The ideal strategy (to expand on SI’s comment) is one where the choice conveys the position of a head and a tail coin flip.

For example, if they agreed ahead of time, that the first one to pick would pick a number where the flip before it was heads and the one after was tails.

So, if Oddetta picks 4, and Evangelina knows this, she also knows that flip 3 is heads and flip 5 is tails. She then selects between them based on what the result of flip 4 was (which she knows)

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