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I came here to quote the same sentence. Here's another way to look at it:

Suppose there actually is a best word choice. The LLM doesn't know what it is but makes a guess. Maybe it's the best one, maybe it isn't. The probability that SynthID changes the best choice to a worse one is equal to the probability that it changes a worse choice to the best one.

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I think that depends on the distribution of good choices and bad ones. There may be 10 choices and maybe 8 of them could be appropriate given a context, and 2 are absolutely nonsensical. Or it could be vice versa. And its a spectrum as well.

But the choices are weighted based on those probabilities. This doesn't affect the weightings, only how the final weighted pseudo-random selection is made.

Right, but that's what makes me doubt this statement in the comment I was replying to

> The probability that SynthID changes the best choice to a worse one is equal to the probability that it changes a worse choice to the best one.

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