If you pick up a 3x3 and turn it randomly after 2.99800 × 10^19 turns it will have a 50% chance of having been solved. I assumed that each time you turn the cube it goes into a random state but this should still be close to the answer. Turning at 10 TPS, this would take 9.5*10^10 years or 6.9...
Last night I watched Noah's video on 4bld, did one practice memo for centers and then went to sleep. This morning I woke up, spent 15 minutes really weakly memorizing the algs and then decided to do an attempt just for fun practice. It was somehow a success. I'm honestly extremely shocked...