account the following info:

1) Player's first two cards
2) Dealer's upcard
3) Count value (TC or RC)

Other players or hands at the table are already included in 3). Now, when you play an index you don't have to look at the other hands in the table. It's just your hand against the dealer's upcard.
I understand that you may want to insure all of your hands since you have already insured one but this is not a good idea. We have three sceneries here:

1) Insure 96 but not T5.
2) Insure both hands.
3) Do not insure any of the hands.

Which scenery do you think will come ahead in the long run? The answer is 1).
Of course, you could place your bet wherever you want provided that you only insure one of the hands. I can insure 96 but place my bet on T5. Also, I could take half insurance on both hands.

If I wanted to be even more accurate I could get an index based on the four cards plus the dealer's but this would be of no use.

> Just to be sure we are on the same page,
> this is intended to maximize EV, correct?
> You also had posts on Risk-Averse Insurance
> (where I can understand why you would insure
> some hands but not others), but this in
> particular didn't mention RI.

Yes, we are maximizing EV.

Sincerely,
Cacarulo

[Cacarulo]

Suppose that you're playing one hand only and that there are other players at the table. The count is again +2.95 and you get 96 (CD-index = +2.92). According to the index you should insure, right?
Now, what if another player is holding a T5? What would you do know?
The answer is that you should always go by your hand. This also applies to other CD indices like 97vT and T6vT.

Sincerely,
Cacarulo

[Don Schlesinger]

This is an interesting problem. I may be wrong, but I think there may be an analogy to the BS algorithms we did for the original hand as opposed to the same hand as part of a pair-splitting situation. The same holding may be played two different ways, as you know.

Here, for insurance, you did your C-D indices based on the player's holding just the ONE hand being studied, v. dealer's ace. But, this is different. We now have TWO hands on the table, and that fact has to influence the ultimate insurance index for both of the hands in question.

In essence, you're insuring the four cards on the table, comprising two separate hands, not each hand individually.

I don't think there can be two separate indices v. the one dealer upcard! But, I may be wrong.

Don

[Cacarulo]

> This is an interesting problem. I may be
> wrong, but I think there may be an analogy
> to the BS algorithms we did for the original
> hand as opposed to the same hand as part of
> a pair-splitting situation.

Sort of.

> Here, for insurance, you did your C-D
> indices based on the player's holding just
> the ONE hand being studied, v. dealer's ace.
> But, this is different. We now have TWO
> hands on the table, and that fact has to
> influence the ultimate insurance index for
> both of the hands in question.

We have two hands but we play them independently. We use the other hand information only for updating the count.

> In essence, you're insuring the four cards
> on the table, comprising two separate hands,
> not each hand individually.

Yes, but we don't have an index for the four cards.

Sincerely,
Cacarulo

[Don Schlesinger]

> Yes, but we don't have an index for the four
> cards.

Again, I may be wrong, but I am not sure that taking insurance, using an index number, is the same thing as using an index to play a hand in a particular manner. When we insure, we aren't interested in the outcome of our own hand, i.e., its expectation (unless considering risk-aversion). Rather, we want to use the index to tell us whether or not there is a less than 2 to 1 ratio of non-tens to tens remaining in the pack.

Regardless of the hands now lying on the table, I should be using the updated count after both hands are considered, to make that determination. It makes no sense to make them one at a time, as both hands are inextricably linked to the dealer's ace.

Give this some more thought. I will, too.

Don

[Cacarulo]

> Again, I may be wrong, but I am not sure
> that taking insurance, using an index
> number, is the same thing as using an index
> to play a hand in a particular manner. When
> we insure, we aren't interested in the
> outcome of our own hand, i.e., its
> expectation (unless considering
> risk-aversion). Rather, we want to use the
> index to tell us whether or not there is a
> less than 2 to 1 ratio of non-tens to tens
> remaining in the pack.

> Regardless of the hands now lying on the
> table, I should be using the updated count
> after both hands are considered, to make
> that determination. It makes no sense to
> make them one at a time, as both hands are
> inextricably linked to the dealer's ace.

I do use the updated count -considering all the cards lying on the table- and then decide whether to insure the hand or not. For me it's the same as any other CD play. T6vT and 97vT both have different indices and when we stand we expect the dealer to bust in order to win. Why I would then stand on one hand but hit on the other? See the analogy?

> Give this some more thought. I will, too.

I will but I still don't see what the problem is.

Sincerely,
Cac

[Don Schlesinger]

> I will but I still don't see what the
> problem is.

The problem is the following: over and over again, we say that the player hand doesn't matter when we take insurance. All that matters is whether the dealer has a ten in the hole or not. So, we use the count to determine whether it's a favorable bet to take insurance. I can understand that that count can be different for different player holdings, when considered one at a time.

But, the dealer has only one card in the hole, no matter how many hands we have lying on the table. It can't be right to insure one hand and not the other. Either the ratio of non-tens to tens is more than two to one or less than two to one. It can't be both at the same time. You can 't look at the first hand and say: The ratio is greater, so I shouldn't insure, and then look at the second hand and change your mind and say, the ratio is now less, so I should insure -- all the while looking at the lone dealer hole card!

Don

[Cacarulo]

[Fuzzy Math]

> I do use the updated count -considering all
> the cards lying on the table- and then
> decide whether to insure the hand or not.
> For me it's the same as any other CD play.
> T6vT and 97vT both have different indices
> and when we stand we expect the dealer to
> bust in order to win. Why I would then stand
> on one hand but hit on the other? See the
> analogy?

If you were dealt those two hands at the same time, you would not ever stand on the first one but then hit the second one -- each will play out exactly the same. Why should insurance be any different?

Let's look at what insurance really is: You get to place a side bet which pays 2:1 if the dealer has a ten in the hole. If he does, then the money you lost on your hand is then paid back to you for winning the insurance betn You lose your initial bet if the dealer has a BJ regardless of insurance -- insurance is simply a side bet whose winning payout happens to be the same as the amount of your losing bet. If the dealer has a BJ less than 1 time in 3 that you insure, then you are losing money. A counter attempts to use his knowledge of the remaining cards to determine if this is a positive-EV bet to take. You are advocating that it will be a positive-EV bet on one of your hands, but negative-EV on another hand -- at the same time!

The thing is that in making your decision you are considering the composition of one hand, but only the total (count-wise) of the other hand. Then you reverse the situation. This could be compared to getting dealt A/4 and hitting to get A/5/6/3 (hard 15) and then trying to use a C-D index for T/5 to make your decision. That index would account for one less five in the pack, but it still could be improved if you could also account for the missing six.

And finally, I leave you with a puzzle: You are playing doubledeck and put out two bets with a RC of 7. You get dealt A/A on one hand, and T/T on the other. You are asked if you want insurance. There are exactly 52 cards remaining to be dealt/seen. The count has now fallen to 2. Your indices for 2D are .46 for A/A and 3.16 for T/T. What would you do to reconcile this large difference -- Does the insurance side bet yield positive-EV?

[Cacarulo]