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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.
After you've spent some time working in the framework of a decision theory where dynamic inconsistencies naturally Don't Happen - not because there's an extra clause forbidding them, but because the simple foundations just don't give rise to them - then an intertemporal preference reversal starts looking like just another preference reversal.
... Roughly, self-modifying capability in a classical causal decision theorist doesn't fix the problem that gives rise to the intertemporal preference reversals, it just makes one temporal self win out over all the others.
This is a genuine concern. Note that most instances of precommitment arise quite naturally due to reputational concerns: any agent which is complex enough to come up with the concept of reputation will make superficially irrational ("hawkish") choices in order not to be pushed around in the future. Moreover, precommitment is only worthwhile if it can be accurately assessed by the counterparty: an agent will not want to "generally modify its future self ... to do what its past self would have wished" unless it can gain a reputational advantage by doing so.
Eliezer, did you mean to evoke stock markets with "You could feed it to a display on people's cellphones"?
Perhaps so, but stock market investors are not trying to "strike it rich" for a single dollar, or even to earn a 3500% return. They have a large stake in the game, and their greatest worry is that a market crash may wipe out their investment.
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.