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James_Miller comments on Is the potential astronomical waste in our universe too small to care about? - Less Wrong
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Although this is fighting the hypothetical, I think that the universe is almost certainly infinite because observers such as myself will be much more common in infinite than finite universes. Plus, as I'm sure you realize, the non-zero probability that the universe can support an infinite number of computations means that the expected number of computations we expect to be performed in our universe is infinite.
As Bostrom has written, if the universe is infinite then it might be that nothing we do matters so perhaps your argument is correct but with the wrong sign.
Forget the erroneous probabalistic argument: it doesn't matter if the universe is infinite. What we see of it will always be finite, due to inflation.
Where do you get the non-zero probability from? If it's from the general idea that nothing has zero probability, this proves too much. On the same principle, every action has non-zero probability of infinite positive utility and of infinite negative utility. This makes expected utility calculations impossible, because Inf - Inf = NaN.
I consider this a strong argument against the principle, often cited on LW, that "0 and 1 are not probabilities". It makes sense as a slogan for a certain idea, but not as mathematics.
I'm not certain of this, but my guess is that most physicists would assign much great than, say, .0001 probability to the universe being infinite.