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There are a few conditions for a successful jump, but the most important one is that there is simply a 2 in 3 chance for the jump to work, so it's mainly RNG-based. 

Besides that, there is something you could call a negative jump buffer. Basically, most platformers will let you jump, even if you pressed the jump button a moment before landing. I did the complete opposite, meaning that you cannot jump for the first 0.2 seconds on the ground.

The last thing might not be a condition, but it might make it seem like your jump didn't work. After pressing the jump button, there will be a delay that lasts for 0 to 8 frames. And because your vertical speed goes downwards if you release the jump button while jumping, and you might release the button in this 8 frame window, because you probably thought the jump didn't work, you will not gain any height.