Meanwhile, in the case where there are uncountably many chocolate NoneĬould be left at the limit, since it would have been chosen once The strategy is simply to fix anĮnumeration of all the possible chocolate types and then eat theĬhocolate available that appears earliest in that enumeration. Types, then the Glutton has a winning strategy thatĭepends only on the chocolates currently on offer, not requiringĪny knowledge of the game history.

Is allowed to extend the offers countably infinitely, and not necessarily just finitely.)įurthermore, in the case where there are only countably many possible chocolate (And this idea works even when the Chocolatier Strategy, simply by keeping track of when new chocolates are addedĪnd making sure to organize the consumption so that every chocolate New chocolate on offer is a uniquely exquisite new creation.Īs I explain at the other the post, the Glutton clearly has a winning In this post, I am interested in the version of the game where theĬhocolatier is not allowed to repeat chocolate types - each Wins if every single chocolate that was offered is eventually consumed. At each stage of play, the Chocolatier can extend finitely the chocolate assortment on offer, and the Glutton chooses from those currently available.

To recap the game quickly, the Chocolatier offers up at each stageĪ finite assortment of chocolates, and the Glutton chooses one toĮat. Introduced in my recent answer to a question of Richard

I have a question about the Chocolatier's game, which I had

Chocolatier 3 game