What is the maximum amount of diamond in one Minecraft game?

I've been wondering - what is the max amount of diamonds I could potentially find in a single Minecraft world?

There is no fixed amount of Diamond per world, but let's do some math...

This is a calculation for the maximum possible amount. This will likely never happen due to the map size and vein & fortune yield chances, but you asked for the maximum, not for the average.

• a world can be 60 x 60 million blocks, that's 468,750 x 468,750 chunks = 219,726,562,500 chunks
• Diamond Ore can appear once per chunk in veins of 1-10 ores
• in the unlikely event of all veins yielding 10 ores that would be 2,197,265,625,000 ores
• mining them all with Fortune 3 could potentially drop 4 diamonds per ore
• 2,197,265,625,000 ores x 4 = 8,789,062,500,000 diamonds... happy mining.
• ...and then you can still find more diamonds in treasure chests

I know the scicraft server has like 103,000 diamonds, but in total (because the mc world is playable up to 12,000,000 blocks in X/Z, which means 750,000 chunks, with an average of 5 diamond ores per chunk) there are about 3,750,000 diamond ores you could mine.

However, with Fortune III you can on average double the diamonds you get from mining ores, so 7,500,000 diamonds, and with the scicraft RNG (random number generator) manipulator and Fortune III you quadruple your diamonds (because you always get the max of 4 diamonds per ore) so 15,000,000 diamonds.

Note: Beyond the 12,000,000 meters there are still chunks, but your game gets laggy and it's a bad time so I excluded that for the sake of having easy numbers.

Edit:

From dly's answer, there are 219,726,562,500 chunks in a 60,000,000 block wide world. On average there is one ore vein with an average of 5 ores per vein, so 1,098,632,812,500 ores in the whole world. However, as stated above, with Fortune III you can on average double your diamonds gained per ore mined, so 2,197,265,625,000 diamonds. With the RNG manipulator also mentioned above you can get the max of 4 for every ore mined, leading to 4,394,531,250,000 diamonds mineable in the whole world.

Additionally, you can find diamonds in loot chests in structures, but calculating the amount is extremely impractical. Diamonds spawn in chests in desert temples, end cities, jungle temples, mineshafts, nether fortresses, shipwrecks, tool smith and weapon smith villagers' houses, and strongholds. All of these but the last are almost unlimited in number and there are no readily accessible figures on how many there are per some amount of chunks.

However, some information can be gotten.

There are 128 strongholds in every world, and .132 diamonds in each portal room chest. So there are ~15 diamonds in all the strongholds.

Additionally, there are jungle temples in 3/4 of jungles and .273 diamonds per chest in each jungle temple, so .546 diamonds per temple, and therefore .4095 diamonds per jungle in jungle temples.

And misc data: every end city chest has ~1 diamond, and there are on average 3 chests per end city, so 3 diamonds per end city. Every 3 nether fortress chests have 1 diamond between them, and every 10 mineshaft and desert temple chests have 1 diamond between them.

If you have data on how often these structures spawn please edit this answer to include it.

If you're up for a non-mathy answer:

Infinite if you have Mystical Agriculture or Bonsai Trees installed. Just grow them.
Alternatively, sieve them from soil in Ex-Nihilo.

In all seriousness though, through normal play, it isn't feasible to get all the possible Diamond in the world. You'll only be limited to whatever you find, which at the rate they spawn at - Is unlikely for you to run out of Diamonds... if you keep on exploring outwards (generating new chunks).

So "more than enough", or what might seem like "infinity".

In minecraft 1.14.3, there is a bug with drowned where you can duplicate an item that it is holding, which makes diamonds basically infinite. Refer to other answers for older versions.