Yes, there are incompatible uses of the phrase "bits of evidence." In fact, the likelihood version is not compatible with itself: bits of evidence for Heads is not the same as bits of evidence against Tails. But still it has its place. Odds ratios do have that formal property. You may be interested in this wikipedia article. In that version, a bit of information advantage that you have over the market is the ability to add log(2) to your expected log wealth, betting at the market prices. If you know with certainty the value of the next coin flip, then maybe you can leverage that into arbitrarily large returns, although I think the formalism breaks down at this point.