The answer is yes if you are calculating the weighted average of the content from the three assays. Take care that the simplified formula of Gy's theory is rarely applicable to gold ore. There are other simplified formulae dedicated to liberated gold or using specific liberation model which has to be calibrated with heterogeneity test.
If you have a good description of the mineralogy of the ore and of the gold deportment to build an heterogeneity model, it is preferable to use the general Gy's formula.

In dealing with gold, unless it is very finely disseminated, the usual approach using heterogeneity tests does not work. If you think carefully, you will come to the conclusion that the only critical aspect of sampling the ore is the number of grains of gold that are contained in your sample. going from 10 to 0.2 mm, you might deform (bend) some larger gold particles, but you will NOT break them into smaller pieces. Consequently, reducing the mass from 500 to some lower mass simply reduces the number of gold particles in the sample of smaller mass. For 30 g at 0.2 mm, the variance at 30 g is 500/30 = 16 times bigger than for the 500 g sample. Even pulverising to say 75 microns will not necessarily break gold particles; they may simply turn into flakes of the same mass. And, on top of that, you may lose some gold by smearing on the mill. With coarse gold, the solution to assay precision is to treat larger sample masses using an accelerated leaching process http://www.mineralprocesscontrol.com.au There is no smearing and much improved precision. Sample preparation is substantially simplified.

Gy's theory states that if you sum together a series of increments, you reduce the fundamental error, so the answer is yes. However, in practical terms, if I had 3 X 30g increments, and got 3 fire assays from them (one from each), and they are not reasonably close together, I would feel uncomfortable about the results, and would want to revisit the protocols for each stage of size and volume reduction.

Gy's formula like most QAQC program are design for the near perfect sample. Gy's formula is design specifically for insufficient number of samples. The problem is to differentiate the sample quality from the assay quality. Assay methods are not a problem compared to sample quality in gold (fire assay). In the case of gold, the sample quality is almost impossible to overcome when gold is "nuggety". Pierre Gy inserted the D factor in his formula to account for sample quality. It is an "arbitrary" value in practice. It represent the ratio of grain volume to surface (shape) depending on grain size distribution plus ductility of the material, inclusions, etc. These can be characterized in a mineralogy study. It does not have to be complicated but it should be systematic to figure the habit of gold in any ore. The magic number is 27 ( 3 x 3 x 3) samples in this case to cover the whole orebody. The D factor in Gy's formula maybe fixed (constant) or variable.

In fine grain and well disseminated gold ore, the probability to have many grains in each samples and further preparation is high. Hence, the sample quality is high. This has nothing to do with assay QAQC. As pointed out in the previous comments, gold behavior makes it difficult to manage in sample preparation. Solid gold grain do not break to make an homogeneous 30g portion for assay.

Increasing the portion from 1 assay-ton (30g) to 2 assay-ton (50g) will increase accuracy marginally. Duplicating assays (check, split core, etc.) does not tell you which assay is better. If you have an odd number of assays, 3 is the minimum, you can do arbitrage. Do not average the values.

Here is what I did in the past which look much like what you try to do. In narrow gold quartz veins, the area available for sampling is limited. An alternative is to split the sample in 3 as you did. It can be done at any level: take 3 samples (equal weigh) or split existing samples in 3 portions (equal weigh) with full fire assay on each. Do arbitrage on the results. It means you eliminate the minority assay results and average the majority (2 samples). The results may be low or high grade but those have better chance to represent what is going on around the sample.

This will increase highs and lows as well as grade variance. Most methods do even split and average. With average of large numbers (samples) you can only expect average results and a strong margin of error (guaranty). In many case, we should value variance because it tells us where the gold is highly concentrated. Do not mix methods in this case. Us a systematic approach in arbitrage to be fair in grade estimation.

I have done the duplicate series analysis (sample tree method) to calibrate the formula. I´m using the weighted average of the three assays, usually they are not far from each other. The idea to take 3 samples was that sometimes we would see gold nuggets (100 microns), and the assay would be 4 or 6 g/t, which I thought it was low.

I´m working with a smoky quartz that averages 7 g/t. I haven´t been able to conclude its granulochemistry, but what we see, when we see, are rarely grains over 300 microns and more often grains under 100 microns. I agree that the gold will bend, roll and might agglutinate but since I don´t know if I´m under or overestimating by crushing/grinding I´d rather do it than let a bigger grain size.

