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Renall, the reason Erika would "win" if she caught team Witch in an act of fakery is that those are the rules of the game - if Battler can't fool Erika at least once, the witch side loses and that's it for Battler and Beatrice. If Battler doesn't preserve the mystery then Battler himself, Beatrice and the whole gameboard just get destroyed. Team Mystery needs to win once and then that's it for the witch.
The reason Erika "lost"(in my opinion she should have won) is Shkanontrice rearing its' ugly head again. To use the words of the translation, Erika didn't have love - which made her completely unable to see what Beatrice's answer was("No, it's a splendid trick! People without love cannot see that ...!"). Erika has no idea about any of the shkanontrice nonsense, and if shkanontrice wasn't true then she would have won the duel.
Shkanontrice is essential to Beatrice's solution actually working at all, because otherwise Kanon ends up in the room and what happened is obvious and Mystery wins. Beatrice's solution was most likely something along the lines of "Kanon rescues battler, resets the chain, hides in the closet and then "dies", leaving behind Shannon/Beatrice."
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