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sixes_and_sevens comments on Secrets of the eliminati - Less Wrong
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Human games (of the explicit recreational kind) tend to have stopping rules isomorphic with the game's victory conditions. We would typically refer to those victory conditions as the objective of the game, and the goal of the participants. Given a complete decision tree for a game, even a messy stochastic one like Canasta, it seems possible to deduce the conditions necessary for the game to end.
An algorithm that doesn't stop (such as the blue-minimising robot) can't have anything analogous to the victory condition of a game. In that sense, its goals can't be analysed in the same way as those of a Connect Four-playing agent.
So if the blue-minimising robot was to stop after 3 months (the stop condition is measured by a timer), can we say that the robot's goal is to stay "alive" for 3 months? I cannot see a necessry link between deducing goals and stopping conditions.
A "victory condition" is another thing, but from a decision tree, can you deduce who loses (for Connect Four, perhaps it is the one who reaches the first four that loses).
By "victory condition", I mean a condition which, when met, determines the winning, losing and drawing status of all players in the game. A stopping rule is necessary for a victory condition (it's the point at which it is finally appraised), but it doesn't create a victory condition, any more than imposing a fixed stopping time on any activity creates winners and losers in that activity.
Can we know the victory condition from just watching the game?
Just to underscore a broader point: recreational games have various characteristics which don't generalise to all situations modelled game-theoretically. Most importantly, they're designed to be fun for humans to play, to have consistent and explicit rules, to finish in a finite amount of time (RISK notwithstanding), to follow some sort of narrative and to have means of unambiguously identifying winners.
Anecdotally, if you're familiar with recreational games, it's fairly straightforward to identify victory conditions in games just by watching them being played, because their conventions mean those conditions are drawn from a considerably reduced number of possibilities. There are, however, lots of edge- and corner-cases where this probably isn't possible without taking a large sample of observations.