Minecraft – What are the exact percentages for likelihood of getting 3 diamonds from a diamond ore with Fortune 3

Further analysis of Diamond probabilities:

Facts we need:

1. Diamond occurs in 0.12% of rock (unverified).
2. Using an efficient strategy we can expose 16* blocks for every 4 we dig (the ascii art doesn't account for two blocks you expose in front of you, so its actually 16, not 14). This breaks down to 4 blocks per dig. We're using Strix's method because diamond ore can appear in veins of 1, so you do not want to skip over any blocks. (if someone wants to do the math for the other methods, feel free to).
3. Diamond pick lasts 1563 blocks.
4. We're assuming worst case scenario of all rocks and no caves, as caves improves diamond probability due to increased surface area with no digging required.

Simple math after this point:

1563*4*0.12% = 7.5

So you can expect to find 7.5 diamonds per diamond pick in the worst case scenario with average luck so you will increase your pick count.

You want the floor of your dig to be at level 11 to avoid dropping into lava, which makes the ceiling at level 16, which is still inside the diamond zone.

Even if the ratio is 0.09%, you should expect 5.6 diamonds per pick, you'll still average more than you spend. The break even point is ~0.048%

The first answer in the link you posted tells otherwise, mining with a diamond pickaxe for diamonds works,

1563*4*0.12% = 7.5

and you only need 3 for a pickaxe. The second poster didn't involve the fact that for each block you mine you can see 3-4 new blocks, which just might be diamonds. What he did was calculating the chance if you are mining quarry style and mine all blocks and not only the ones you need to see what all blocks contain.

BTW to improve your diamond mining I would suggest you get yourself a fortune diamond/gold pickaxe and only use it for diamonds.

Also mining for Emeralds is not worth it:

1563*4*0.12%/40 = 0.18756 Emeralds per Diamond pickaxe

Emerald Ore is approximately 1/40 as common as Diamond Ore (40 times more rare then Diamond) (174 Emerald Ore in 2382 chunks, compared to 6637 Diamond Ore). Source

And you need 10 to 11 of them. So you need around 53 pickaxes...