On the granulochemistry topic, I have tried to check rock samples on the microscope, I have done several fractions to check for liberated gold and last I concentrated 20 kg on a lab falcon then on a Mozley mineral separator to validate its grain size. On the rock sample since the grade is low, it is hard to find many gold grades, and when looking at comminuted fractions, the gold has already face some type of deformation that changed its original size and shape.

Use of Arbitrage is very interesting --discard the outlier and average the other two. Gold ores with coarse gold are very difficult to sample properly due to the nugget nature. It it's being done for commercial purposes, whatever procedures are used need to be documented and carefully followed uniformly.

If you are seeing particles larger than 300 microns, you have a potential coarse gold problem. Do you have vein structures where the gold clusters? By doing some gravity separation, you are on the right track but may have to treat more sample to find your larger gold particles.

On the matter of 'arbitrage', throwing out assays is not a sound practice. There is no logic in throwing information away.

The deposit here is a lode gold fault related. The ore sites at a massive vein (2 to 8 meters width) in between a banded iron formation and black shale that are folded. The gold grade is higher at the hinge zone, but it has at least 100m length depending on the level and the nuggets are disseminated there.

The gravity concentration is the method I found to try to delimitate the distribution of gold by its size, tracking how much each size of the gold nugget contribuite to the final grade.

I call coarse gold any nugget over 100 microns, which could be recovered by gravity. But I don´t know when I could state that the deposit is made of coarse gold. Is it when 80% of its grade is made of coarse grains (over 100 microns for example), or 50% coarse? Do you know how to define it?

I forgot to mention that arbitrage is the foundation of Indicator Kriging which inspired me later in my career. If you favor adding assays that are not representative and giving a minority and false value of the ore rather than use SYSTEMATICALLY the majority rule? Is that it? Or perhaps taking millions if dollars worth additional and worthless samples. Or hidding the problem of sample quality in gold behind super duper assay quality. The best assay method cannot transform a bad sample into a good sample. Arbitrage on split samples at some level works and save time and money. It is well documented in many fields and I used it successfully in mining. 

Using the fact that the number of particles of any one type (size and grade) in a broken ore follow independent Poisson distributions, it is possible to calculate the sampling distribution (not just the sampling variance as done with Gy's work) for the ore in that particular state of comminution. For gold, this is an invaluable tool for determining whether or not you are going to observe skewed or highly skewed distributions of assays at a particular aliquot mass (such as a 30 g fire assay aliquot). From a sampling viewpoint, one might choose to define a 'coarse gold' problem to be one when the sampling distribution becomes skewed. To make the calculations for a gold ore, it is necessary to know the distribution of the gold particle masses (mass fraction of the gold falling into a particular particle mass interval). At 5 g/t, if half of the grade is due to +100 micron gold, your assay distribution for 30 g aliquots will be skewed. If that particle size is 200 microns, your assay distribution will be seriously skewed and you can expect to see assays that appear to be outliers but are not. At this point, you should be using a substantially larger aliquot mass for your assaying. The solution is to go to accelerated leaching and pulverisation of your sample.

The use of the word 'representative' must be done carefully. What does the word mean - it should be taken to mean that the samples are 'fit for purpose'. Samples, be they diamond core or RC chip, must be large enough to limit the sampling uncertainty to a level that does not introduce unacceptable risk in using the number for a particular purpose. In the geostats context, and for gold, that would mean, to me, that my variogram had an acceptable low nugget value so that the regionalisation of the grade was clearly defined. Samples of too small a mass cause the nugget value to rise and are therefore not 'fit for purpose'. Larger samples would result in a lower nugget value for the variogram by reducing the analytical variance component of the nugget variance.

I don't think that there is a technical definition of when a deposit is considered to be a Coarse gold deposit or not. If you can see visible gold, that is often enough to make the decision. I think it's more important to determine when additional steps are needed to determine within the gold content with the required level of accuracy.

In an underground mine, which is the sole source of feed for a processing plant, the required level of accuracy may be ensuring that ore/waste routing calls are done properly, and ore/waste boundaries are properly distinguished.

If you are processing ore at a plant that also processes other ores, you need to a much higher level of accuracy, and precision.

A couple of practical ideas that have worked at various mine operations. First, I often suggest an experiment called "assay to extinction" for selected high-grade samples. The sample pulp (often 1,000 grams) is assayed in 30 gm or 50 gm aliquots (according to the standard protocol) until it is all consumed. A broad range of results can be reported (1 to 200 g/t in one case) and this is a good exercise to demonstrate the risks for geologists and management.

This discussion has not included the option of using a screened metallics assays. All of the pulp is screened (usually at 150 mesh) and the entire +150 mesh fraction is assayed plus 2 assays of the -150 mesh fraction. The results are then weight-averaged to achieve a better estimate of the gold content. If you are paying for 3 gold assays, this is a similar cost and a better representation of grade for a pulp.

