Fuzzy Math: Cacarulo

Cacarulo · 03-03-2004, 08:34 AM

> 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

Zenfighter · 03-03-2004, 02:08 PM

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

Cacarulo · 03-03-2004, 03:20 PM

> 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

Pete Moss' formula

Cacarulo · 03-03-2004, 03:25 PM

> 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

Zenfighter · 03-04-2004, 09:10 AM

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

Cacarulo · 03-05-2004, 12:22 PM

> 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