To update: Replace all instances of level 50 with level 30, redo all the math, and treat this answer as more updated than it actually is.
In Short, yes, getting to level 50 gives you the best chances of multiple high-end enchantments.
In Long:
You're kind of riding a grumpy horse on this one. You want the most efficient level to get enchantments. That would be level 50, there is no ifs, ands, or buts about it. Flat out, a higher level gives you the greatest chances of getting multiple enchants. Period.
You can still get the highest level of specific enchants at some levels lower than 50 depending on the type of item you enchant, but generally speaking, I would strongly suggest you enchant diamond tools\weapons\armor only, because they last longer so you get more bang for your 'buck' of experience. As listed on the wiki, Diamond Items don't have the best qualities for enchanting, but 1,300+ uses from a Pickaxe of Fortune III is just too good to pass up if you ask me.
Multiple Enchantments
The formulae for multiple enchants works like this:
1--After the first element is selected, there is a chance of receiving more, based on this algorithm:
2--Divide the modified level in half, rounded down. (This does not affect the possible enchantments themselves, because they were all pre-calculated in Step Two.)
3--With probability (modified level + 1) / 50, keep going. Otherwise, stop picking bonus enchantments.
4--Remove from the list of possible enchantments anything that conflicts with previously-chosen enchantments.
5--Pick one enchantment from the remaining possible enchantments (based on the weights, as before) and apply it to the item.
6--Repeat from step 1.
Now what this means for you is that the higher your MODIFIED LEVEL is during your enchantment instance, the greater chance you have for the keep going. And those two words are what gives an item multiple enchantments.
In the second step of the process, you can see that it divides your modified level in half. I will go into what a modified level is later in the post, but let's just say it's your actual level (50), for the sake of argument. Now divide 50 in half for twenty five, add one to it (26) and throw it on top of /50. That gives you just a bit better than a 50\50 shot on two enchants for your weapon. That's not bad. It gets much much worse as you keep going though. Each time the respective chances are halved. Rather than do all the math here on Gaming.SE the wiki states:
A level 50 diamond pickaxe would have a 16.10% chance to have 3 enchantments, a 48.09% chance to have exactly 2 enchantments and a 35.80% chance to have exactly 1 enchantment.
You can see there that at level 50 you actually have a Greater chance to get two enchantments than you do to get one. And only 16.10% chance to get three. If you want to get three your best chances are at level 50, and they are still not very good.
Specific Enchantments by Level
This part is somewhat less tricky because the wiki provides us with a wonderfully easy to read graph. I however, suck at Microsoft Paint, and cannot make a sexy.jpg of it. I'll do my best here.
(Modified Enchantment Level in parentheses)
Efficiency Enchantment
Level 1 (1-51) Level 2 (15-66) Level 3 (33-81) Level 4 (46-96) Level 5 (61-111)
Silk Touch Enchantment
Level 1 (25-75)
Unbreaking Enchantment
Level 1 (5-55) Level 2 (15-65) Level 3 (25-75)
Fortune Enchantment
Level 1 (20-70) Level 2 (32-82) Level 3 (44-94)
This section is pretty straightforward. If your modified enchanting level falls into any of these number brackets you have the possibility to get that enchantment.
Some notes:
This part is decided before the number of enchantments are decided. So the halving of your MEL (modified enchantment level) doesn't affect this adversely. All possible enchants are decided before the # of enchantments comes into play.
If your MEL falls into TWO different level brackets of the same enchantment, then the highest possible level is used.
You cannot get Silk Touch and Fortune. Getting one automatically disqualifies your item for the other.
Modified Enchantment Level
All that stated, you're going to need to know how to get your MEL. Which is easy.
modified enchantment level = enchantment level + Random(0, enchantability) + 1
Enchantment Level = Your Experience Level
Random(0,enchantability) + 1 = a random number between 0 and the items enchantibility, and then add 1 to that.
(enchantibility is an items enchantibility determined by the type of item it is, diamond, gold, wood, etc. These are listed on the wiki as well.)
Once you have your MEL from the above formulae, the game modifies it further one last time, either increasing or reducing it by a random percentage that caps at 25% more or less than it was originally. (100 can turn into anything from 75 to 125)
I think this is everything you would need to know. Let me know if I missed something in comments and I'll be sure to add it in or clarify it.
