Explanation of *The Trial of the Pyx* from this article From this article, in section 1.2 The Trial of the Pyx, I'm confused about the arbitrage the author describes. Can someone explain the idea more clearly?
 A: In the trial of the Pyx, the master of the mint was required to randomly sample a small fraction of all of the coins that were supposed to be minted (say 1 in a thousand for purposes of this example.)  Suppose that the mean weight of the coins produced by the minting process was exactly correct, but the standard deviation was large (to make the example specific, suppose that the standard deviation was 2% of the correct weight.) 
After taking the random sample out for the trial of the Pyx, the master of the mint could examine the rest of the coins and select a group of 100 coins that were all 1% or more above the correct weight.  He could then melt these 100 coins down and produce 101 coins using that gold.  He'd then turn over 100 of those coins to the government and pocket one coin for himself. Multiply this by hundreds of thousands of coins per year, and the scam becomes very worthwhile.   
This scheme becomes impractical when the standard deviation of the weights of the coins is sufficiently small that it becomes hard to find coins that are overweight by enough to make the extra work worth while.  
A: An alternative answer is provided by this blog post in which someone has written a summary of the book. Basically, if the mint are weighing a hundred coins and a single coin is allowed to be off from the exact weight by up to $\pm \sigma$, then Wainer is claiming that the acceptable error for a batch of $100$ coins was set at $\pm 100\sigma$, whereas it should actually be $\pm 10\sigma$, because standard deviation scales as the square root of $n$. 
Wainer goes on to say:

... if the variability were too great, it would mean that there would be an
  unacceptably large number of too heavy coins produced that could be collected,
  melted down, and recast with the extra gold going into the pockets of
  the minter.

I would not be surprised if Wainer is getting this from Stigler in Statistics on the Table, who reports that claims of this kind are given in Sir John Craig The Mint, 1953 (which is probably the one to read if you want to know more about the Pyx.)
Specifically, Stigler says

In the mid-1600s, overweight coins were nicknamed "come-again guineas"
  by the Mint because they could be returned to be remelted and reminted
  at profit to the recieving merchant.

This suggests to me that having too much variability was allowing too many overweight coins to be minted, and people could profit simply by extracting the metal from these. I don't think Stigler is implying fraud on the part of the Mint when he refers to "the minter". It just means that whoever happened to find a coin that was too heavy had the opportunity to profit by it, and that the misunderstanding about the standard deviation was causing too many such overweight coins to be produced.
I can't find any information about fraud on the part of the Mint itself as Wainer seems to be claiming. [Edit: apparently the counterfeiter William Chaloner did accuse the Mint of doing this.]
