3 ms·
The "solution" relies on the fact that positive numbers arbitrarily close to 0 are still technically positive. If you assume that the range of numbers is finite
by lonelappde 7y ago
The "solution" relies on the fact that positive numbers arbitrarily close to 0 are still technically positive. If you assume that the range of numbers is finite, the solution is much more intuitive. If you assume that the range of numbers is actually infinite, and don't use a misleading python program, a win ratio of "0.5 + unknowably arbitrarily small episilon" is the least impressive "strictly greater than 0.5" you can imagine.
You can't win real money gambling in this game if you actually have infinite range of numbers.
- dTal 7y agoThe improvement in guessing accuracy over 50% is a measure of the overlap of the density functions used by the two players (specifically, I believe it is the area under both curves). The result notes that if Player 2 uses a density function +/-inf, they can guarantee at least epsilon overlap. However, it's interesting to note that, practically speaking, if you played this game in a pub, Player 1's density function would likely be highly predictable -especially if they came up with the numbers mentally. As long as Player 2 chooses a reasonably similar density function they can likely do quite significantly better than 50%. It would take some patter, and you might lose a friend, but I could see it being possible to win "real" money this way.