If there is complete randomness – for instance – if the bot makes completely random moves, then, within an infinite amount of time, the bot would win an infinite amount of times against a strong AI.
However, if things are not random, this is not the case. So if the 30kyu bot does not play random, then in an infinte amount of time, it might not win one game. It just depends on the way it is programmed. I suppose there is a kind of treshhold for how random it needs to be, to be able to win.
As to the monkeys and the type-writers: monkey behaviour is not random, and they would likely not even produce the lyrics of “twinkle twinkle little star” within an infinite amount of time, because their behaviour is far from random.
Again, a truely random sequence of letters of infinte length would contain shakespears works infinite times.
A bot that captures when it can, runs out of atari and avoids filling its own eyes is much stronger than a pure random bot.
A pure random bot doesn’t know when to pass, so it just keeps playing legal moves (even filling its own eyes when it happened to make some randomly) until it runs out of legal moves (because everything is suicide). So it basically always loses, except maybe when it plays against another pure random bot.
But a game between 2 pure random bots would last extremely long. It would only be stopped eventually by some repetition rule, after the board has been cleared and refilled a gazillion times.
An interesting question may be if one can construct a bot that always loses to a pure random bot.
If the weaker-than-random bot always passes while their pure random bot opponent bot fills up the board, the game will end when there is only one empty intersection left (no legal move left for pure random bot).
If you then score the game under Tromp-Taylor rules (all stones on the board after passing are alive), I guess the pure random bot would always win (assuming the number of intersection on the board is more than komi when the pure random bot has black).
In my mind, the random bot may pass at any move. There doesn’t exist any strategy that loses for sure whatever your color, since both players could use that strategy and this would lead to a contradiction.
I don’t get the point that a random bot doesn’t pass.
If I build a go bot that plays randomly, then if x is the amount of squares that can be legally played, then the amount of moves it can make is x+1, namely, any of thoses legal moves, or pass, and each would be assigned equal probability.
this bot would, sometimes, play a perfect game.
Any additional rules might make the chance smaller that it wins against a strong AI, for instance, if it would always flee from atari, and always capture a group that is in atari, because often there is a stronger move.
Maybe you have seen this video about weird chess algorithms in a competion to determine their relative Elo ratings? 30 Weird Chess Algorithms: Elo World - YouTube
Some of those are weaker than random.
A player that needs 9 stones handicap against a strong pro (about 9d EGF) would be about 1k EGF. A player that needs 9 stones against 1k EGF would be about 10k EGF, etcetera until you reach 30k.