«As such, you want to pick a pair where the odds are as close to 50/50 as possible.»

This is incorrect, the correct strategy is mostly to check the most probable match (the exception being if the people in that match has less possible pairings remaining than the next most probable match).

The value of confirming a match, and thus eliminate all other pairings involving those two from the search space, is much higher than a 50/50 chance of getting a no match and only excluding that single pairing.

> This is incorrect, the correct strategy is mostly to check the most probable match (the exception being if the people in that match has less possible pairings remaining than the next most probable match).

Do you have any hard evidence, or just basing this on vibes? Because your proposed strategy is emphatically not how you maximize information gain.

Scaling up the problem to larger sizes, is it worth explicitly spending an action to confirm a match that has 99% probability? Is it worth it to (most likely) eliminate 1% of the space of outcomes (by probability)? Or would you rather halve your space?

This isn't purely hypothetical, either. The match-ups skew your probabilities such that your individual outcomes cease to be equally probable, so just looking at raw cardinalities is insufficient.

If you have a single match out of 10 pairings, and you've ruled out 8 of them directly, then if you target one of the two remaining pairs, you nominally have a 50/50 chance of getting a match (or no match!).

Meanwhile, you could have another match-up where you got 6 out of 10 pairings, and you've ruled out 2 of them (thus you have 8 remaining pairs to check, 6 of which are definitely matches). Do you spend your truth booth on the 50/50 shot (which actually will always reveal a match), or the 75/25 shot?

(I can construct examples where you have a 50/50 shot but without the guarantee on whether you reveal a match. Your information gain will still be the same.)