Completely luck-based. There are so many variables to going mining in Minecraft. How long you look, where you look or even whether or not you happen to dig into a random wall that happens to have diamonds behind it. I usually see them, if you don't see any, then your just not looking hard enough. Sometimes you get lucky and a lot of diamonds are exposed, sometimes you have to dig around a little.
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I am currently lurking more than I am posting. I haven't gone anywhere.
This question doesn't really even make sense; for example, what is the length of the tunnel, or size of the cave? You'll be guaranteed to find diamond given a long enough tunnel and/or large enough cave (the large cave systems prior to 1.7 are almost guaranteed to contain at least one vein of diamond; I average a couple dozen diamond ore per play session, although that is out of around 3,000 total ore, so they certainly aren't that common; rarely I've found none at all; some of the diamonds I find are also behind other ores, or in those caves with less than 2 blocks of space above lava, requiring mining to get through them, so they aren't visible just by looking).
I haven't found a single diamond ore in my current world.
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My avatar-Madison Gotha. She knows various weapons, she's a mage/sage, and is somewhat immortal. Madison has the capability of taming and communicating monsters, a genetic trait passed down by her father. 26 physically, 1400-something mentally, and a Lofty Peakian/Zenithian mix. Doesn't really like being called an elf and hates being called human..
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People like me, who mine waay to much are likely to find diamonds. In one trip I was capable of finding 18 diamonds. I spent nearly an hour or two doing so in deep large caves. But again, diamonds are rare, so its not likely you will always see them.
See, I assumed you were talking about missing a diamond vein while caving. It could be easy to miss any kind of ore doing that, but you may not ever go back by that area again, or even if you do, not realize you had been there.
I've never missed one while branch mining. I'm not sure how that would be possible. I guess if you were just mindlessly mining away and day-dreaming about something else, but even then, wouldn't your "muscle-memory" automatically just mine any ore you see, even if you're not really paying attention to what it is?
Minecraft is a spicy meme

I used to have a good signature, but it got nerfed.
TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.
TheMasterCaver's World - my own version of Minecraft largely based on my views of how the game should have evolved since 1.6.4.
Why do I still play in 1.6.4?
No, that's never happened to me. Probably won't they catch my eye so fast I don't miss it.
The cave was unexpectedly very big and very deep as I went
Soon I was low enough, and I found one diamond ore on the ground
I scream XD
I got 6 diamonds
(And because of my habit, I deleted my world
But if you passed by because you didn't see it, how would you know you missed it?
By going back down your mine and finding out you missed a vein of Diamond Ore.
Minecraft is a spicy meme

I've never missed one while branch mining. I'm not sure how that would be possible. I guess if you were just mindlessly mining away and day-dreaming about something else, but even then, wouldn't your "muscle-memory" automatically just mine any ore you see, even if you're not really paying attention to what it is?