Let's do some experiments!
I'm going to assume we're interested in making square holes, for several reasons:
- It's easier to measure and compare that way.
- You probably want flat walls.
- If you find a good blast pattern, you can do the same thing side-by-side to clear a larger area in multiples of the pattern without wasting any blast power.
I am also going to ignore the possibility of encountering a vein of dirt or gravel, which is much easier to blast and results in much less predictability of the results due to irregular obscured shape.
That 3×3×3 cube fact is true, but only if the TNT is actually fully encased — which would be a waste of time since you would have to light the TNT and then plug the hole. The way I have used TNT to dig is to make a 3-deep hole and place TNT at the bottom of it (or drop lit TNT down from the top, which requires less careful cursor work). In addition to blowing out the cube, it will also take out nearly all of the fourth layer above (say, with one block remaining). I have found this to be a very convenient strategy.
In this case, each TNT will blow up 3×3×4 - 3 - 1 = 32 blocks, and 4 (11%) were removed by hand.
Suppose we place a single TNT on a flat stone surface and ignite it. I did this and got a 7×1×7 hole where the outside was only partly exploded, leaving 12-15 blocks [3 trials].
7 × 7 - 14 = 35 blocks, and you'll want to clear the remaining 14 (28%) by hand since they're irregularly shaped so a blast would be wasteful.
How about the same as above but with the TNT inset into the ground by 1 block? That turns out to be the same as the first case without the blocks above, so it removes only 9+8 = 17 blocks.
Let's go higher. Placing a TNT on top of some leaves (blast resistance = 1) results in another 7×7 pattern, but with only 9 blocks left unexploded.
Another block higher and there are many more blocks remaining; I'll stop here for now and assume this direction isn't useful.
So, the on-the-surface configuration blasts more area, but surely it wastes all that blast going sideways and upward. Let's try setting off a TNT in the center of a 3×3×4 hole produced by the first method (supporting the TNT with a block of leaves).
Whee! The second blast nearly perfectly enlarged the cube, leaving only 4 corner pieces. That means we destroyed 5×5×5 - 4 = 121 blocks, or 60.5 per TNT, with 3 + 4 = 7 blocks (6%) to clear by hand.
A third TNT, supported 2 spaces above with 1 block of leaves, after clearing the irregularities, resulted in an irregular 7×7×6 hole with 52 blocks left in it, meaning 7×7×6 - 52 - 7 = 235 blocks = 78.3̅ per TNT were destroyed. This is an excellent efficiency, but notice that the amount of hand-work has gone up to 59 blocks (20%).
A fourth centered blast, after clearing the irregularities, only scarred the walls a bit; I'm not going to bother working out the numbers.
In conclusion, based on the patterns I've tried, the most efficient pattern (in terms of blocks exploded per block of TNT) is three blasts at the same center point, starting with a 3-deep hole in the ground, manually smoothing off the walls between each step.
(However, these tests were conducted in creative mode, so I did not concern myself with safety (i.e. getting out of the hole). The temporary stairs required to exit after the second and third setups may affect the patterns; or you could use a water stream or drop lit TNT from a frame above.)
On the other hand, if you want to minimize manual effort while making a square hole, then I recommend using two blasts, as that has the lowest manual work percentage while still being quite efficient in TNT.
My experimental setup was a flat stone surface with a surrounding 11×11 obsidian ring to aid counting and provide a height reference in case I blew up all the surface. Shown here is the situation immediately after the fourth blast discussed above.
Also, thanks for asking this question! I have learned an improvement to my own blasting technique.
Best Answer
A larger spiral is most efficient, as you'll have less turns (you can't go up and turn) per straight track piece. For the tightest spiral, 3x3, the number of turns/straight is 1, so you'll only be climbing 50% of the time. With a 15x15 spiral, you'll only need four turns to climb 60 units. This means you can use less booster pieces at the base of each straight section to maintain maximum speed up the spiral.
As for the ratio of booster/normal pieces required to maintain maximum speed up the spiral that shouldn't be too hard to work out with trail and error.