# Thread: Fuzzy Math: Cacarulo

1. ## Cacarulo: Adjusting Insurance in 6D

Same concept as above and again using Hi-Lo:

Generic = +3.01 (+3.0)

```A = -0.32 (-0.3)
T = +0.13 (+0.1)
Z = -0.13 (-0.1)
L = +0.04 (0.0)```

In 6D the difference between the correct index and the adjusted index is narrower than in 2D. I would say that it's insignificant.
Let's see:

```A,A v A = +2.38 (3.01 - 0.32 - 0.32 = +2.37)
A,Z v A = +2.57 (3.01 - 0.32 - 0.13 = +2.56)
A,L v A = +2.73 (3.01 - 0.32 + 0.04 = +2.73)
T,T v A = +3.28 (3.01 + 0.13 + 0.13 = +3.27)
T,A v A = +2.82 (3.01 + 0.13 - 0.32 = +2.82)
T,Z v A = +3.01 (3.01 + 0.13 - 0.13 = +3.01)
T,L v A = +3.18 (3.01 + 0.13 + 0.04 = +3.18)
Z,Z v A = +2.76 (3.01 - 0.13 - 0.13 = +2.75)
Z,L v A = +2.92 (3.01 - 0.13 + 0.04 = +2.92)
L,L v A = +3.09 (3.01 + 0.04 + 0.04 = +3.09)```

```A,A,T,T v A = +2.62 (+2.63)
T,5,9,6 v A = +3.09 (+3.05)```

Very interesting study! Thanks Fuzzy Math.

Sincerely,
Cac

2. ## Zenfighter: Re:Nothing to write home :-)

```

Hand		cd index		hl corr.

T-5		2.31357		        .780184

9-6		0.823979		.790695

```

I used 1.81 and - 4.0725 in the original post, anyway.

Sincerely

Z

3. ## Cacarulo: T5 v A simulated

> Hand cd index hl corr.
> T-5 2.31357 .780184

I've simulated this particular play to a precision of one decimal (I can't do it with more than one) and got for 1D:

T5 v A = +2.4 which is closer to +2.38 (+2.375) than to +2.31.

If the problem is not in the EORs then you should look somewhere into your program. I've run out of ideas

Sincerely,
Cac

4. ## Zenfighter: Re:No bugs at all

As a general rule EoR's derived indexes do not take into account cut card effects (penetration). Any estimate you can get while using them, no matter amount gained (see TOB, my working agenda), efficiencies or other things, are linear estimates that aren't trustful for small subsets of cards in which the optimal decision may differ greatly from its best linear estimate.

With this in mind, simulated indexes seem to be better ones, among other things because they tend to be rounded to whole numbers, a lot easier for players to memorize and use them appropiately.

The only problem we have here, as Prof. Griffin correctly pointed, is that the proper use of them, by rounding e.g., can contain as much as a 10% of error in playing decisions.

Btw, there is no indexes-seller developed via montecarlo simulation, in his right state of mind, who doesn't claim the superiority of them over the algebraic ones.

You have to give me at least, that the later ones are a lot cheaper!:-)

Sincerely

Z

5. ## Cacarulo: Re:No bugs at all

> As a general rule EoR's derived indexes do
> not take into account cut card effects
> (penetration). Any estimate you can get
> while using them, no matter amount gained
> (see TOB, my working agenda), efficiencies
> or other things, are linear estimates that
> aren't trustful for small subsets of cards
> in which the optimal decision may differ
> greatly from its best linear estimate.

> With this in mind, simulated indexes seem to
> be better ones, among other things because
> they tend to be rounded to whole numbers, a
> lot easier for players to memorize and use
> them appropiately.

> The only problem we have here, as Prof.
> Griffin correctly pointed, is that the
> proper use of them, by rounding e.g., can
> contain as much as a 10% of error in playing
> decisions.

> Btw, there is no indexes-seller developed
> via montecarlo simulation, in his right
> state of mind, who doesn't claim the
> superiority of them over the algebraic
> ones.

> You have to give me at least, that the later
> ones are a lot cheaper!:-)

My indices for insurance were algebraically derived as well. I ran the sim just to see how good they are. So, what I'm trying to say is that we have a difference in the algebraic algorithm.

Sincerely,
Cac

6. ## Zenfighter: Re:With a pocket calculator, then

m = -7.69231

After removing t,5,a:

m = -8.16326 reversing the sign:

m = 8.16326

inner product after removing dealer's and player's cards ?

i = 90.04551

t = 51/49 *((-1)+( 1)+( -1)) = -51/49

p = sum of squares; after removing 3 cards, p = 37 (for hi-lo)

So we have:

mp/i + t= (8.16326*37)/90.04551 - (51/49) = 2.3135

Note that a direct attack yields:

(7.69231*40)/90.04551 - (51/49) = 2.3763

That's easier, but not precisely better, IMHO.

Sincerely

Z

7. ## Cacarulo: I see where the problem is

> m = -7.69231

> After removing t,5,a:

> m = -8.16326 reversing the sign:

> m = 8.16326

> inner product after removing dealer's and
> player's cards ?

> i = 90.04551

> t = 51/49 *((-1)+( 1)+( -1)) = -51/49

> p = sum of squares; after removing 3 cards,
> p = 37 (for hi-lo)

> So we have:

> mp/i + t= (8.16326*37)/90.04551 - (51/49) =
> 2.3135

> Note that a direct attack yields:

> (7.69231*40)/90.04551 - (51/49) = 2.3763

> That's easier, but not precisely better,
> IMHO.

Your calculations are right. The problem is that Snyder's formula (mp/i+t) have been proven to be not correct. You might want to try with Moss algebraic formula instead.

Sincerely,
Cac

8. ## Cacarulo: Typo

> T5 v A = +2.4 which is closer to +2.38
> (+2.375) than to +2.31.

T5 v A = +2.4 which is closer to +2.36
(+2.357) than to +2.31.

Cac

9. ## Zenfighter: Re: I see where the problem is

Columns

a) Hand

b) Pete Moss formula with the aid of Ted Jennsen spreadsheet. Reid's contribution should be mention also.

c) Snyder' formula with single precison EoR's.

d) Karel floored indexes. Precision sigma = 3.5

e) Same as d but rounded.

SD, H17
```
a		b		   c		d		e

16 vs T	       -0.3	       -0.119879        0		0

15 vs T		3.6		3.58603		3		4

16 vs 9		4.2		4.11778		4		4

```

Cac, I read the thread at bjmath a while back ago. I accept that the methodology is fine,
(a little akward for my taste), but I haven't see any motives so far to change my mind, not with indexes, where rounding approximations can take the money, as you know.

Admitedly, Ted's spreadsheet is marvellous, a multiparameter treasure!

Sincerely

Z

10. ## Cacarulo: Re: I see where the problem is

> Cac, I read the thread at bjmath a while
> back ago. I accept that the methodology is
> fine,
>
> (a little akward for my taste), but I
> haven't see any motives so far to change my
> mind, not with indexes, where rounding
> approximations can take the money, as you
> know.

Well, if you're satisfied with the approximations then I can't argue with that. At least you have been warned

I haven't done a comparison between the two methods so I can't tell you exactly where the big differences are. I know for example that Snyder's formula doesn't work with unbalanced systems like TKO.

Sincerely,
Cac

11. ## Zenfighter: Re:Fine for balanced one level counts only

That's the reason I use SBA indexes for my Halves :-)

Thanks for all, Cac.

Sincerely

Z

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