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A while ago, the computer game Infinity Blade 2 was given away for free as part of some advertisement campaign and I got myself a copy at the time.

One of the features in the game is a "gem forge", where one can put in three gems and, after a few hours, gets a different gem in return. Gems have both financial value (gems can be sold) and practical value (gems can be used to enhance fighting skills and equipment). I searched for advice about how to best use the gem forge, but found only vague rumours and incomprehensible to me lists.

To understand the gem forge better, I started taking notes about which output I got for which combination of inputs. The procedure is a bit slow, so I have only 16 data points so far, but I got a few results:

• I found two cases where the information displayed for the input gems was identical, but which resulted in different output gems. Thus, either randomness is involved, or the gems have some hidden state which is not displayed in the gem screen.
• For all 16 cases I have data for, the time to forge the new gem (in hours wall clock time) can be found by taking the price of the most expensive input gem, dividing by 15000, adding 0.25, and rounding to the nearest 30 minutes. (I found this rule using linear regression.) Let's see whether this rule allows to successfully predict the forging time for future gems.
• In all cases I observed, the sale price of the output gem was higher than the sale price of the most expensive of the input gems.
• The correlation between the sale prices of the output gem and of the most expensive input gem is higher than the correlation between output price and the sum of the input prices.

I haven't looked at other properties (shape, colour, function, etc.) of the gems yet.

If anybody knows more about the gem forge, or if there is a good reference available on the internet, I'd be happy to learn about this.

This is an excerpt from Jochen's blog.