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Will_Sawin comments on Counterfactual Calculation and Observational Knowledge - Less Wrong
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This is the intuition I find helpful: Your decision only matters when the calculator shows odd. There is a 99% chance your decision matters if it's odd and a 1% chance your decision matters if it's not odd. Therefore the situation where you're told it's even is evidence that it's odd.
In this scenario, we are the counterfactual. The calculator really showed up odd, not even.