it should cost 10 dollars because other players
can see it but only for some seconds
Respectfully disagree. Players like me make note of all other player's assays on paper. So no matter who does the assay, I get the information. There's already a built-in penalty for doing the assay (it takes time/food, and thereby reduces the average amount you'll win in the pub gambling after wasting time doing assays).
On the other hand, 10 dollars is a pretty small additional penalty, so it wouldn't change the gameplay much. But it also wouldn't really do anything to improve the game, either, in my opinion.... so why add a feature that doesn't really make the game better?