@Olivier5,
"How would you calculate that, again?"
Well, you can start here e.g.
https://www.youtube.com/watch?v=slf1HocG9Mk
"I made this video for mathematicians, so I did not explain the calculations, because someone with a strong background in Mathematics would figure it out pretty quickly.
(1/20)^1000 comes from assuming that we already have the 20 amino acids that are found in proteins and that they somehow can link themselves together. Each amino acid in the chain has a (1/20) chance of being right, so a 1000 amino acid chain would have a (1/20)^1000 chance of having the right sequence.
Even if we had 15 billion years (the supposed age of the universe) and we had 10^80 new "lottery tickets" (the number of individual atoms in the universe) every second, then we still do not come close to having enough "lottery tickets". The odds of winning the "Cosmic Lottery" for 1 protein is (1/20)^1000. Even if we double the supposed age of the universe to 30 billion we still do not come close.
Even if we had an obnoxiously small protein of 100 amino acids, it still does not cover the odds of winning the cosmic lottery.
Keep in mind that we would need hundreds of proteins just to have the simplest living cell, as I explain painfully in detail in the video.
Someone commented that there have been experiments that have shown that the building blocks of life could have formed naturally. This is nice, but it does not address the mathematics that I am putting forth here, because video already assumes that those building blocks are there. The argument in this video has to do with the order of the sequence of the building blocks. We can have a bunch of scrabble letters, but that does not mean that they can form a poem on their own if we drop them on the ground. Neither is there any reason to believe that amino acids (or nucleotides, or ribonucleotides for that matter) would ever form themselves into the right sequence to form a protein (or a code for just one protein) to make life possible. Also, like I mentioned in the video, hundreds of proteins would be needed just to form the simplest life forms, and I explain why."