I think you detached them in the opposite way here. In the original problem both the conditional probability and optimal betting odds are 0.6667. In /u/4bpp version (and the version I attempted to describe) the conditional probability is still 0.6667 but the optimal betting odds go to 0.5. In your version the conditional probability is 0.5 and the optimal betting odds are 0.6667. You are correct that this is an easier way to describe how betting odds and conditional probabilities can detach.
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I think you detached them in the opposite way here. In the original problem both the conditional probability and optimal betting odds are 0.6667. In /u/4bpp version (and the version I attempted to describe) the conditional probability is still 0.6667 but the optimal betting odds go to 0.5. In your version the conditional probability is 0.5 and the optimal betting odds are 0.6667. You are correct that this is an easier way to describe how betting odds and conditional probabilities can detach.
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