RC Sample Splitter Statistics

Why a splitter can mislead

A riffle splitter keeps a fraction f = 2-n of the lot after n splits. The sample is only representative on average: which particles end up on the kept side is a random draw. If the lot contains Nv ore-mineral particles, the number kept after a split with probability p = 1/2 is binomial, so the final sample has mean f Nv and variance Nv f (1 - f).

That gives the relative variance of the sample grade σ2 = 1/ns - 1/Nv with ns = f Nv. This has the same form as Gy's fundamental sampling error, σ2 = C d3 (1/Ms - 1/ML), because for a fixed lot mass the number of particles falls as 1/d3. When the sample holds only a handful of ore grains (gold, diamonds) the scatter is huge: the nugget effect.

What the simulation does

Lot mass and top size give the particle count N = M / (ρ π d3/6) with ρ = 2700 kg/m3. Each pour repeats the whole cascade of n binomial splits for the ore grains (exact for small counts, Poisson or normal approximations for large ones) and records the grade in ppm of particles. The segregation slider biases the kept-side probability to p = (1 + s)/2, which shifts the expected grade by (1 + s)n - 1.

Honest simplifications

• All particles have the same size and mass; real lots have a size distribution, and the liberation, shape and mineralogical factors in Gy's constant C are not modelled.
• The grade is a particle-count fraction, not a mass or assay grade. Drawn particles are scaled up for visibility.
• Splitter bias is a single probability, not a flow model; sample preparation and assay errors are ignored.

• Load Coarse gold nuggets and watch the histogram become skewed; add splits and see the scatter get worse, not better.
• Halve the particle size: the standard deviation falls by roughly a factor of 2.8 because there are 8 times as many particles.
• Switch on 20 % segregation: the running mean settles on a biased value no matter how many pours you average.