Indeed, the law of large numbers applied to quadrillions and quadrillions of atoms and essentially uncountable numbers of interactions between them yields a large likelihood for even very unlikely independent events. The important thing to remember is that bootstrapping means it only has to happen purely by chance a relatively small number of times - perhaps only once. It turns out that the number of rock clock trials are far, far fewer and they don't bootstrap and so it is much less likely for one to exist even if the independent probability may be much higher. Statistics is often paradoxical, but then again, that's why we have logical systems for dealing with it. We'd be much better off, as a species, if a better understanding of statistics and statistical analysis were more widely spread and valued. Dawkins's explaination in "climbing mount improbable" is a good one.
> the law of large numbers applied to quadrillions and quadrillions of atoms and essentially uncountable numbers of interactions between them yields a large likelihood for even very unlikely independent events
It’s not so simple. If something is extremely unlikely but also has many chances to occur, the probability of the thing occurring is a very large number divided by another very large number. In these cases, it’s not always clear if the resulting probability will be high or low.
Just stating that there are quadrillions of potential interactions is meaningless if the chances of any one forming something useful can range from one in a billion to one in a quadrillion quadrillion quadrillion. Much like zero divided by zero (or in this case infinity divided by infinity) the overall probability is pretty much undefined.
True, there's no known analytical solution to the statistical likelyhood of abiogenesis. How one defines likelihood is rather important when discussing a statistical analysis.
