It's an interesting idea.
There are about 10^50 unique positions, so even though engines are pretty good, to get any kind of statistical certainty I assume would carry a big price tag in terms of equipment and time.
Has Anyone Tried to Approach Solve Chess?
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How about using something like a weighted Monte-Carlo search to "solve" chess within a certain level of certainty? So we get something like 70% forced draw 27% forced win for white 3% forced win for black. It would be interesting to do something similar to this for various openings as well.