> If you have a proof that coin flipping will produce such a tiling with non-vanishing probability, then, presumably, embedded in your proof, you will likely fi

> If you have a proof that coin flipping will produce such a tiling with non-vanishing probability, then, presumably, embedded in your proof, you will likely find a decision procedure for producing an aperiodic tiling deterministically. I'm not sure it's obvious to expect a proof that something happens with positive probability to embed a constructive proof of existence (which seems to be what you mean). The difference between these two ideas in combinatorics is exploited with the probabilistic method (https://en.wikipedia.org/wiki/Probabilistic_method https://en.wikipedia.org/wiki/Probabilistic_method).