The origin of the logical coin seems relevant if you can compute it. Even if you know which side is counterfactual according to a particular logical coin, you might still be uncertain about why (whether) this coin (puzzle) was selected and not another coin that might have a different answer. This uncertainty, if allowed by the boundaries of the game, would motivate still paying up where you know reward to be logically impossible (according to the particular coin/puzzle), because it might still be possible according to other possible coins, that you can’t rule out a priori.
The origin of the logical coin seems relevant if you can compute it. Even if you know which side is counterfactual according to a particular logical coin, you might still be uncertain about why (whether) this coin (puzzle) was selected and not another coin that might have a different answer. This uncertainty, if allowed by the boundaries of the game, would motivate still paying up where you know reward to be logically impossible (according to the particular coin/puzzle), because it might still be possible according to other possible coins, that you can’t rule out a priori.