You have made some really good points. I like the "Assaying to Extinction" exercise. Screened metallics assaying can have a lot of benefits in dealing with coarse gold. It's important when you embark on it that you understand what you are getting. Different commercial labs offer it, and what you get depends on exactly how they do it. Often there will be a sample protocol in place where all samples are fire assayed, and when the first assay returns a value above a set limit (e.g.: 10 gmt), or if visible gold is observed, there will be a re-assay by Screened metallics. That is not the technically correct thing to do, however, the result is often a population of initial fire assays, plus a population of screened metallics assays. Study of the variability between the pairs of samples can help quantify the impact of coarse free gold.

For a set of screened metallics assays, it is also useful to determine the portion of the gold contained in each sample that is concentrated in the +150 mesh fraction. If there is clearly concentration of gold in the +150 mesh fraction, it is evidence that there is value in doing the Screened Metallics assays.

Yes your comment is a very good one, especially the assay to extinction for a relatively large volume of sample. At the 50 g level, there are 20 FA aliquots that when assayed will start to display the sampling distribution for the ore under scrutiny. The high assays that appear are not 'rogue results' or outliers; they are an indication that the gold is nuggetty and in fact that the 50 g aliquot is not sufficient to obtain a clear indication of the grade of the ore. When a highly skewed distribution is discovered, the assaying should move to accelerated leaching of larger samples (> 1kg).

Consider further crushing or milling of the entire sample, prior to taking your sub samples. A more fundamental problem is that you may be taking a 500 gram sub sample from a 2 kg sample at 95% minus 10 mm, without first attempting to make more gold particles, accessible to your sampling process.

A single rock chip containing multiple gold particles, is effectively one gold particle - until broken.

When taking a sub sample, there are only two possibilities for each rock chip - so if your sampling process is a scoop, or the worlds best rotary sampling device, the rock chip falls into the reject, or - it falls into your sub sample.

A sampling device cannot discriminate between - one gold nugget, a barren rock chip, or a rock chip containing 100 gold particles - it makes no difference to the device.

If a single 10 mm rock chip, for example, containing say, 20 x 100 micron sized gold particles falls into the reject, this will eliminate any possibility, of even 1 of the 20 gold particles reaching the 500 g. sub sample.

But if you crush the same 10 mm rock chip, there is now a good chance you will now have two, or possibly, many more, smaller rock chips containing multiple gold particles.

You may not achieve the separation of all 20 individual gold particles - but in the sampling casino, two bets - or more, are better than one.

Fine crushing will not break individual gold grains to produce more gold particles - it is primarily a process to make inaccessible gold particles, accessible for a sampling process/device.

If you are using a jaw crusher or any continuous crushing ( including RC drilling ) or mill process, do not assume that rock chips containing gold will be dispersed perfectly throughout all of the sample material.

It is safer to assume the opposite, as with any continuous process, it is usually first rock in - first rock out, so expect the sample material to be layered to some degree.

Also expect segregation related to size and hardness, hard rock survives a crushing process better than soft rock - so with larger rock chips, segregation can be linked to harder materials.

It is best to assume you are dealing with layers of material and pockets of larger, segregated rock chips , so consider a mix/blend process to break up potential layers and pockets.

By crushing - you improve access to the available gold particles, but the particles may still be concentrated in layers or pockets. By mixing - you improve the spread or dispersal of these same particles, resulting in better distribution, to further improve access.

This additional work should improve the efficiency of your sampling process/device.

Subsequently, the options of the 1 kg accelerated leach or the screened fire assay methods, should have a better chance of success.

Any thoughts on the pro's and con's of a 1 kg pulverize / accelerated leach process, compared to say a 1 kg screened fire assay process ?

Having adapted 24 inch industrial sieve shakers in the past to improve the labor efficiency of sieving large 75 micron screened fire assays - I know it can be done, but labor costs remain high although capital outlay is relatively low.

Another possibility, may be to combine the pre - concentration side of the screened fire assay process, with the 1 kg accelerated leach process.

It may be possible to mill say 4 kg to 85 - 95% minus 75 microns, using a LM2 mill or similar, subsequently sieve the entire 4 kg to approximately 75% minus 75 microns using a large sieve shaker - followed by the accelerated leach on the resulting ~1 kg coarse concentrate and a 30 g assay for the fines.

The comment that most QAQC is designed for the near perfect sample, is worth keeping in mind.