4 ms·
The idea here is that any choice by the player yields a strategy which will not lose money, and may make money, depending on factors that are left undefined (i.
by fenomas 11y ago
The idea here is that any choice by the player yields a strategy which will not lose money, and may make money, depending on factors that are left undefined (i.e. whether or not the player and opponent choose similar numbers).
The fact that the author calls this state of affairs "a winning strategy" seems to be confusing a lot of commenters here. In practice you only benefit if your number sometimes falls between your opponent's choices, and your opponent can make the chances of that happening arbitrarily small. But suffice to say, if you actually play this game with a real opponent then the author's strategy will indeed let you win "at least as often" as choosing randomly, and possibly more often depending on how your opponent plays.
- ars 11y ago> In practice you only benefit if your number sometimes falls between your opponent's choices Or in other words if your range for random numbers is similar to the opponents range. Or in other words there is more information being transmitted here than just an envelope - you also need to know the range, making this paradox not actually a paradox.
- fenomas 11y ago> Or in other words if your range for random numbers is similar to the opponents range. There's no such animal as "the opponent's range" here. The problem doesn't specify that the opponent chooses their numbers from a range, or anything else - all that's given is that there are two numbers and we know nothing about them. And if that's the case then it follows that any random number we choose might be between them, in which case our strategy beats chance. Note that nobody's claiming our choice is likely to be between the opponent's choices, just that the possibility hasn't ruled out. None of this makes any assumptions about their numbers. If you're hung up on the possibility that the opponent chooses numbers so as to counter this strategy, the author points out elsewhere that if you pick a number from an unbounded range (like a normal distribution) then you'll have a nonzero (though vanishingly small) chance of falling between any two numbers the opponent chooses.
- marvy 11y agoNope. The article explains this poorly. This one: https://www.quantamagazine.org/20150707-can-information-rise-from-randomness/ https://www.quantamagazine.org/20150707-can-information-rise... does much better. I would have never understood how this works if I hadn't come across the quanta article myself a few days ago.