The simplest way to solve the jester’s puzzle is to make a table of the four cases … then determine for each case whether the inscriptions are in fact true or false as required for that case. The conclusion is that the first box has the frog and the true inscription.
If you do this, the case where the second inscription is true and the first box contains a frog is also consistent.
Surely one could easily replicate this “lottery” by buying path-dependent options with low exercise probability on the financial markets. People are not doing this, so this service must be less appealing than it intuitively seems.