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comment How to find sequence of digits in pi?
This is a good answer. But I don't think "in the vast majority of cases" is true. I would expect that $A$ would be at least as large (asymptotically) $e^{-1/16}\approx93.9\%$ of the time using hexadecimal, and so 6.1% of the time you come out ahead. (Obviously, you can't capitalize on this to shrink losslessly on average, since sending a bit to say if you're using the scheme or not obviates the benefit.)
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