Assuming use of the optimal mining pattern from this question at levels 11-15; will a diamond pickaxe on average find enough diamonds to make another before it runs out? Or, put another way, is mining for diamond with a diamond pickaxe sustainable?
Answers covering both single player and smp would be nice.
Further analysis of Diamond probabilities:
Facts we need:
- Diamond occurs in 0.12% of rock (unverified).
- 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).
- Diamond pick lasts 1563 blocks.
- 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%