This reply is more about the video and one particular clip, than your message, but you did post it and I want the link back to work...
At about 2 minutes in, the Narrator introduces the cosmological constant and says cosmologists say that it must be finely tuned. Then (transcribed):
Leonard Susskind said:
The fine tunings.. how fine tuned are they?
Most of them are 1% sort of things. In other words if things are 1% different everything gets bad and the physicist could say 'maybe those are just, luck'.
On the other hand, this cosmological constant is tuned to 1 part in 10^120, 120 decimal places. Nobody thinks that's accidental. That is not a reasonable idea that something is tuned to 120 decimal places by accident. That's the most extreme example of fine tuning.
As I said before, Susskind is wrong (or had been edited so.) Here's why...
The quantity the cosmological constant is compared to is the vacuum energy density of empty space. Let's call that "V". When the theoretical physicists calculate it with their renormalization of infinity, they arise at the value V. If you plug that into the standard FLRW expansion metric for the Universe, you would see that V is a ridiculous value, causing the Universe to expand so rapidly nothing would have ever happened. As such most assumed that the true value was zero, and they just didn't know how to properly cancel the infinities.
When the cosmologists measure the acceleration of the expansion of the Universe and plugged it into the FLRW equation, the found a cosmological constant, L. When L was compared to V, they were very different, in fact:
L = V * 10^-120
This is not a "part in 10^120" error, but a multiplicative factor of 10^120 error. It is a question of accuracy, not precision.
If the calculated values are either: 0, or V, and the the measured value is V * 10^-120, then either the calculation is not done correctly, or missing important physics, or not even relevant in the first place.
A "part in 10^120" error would be if
V = 1.234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901
and
L = 1.234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678900
(I've intentionally created values with repeats so that you can see the difference in the last decimal place. Since units are arbitrary human inventions, I could always create units in which that *was* the value.)
The error, (L - V)/L = 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001.
That's a "part in 10^120" error.
The Universe also isn't anywhere near as sensitive as a "part in 10^120 error" to the cosmological constant. Life would be unaffected if it were 0. It could at least double without harm to life either. There is an upper limit to the "life safe" values of the cosmological constant, but it is somewhere around "several times" the measured value.
[Beyond this, there is no know physics for *setting* the cosmological constant if it's not the vacuum energy, so we couldn't determine a random probability for any particular value, including the one we have.]