I am struggling to generate the number of decision functions required for this. Please assist. Also, if possible please explain concept behind this or technique required to answer such a question as am struggling to figure it out and the notes don't explain much.
Say, Dice I is conventional dice and Dice II is the one with three 2's and three 4's Now we've to identify whether it's die I or II after being told the result. Although there are 64 possible decisions functions but only 4 are meaningful, because a sane person won't say it was dice II, after seeing 1,3,5 or 6. 4 decisions functions and expected payoffs: For calculating payoffs, say our choice was decision 1, and dice was I, so We would win 1 if (1,3,5,6) lands with probability 4/6 win 0 if 4 lands with prob. 1/6 and, win 1 if 2 comes with prob. 1/6 So expected payoff is "5/6" Rest try yourself Now minimax, expected payoff and of-course common sense! , everything tells us that decision 4 is the best choice.
