It's possible, but not probable. Probably, both players would maintain a constant win rate for infinity, but Magnus' would consistently be higher, thus allowing him to always stay ahead. (The number of wins would be much more likely to even out if Magnus were to worsen at chess over time, the 0-rated player were to improve over time, etc.)
Chess Riddle: A 0-rated player plays against Magnus…
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it depends on if you consider infinity plus 2 to be more than infinity.
This is simply a question of the value of infinity (a set of every possible number from all sets) versus a value of omega (a number that might POTENTIALLY be infinite because we don’t know the value, sometimes described as being “infinity-th” or something along those lines). As long as we assume there will be an infinite number of games, both players will have a score of omega, no matter what the other conditions will be. Since both players’ scores are omega due to the infinite number of games, Magnus and the 0-rated player will be tied for all eternity according to mathematical structure. This will work for any 2 parties playing a chess game, by the way. Even if you have a bedside lamp playing against a horse, eventually a proper chess game will emerge, and another, and an infinite series of games will somehow occur. And the lamp and the horse will also be tied by the principle of omega.
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GraysonKellogg wrote:
Riddle: Is this following Chess statement true? Why or why not? Can you formally prove or disprove it?
A 0-rated player plays against Magnus... They make essentially random moves, with a bit of strategy. Just like how I used to (and sometimes still do) play.
Magnus is playing this person. He is just as good at chess as ever.
Both people are immortal in a timeless universe. The only things there are them and the chess set. They are doomed to play Chess. Match after match. Forever.
Magnus will never ease up. He will be as merciless as ever. Both players never grow tired, physically, mentally, or of the game.
The first game commences. Magnus wins. And he wins on the second game, the third, and so on...
...But, because the 0-rated player essentially plays random moves, they will, over infinite time and infinite games, win a game, through sheer luck, just happening to pick the right moves. In fact, given all time, the 0-rated player will win infinitely many games.
However, by the same reasoning, Magnus will also win infinitely many games over infinitely many matches.
So, Magnus will most likely have more games won than the 0-rated player over any finite number of matches. But, over an infinite timespan, they are evenly matched, both having won the same number of games.
I think I got brain damage
Riddle: Is this following Chess statement true? Why or why not? Can you formally prove or disprove it?
A 0-rated player plays against Magnus... They make essentially random moves, with a bit of strategy. Just like how I used to (and sometimes still do) play.
Magnus is playing this person. He is just as good at chess as ever.
Both people are immortal in a timeless universe. The only things there are them and the chess set. They are doomed to play Chess. Match after match. Forever.
Magnus will never ease up. He will be as merciless as ever. Both players never grow tired, physically, mentally, or of the game.
The first game commences. Magnus wins. And he wins on the second game, the third, and so on...
...But, because the 0-rated player essentially plays random moves, they will, over infinite time and infinite games, win a game, through sheer luck, just happening to pick the right moves. In fact, given all time, the 0-rated player will win infinitely many games.
However, by the same reasoning, Magnus will also win infinitely many games over infinitely many matches.
So, Magnus will most likely have more games won than the 0-rated player over any finite number of matches. But, over an infinite timespan, they are evenly matched, both having won the same number of games.