On 06/11/2014 14:40, James Propp wrote:
Does anyone have handy a copy of Martin Baxter's article "Unfair Games", Eureka, 50 (1990), 60-68? If so, and if I'm right in suspecting that it's about games like Brussels Sprouts in which the winner is predetermined, could someone list for me the games of this kind that Baxter discusses?
I have a copy. (I didn't reply earlier because I couldn't find it. Then I looked at the big pile of junk beside my desk, and all my old Eurekas were right on top of the pile!) The discussion covers, in order: Brussels Sprouts (including the small generalization to playing on surfaces other than the plane) Nim (which of course isn't unfair in quite the same way as Brussels Sprouts, but does have the property that one who understands the game can immediately tell who can win given the initial position) Lotteries and insurance (with the usual remark that they are rather alike) Various gambling games with St-Petersburg-esque paradoxes: one where your outcome -> -oo with probability 1 even though E(outcome) = +oo, and one where at every stage E(outcome)<0 but outcome -> something positive with probability 1. Calling these all "unfair" seems a bit of a stretch to me. In view of the recent discussions of the late Alexander Grothendieck, I cannot resist quoting a pair of clerihews also found in this issue of Eureka. Pierre Deligne Invented a machine, And just for a laugh He called it SGA 4 1/2. Pierre Deligne Inventa une machine, Et pour faire rire ses amis Il l'appelait SGA 4 1/2. -- g