Why are you minmaxing over expected values of policies, instead of over outcomes? Isn't the worst case for the "tails only" policy "I'm in COPY and the coin is heads", not "'I'm in COPY"?
Basically I don't understand why "past me, who is screaming at me from the sidelines that it matters whether I pick tails or not" once I see that the coin comes up heads is actually correct and the "me" who's indifferent is wrong; one man's modus ponens is another man's modus tollens.
Here's another example that makes my intuition go "ouch" - suppose that choosing heads in REVERSE HEADS when the coin is heads gives 0.1 utility. Then the "match the coin" policy has an expected value in REVERSE HEADS of 0.3 instead of 0.25 and the minmax rule you picked still tells you to "always pick tails", but conditioning on heads, "pick heads if you see heads" gives you 0.1 utility or 1 utility, while "always pick tails" gives you 1 utility or 0 utility, so isn't "pick heads" a better strategy?
Maybe I'm understanding this wrong... but isn't there another kind of dynamic inconsistency here?
Suppose you walk into an empty room. Then you're told you're in either WORLD A, which gives reward 1 for choosing heads and reward 0 for choosing tails, or WORLD B, which gives reward 0 for choosing heads and reward 1 for choosing tails. You have Knightian uncertainty between the worlds, so you minmax and end up indifferent between them; you arbitrarily choose heads.
Then you hear a voice:
"Actually, I flipped a fair coin that came up heads. If it had instead come up tails, in WORLD A you would have gotten reward 1 for choosing tails and reward 0 for saying heads, but in WORLD B you would have gotten 0.5 reward no matter what. (And my monologue would have changed appropriately.)"
Should you reconsider your decision to choose heads? What you learned doesn't actually change the decision you're faced with, does it?
The work of Dr. Mew and people making similar claims, such as the authors of the book "Jaws", is controversial at best.
(The comments include back-and-forth responses by the reviewers and the book's authors. Don't ignore them.)
Sports bookies deal with "investors" that have net biases - lots of people will, for example, bet on the home team because they're fans. I also have it on pretty good authority that people drastically underestimate the variance in soccer matches between closely matched teams; when the World Cup comes around, a simple strategy of "bet on the underdog in every match" makes money.
I have a bit of a dilemma. What do you say to someone who says things like "I believe in ghosts because I see and have conversations with them"? (Not a hypothetical example!)
Calculus itself isn't inherently more difficult to learn that earlier math, but it is where many math students hit a wall because it has a lot of prerequisites; if you were a mediocre student in algebra and trigonometry, there is a good chance that you will have trouble with calculus because you never completely mastered other skills that you have to use over and over again when doing calculus.
There are bootleg videos on YouTube, and if you happen to be in New York, the public library system there records all major Broadway shows and lets people watch them for free.
Reminds me of this...