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You said it. It is in fact 10c6 / 30c6 = 0.00035, about 1 in 3000.
The amount of gold you will have to spend on crafting in order to obtain an item of a specified value will ALWAYS exceed the gold you can spend to get an item with the same value on the AH. This is the ONLY reason that the crafting system does not work and will continue to fail.
Economics guarantees that outcome. For anything listed on the AH comparable to that produced by crafting to sell, it must be cheaper than crafting it yourself. Unless the cost of crafting drops to the point where people wouldn't feel it's even worth it to list comparable items on the AH, that will be true. For both options to coexist, the cost of crafting must be high, or drops would have to be so rare that you couldn't reliably find whatever you want on the AH.
Unless they refuse to use the AH, for whatever reason. The new crafted items exist to provide an additional opportunity for people who refuse to use the AH to get some good gear, while simultaneously spending all the gold they're not spending on the AH.
This isn't about "reason" or "rationality". It's about satisfaction.
Increasing the main stat range is nice, but doesn't adress all the other affixes that a piece can roll, and THOSE values as well. A chest piece with 230 str but 20 vit, reduced level requirement, thorns and pickup radius is still craptastic.
Guaranteeing one of your affixes to be GG still dramatically raises the chance of the item being very good.
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