Diamonds spawn completely randomly between Levels Y1 to Y16. On average 3.97 diamonds will spawn per chunk; but note, that's ON AVERAGE. Some chunks might not have any and other chunks might have more. I prefer digging straight down to Y12 and tunneling along on that level. The rationale for that it that most of the lava lakes top out at Y11, so I can travel farther faster just by bringing a bucket of water and turning the tops of those lakes into obsidian as I go. I'd likely find about the same number of diamonds, however, by doing the same thing on any of the levels between Y1 and Y16.
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best method to find diamonds fast