Probability and Diamonds

[roksinmymind]

Heh...

maybe this is an exercise in neuroticism...

I put a deposit down on a 1.44 carat, 57% table, 62.6% depth diamond. It is 7.14x7.23x4.5 in size with a medium to slightly thick girdle. Although this diamond would be considered a non-branded american ideal cut by a company such as Blue Nile that considers only table and depth %'s, anyone who reads the Holloway's tutorial knows this means diddly squat. I tried to get a sarin report, but it was impossible at the time (its being currently shipped).

Being very uncomfortable with uncertainty (I have a master's degree in statistics), I wanted to see what the probability that this might actually be a good cut. So first, I had to make several assumptions.

1) the medium (1.7-3%) to sl thick girdle (3-4.5%) would equate to approx 3.1% of the diameter. It leaned on the thicker side of the indicated range because the actual size of the diamond is a bit smaller than the weight indicates (it should be 7.34 mm according to Tolkowsky proportions).

2) the "no culet" would be 0.2%

These assumptions allowed me to make a sliding range of the associated crown and pavilion %'s and punch them into the HCA formula.

Interestingly, given these assumptions, if this diamond actually ended up being AGA 1B ideal (with the crown and the pavillion %'s falling into the AGA 1B ranges), the HCA would only give the diamond a rating of 2.0-4.0.

However, if the crown angle was steeper than AGS 1B, then I would get a range of 0.9-2.2 on the HCA (FIC) before falling off the meter (crown too steep).

If the crown angle was less steep than AGS 1B, then I would get a HCA range of 3.7 to 5.1 to 2.5 before falling off the meter (pavilion too deep).

Since a diamond with a smaller spread for its weight usually indicates a diamond with a steeper crown angle (is this correct?), I'm hoping that this diamond will fall within the range of FIC.

What do you think- is it all a bunch of nonesense?^^

In the end, I will get the diamond (1wk or so) and get it independently appraised and measured, and if it doesn't meet my expectations, I can get my deposit back. It will be interesting to see if my assumptions were accurate or not.

I just wanted to share my neurotic obsession with this little rock and some of the relationships I found.

 

[roksinmymind]

Maybe somebody could devise a table and depth % probability program for the HCA...

Rather then being really helpful, it would be an exercise in demonstrating how useless those two %'s are in predicting a good cut.

 

[pricescope]

Roksinmymind, I like your exercise.

GIA grades girdle as following:

Extremely thin: 0.00 - 0.08 mm
Very thin: 0.08 - 0.12 mm
Thin: 0.12 - 0.15 mm
Medium: 0.15 - 0.20 mm
Slightly thick: 0.20 - 0.23 mm
Thick: 0.23 - 0.33 mm
Very thick: 0.33 - 0.40 mm
Extremely Thick: greater than 0.40 mm

Let’s assume the girdle thickness = 0.2 mm, i.e. 2.8%

Total depth less girdle will be 59.8%. (Average girdle thickness can be different though).

We had calculated possible max and min HCA scores for known table and depth % (assuming pavilion and crown angles can change from 39° to 43° and from 28° to 40° correspondingly).

For 57% table and 59.8% depth we’ve got.
HCA min = 1.2
HCA max = 4.4

However, I tried to plug the measurement in to Diamond Calculator and it shows quite reasonable crown and pavilion angles for this combination of proportions, measurements, carat weight, and girdle thickness.

If you’ll get more detailed info, please let us know

 

[roksinmymind]

Lenoid,

Thanks for redoing my calculations with angles (and a different girdle assumption). I chose to do it with crown and pavillion %'s because the math was easier.^^

Anyways, given the measured size of the stone vs. it's carat weight, are there any more assumptions I could make concerning the crown and pavillion angles?

I made one when i said I "hoped" for a steeper crown angle because it would lower the HCA into FIC levels. (steeper crown angle = less spread for carat weight)

Is it wrong to do this?

Or is hope a good thing?

 

[roksinmymind]

Oh yeah,

Could you tell me what the diamond calculator predicted as my crown and pavillion angles? (I didn't know that it could do that)

I would like to compare those predicted values with the real values when I get them.

 

[roksinmymind]

OOPS,

leonid, not lenoid. ^^

 

[pricescope]

Roksinmymind,

I've got 33.6° and 41.0° crown and pavilion angles in DiamCalc using 2.8% girdle, 1.44 carat, 7.14x7.23x4.5 measurements and 57% table size.

Keep in mind these are just estimations. We don't know exact girdle thickness and measurements are only min and max (we don't know real average diameter). I also used pointed culet.

Real crown and pavilion angles can be different.

 

[roksinmymind]

Thnx leonid.

That prediction indicates a .7 TIC! I know its only a prediction, but HOPE IS a good thing.

It's strange that the GIA doesn't include more information on their certs... they measure min and max diameters so they could easily give the average diameter as well. In fact they could include a sarin report on every stone if they wanted to. Why the lack of info on their certs?

I assume its for both politics and economics- the less "objective" info they include, the more they empower the dealers and wholesalers.

Dealers (people who pay GIA for certs) can hide info from consumers... artificially inflating the value of a poorly cut stone. Maybe they fear if they include more info, people would ask more questions and actually inform themselves a bit more before they buy? An informed market would dramaticly reduce demand for the vast majority of diamonds out there.

The fact that a poor AGS report (which includes more info) can devalue a GIA cert stone (which includes less info) is a classic example.

I wish this wasn't the case, but who can argue against money?

 

[roksinmymind]

Kudos to Gary Holloway and Pricescope for developing more objective measures of cut and making them available to anyone with a internet connection, so that people such as myself can try to get more realistic assessments of a diamond before we even see it.

I hope GIA falls in line. Maybe online diamond market pressures can eventually make this a reality.

Keep crusading.