The exo-planets were expected to be far fewer in total (rocky and gas giants), and the bias towards gas giants is quite possibly an artifact of our detection techniques which are not really fine enough to detect the smaller planets accurately, however, time will tell as we get better at that....

Agreed, the lottery example was a simplistic one... however, I do disagree with some assumptions that you make for your examples as well.

Yes, I agree that the temperature on a macroscopic scale is practically zero for increasing in the cooler to hotter direction... however, in this particular case, we aren't talking about that sort of thing. We are talking more along the lines of (given the right planet...) if some random chance of a few amino acids or otherwise forming in a soup of chemicals... and not if life would spring from the soup to a bacteria level. So, more along the lines of will a few of the molecules in your example increase in energy due to an odd collision... rather than a large scale temperature change?

Agreed that 1 in 10^50 is pretty improbable in the lifetime of the universe... IF you only attempt once every second. I would argue that you are rolling the dice orders of magnitudes greater than that, once per second is pretty damn slow! The other problem (in both your favour and mine... as it is unknown), is that we just don't know enough about the probabilities involved... orders of magnitude either way would make a huge difference!