I'd like to have an item enchanted with silk-touch, but of course the enchants are all random. Is there a combination of enchantment level and item material that would give me the best odds of getting the silk touch enchantment?
Stuart Pernsteiner's enchantment strategy guide is an excellent resource. (In theory. I haven't collected enough XP to apply it well yet, but I haven't heard anyone saying it's incorrect.) It provides tables and charts which list the conditions for the minimum XP or item cost for a given enchantment.
According to the table for Silk Touch, you typically want to be at level 50 to get the best chance, unless you are enchanting a gold tool in which case you should be level 49. However, you should still expect to enchant an average of 7 tools before getting Silk Touch rather than another enchantment.
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From looking at the Minecraft Wiki page on enchanting, it looks like the best chances of getting silk touch would come from:
The number in parentheses is the level range where you have any chance at all of getting Silk Touch. The level range outside of parentheses is where you have the maximum chance of getting Silk Touch.
Of course, even with that, you still don't have a very good chance of getting silk touch. Minecraft uses a weighting system to determine what enchantment(s) a tool gets.
So, even in the proper tool/level ranges, you would still only have a 1/18 chance of getting Silk Touch. I had hoped there was a way to be in the range of Silk Touch, but out of the range of one or more other enchantments, but no such luck. They all overlap Silk Touch.
Silk Touch can occur within a
The game then multiplies the MEL by a number ranging from .75 to 1.25 to get the final MEL. To find the range inside the parentheses, I multiplied the lower bound by 4/5, and the upper bound by 4/3. To find the range outside the parentheses, I did the opposite.
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The best way to determine your chances of getting any enchantment at any level is to run the Minecraft Enchantment Simulator (which is posted on the wiki Enchanting page) in 'Graph Levels' mode. If you want small error bars, I suggest running it in chrome with a lot of simulations (warning: CPU intensive!)
It will do many trial simulations at every level using the same enchanting algorithm Minecraft does, and give you the results, which takes into account everything - including multiple enchantments.
For a diamond pickaxe, (which most people will try for, since once acquired it will last the longest) here are the probabilities to a pretty high certainty:
Here is the generated data for the above graph (Parameters: Diamond > Pickaxe > Graph Levels > SilkTouch I > 800 x 200 simulations > Show confidence intervals ):
You can easily do this yourself for any enchantment, tool, or material.
I have done some enchanting with diamond picks and I figured out that level 50 is the best for diamond picks.