Profitability for Non-Chanter Jewelers?

[Verdandi]

The idea that a random result can be predicted by looking at what has come previously is known as the Gambler's Fallacy. You can Google it for more reading material than you could possibly want. For example, from The Skeptic's Dictionary: the gambler's fallacy:

This fallacy is commonly committed by gamblers who, for instance, bet on red at roulette when black has come up three times in a row. The odds of black coming up next are the same regardless of what colors have come up in previous turns.

There is also the closely related Reverse Gambler's Fallacy (bottom of that page), in which people erroneously believe that getting a string of one result means that you are more likely to get another of that same result. In our terms, this means that it is incorrect to believe that getting 10 successes in a row means you are any more likely to succeed on an 11th try.

The article on that same site about the clustering illusion explains another common misconception, that getting a bunch of the same result means that the results are not really random. On the contrary, clusters (or strings, streaks, etc) are normal and to be expected in randomness.