The elder Free-Ride offspring has lately gotten into playing “poison”, a nim-type game for two players. You start with a pile of twelve items that are the same and one item that is different (the poison). Each turn, players can remove either one or two items from the pile. The object of the game is to leave your opponent with no option but to take the poison.
In theory, it is possible to win the game every single time if your turn is second. (Thanks to MarkP for straightening me out on this one.) What the elder Free-Ride offspring has discovered in playing with the younger Free-Ride offspring, however, is that there are circumstances in which a five-year-old will find it psychologically impossible to exercise a winning strategy even when given the second turn.
Say, for example, the twelve items that are the same are M&Ms. Even though it may be advantageous (from the point of view of sticking your opponent with the poison) to take only one M&M from the pile when it’s your turn, a five-year-old will always take two M&Ms from the pile. More M&Ms are always better than fewer, aren’t they?
Similarly, if the poison is some very attractive item (like a gingerbread person), a five-year-old who is already hell-bent on maximizing the M&M take will not feel terribly put out at being stuck with the poison. You’ve lost? How is it, then, that you’ve scored six M&Ms and a cookie?
It remains to be seen whether playing the game with dried beans and a turnip dreate conditions in which a five-year-old can develop a winning strategy.