I disagree with your characterization of Tony as betting as "only slighly irrationally". I think that 2nd place going all in (or close to it) is betting "only slightly irrationally". With both those wagers Tony would need to get FJ and have the leader miss it to win. At least with the bigger wager, his payoff is greater if he actually does win.Turd Ferguson wrote: The risk (gambit) of such a small wager is, of course, that it leaves the leader vulnerable to losing on a double get and a big "irrational" bet from second place. Part of the problem with Tony's bet is that it wasn't big enough to take the lead if William had actually tried "Pawson's Gambit" (another argument for going all in if you're betting on yourself to win) So, in this case, I think Pawson's Gambit of "assuming the trailer will bet rationally, or only slightly irrationally" would have been the optimal wager, given that Tony did the latter.
It seems that Tony did a slight variation of what we've seen many 2nd place contestants do, bet to exceed the leader's pre-FJ! score by $1. Tony's wager was a bit better than that since he avoided the leader wagering something like $2 to counter that common wager (though this strategy is most commonly seen in the QFs of tournaments when wildcards are available).