Thanks for moving this over.
For the snapback example, if your opponent makes a mistake, and gives you points, could that not be interpreted as increasing the value of your previously played stone(s) that setup the snapback? Go is a very dynamic game. It is impossible to predict with 100% certainty (nobody plays perfectly) how a stone will be used later in the game. A stone might become a ladder breaker 50 moves later, help to setup a better endgame posiiton (allows you to keep sente), provide ko threats, etc.
If you can’t assign a fixed, 100% certain value to a move, I contend a more appropriate view is that moves have a fluid, dynamic value which evolves with the game (and also depend on your opponent’s moves).
I understand it is generally good strategy find the most efficient and solid moves to limit the risk of complications later in the game, but there is a delicate balance between playing too slow and cautious, and overplaying and being punished. If you think you can get away with a slight overplay, you should seize the opportunity.
Higher efficiency can be achieved by making slightly greedy moves in the opening and early middle-game, with the understanding you won’t be able to save everything (playing fast and loose). Determining which stones you will need to sacrifice with 100% certainty, at the time you play them,is not possible because you do not have sufficient information about how your opponent is going to play.
I suppose you could go down the statistics rabbit-hole and try to maximize the value of each play (minimize the risk), but has anyone been able to mathematically prove that playing sequential “best moves” leads to a global optimum? I would not think this would be the case, because perfect play can only be practically achieved in the simplest of situations (L&D and endgame problems).
What are your thoughts on this (in the spirit of friendly debate)?
Well, I think there’s a slight leap here. Sure, you will make mistakes in trying to play as optimally as possible, walking as finely as possible on that line of “aggressive enough, but not enough to be punished”, but I don’t think that considering clear opponent mistakes is the way to go unless very behind and it’s a very difficult sequence to read out in the time given. Go is a very complicated game, and just playing accurately is hard enough to read out, much less trying to make calculations about “how likely the opponent is to throw away points here”, and while we often run the risk of our reading being wrong, or our intuition when the reading is not clear being wrong, I find that “trick moves” where you play moves where you have already read out the proper punishment are not actually helpful in reading in most game situations, and don’t really help improvement.
I’m not quite sure what you mean, but by the laws of game theory, all perfect information games can (theoretically) have perfect play determined by backwards induction. The issue is if the game tree is too large, it is not practical to search the entire game tree to prove you’ve found an optimal play.
4 Likes
Here is what I was thinking with the “global optimum” thing.
Consider a magical function called “winrate” that can accurately calculate the probability you’ll win a game for any game position, considering both players play perfectly for the remainder of the game.
If you choose each move so it maximizes the winrate function (“best move” calculated at that time), has it been proven that no situation can arise where playing a “sub-optimal” move can cause the winrate to end up being higher than if you played only “best moves” at some later time in the game? (Kind of like the local maximum vs global maximum of a function).
1 Like
soo… In go, with non-integer komi, this will always be a 100% or a 0%. There will always be a way one side can force a win with perfect play and you can find it via backwards induction. If there are draws, it’ll either be 100%, 0%, or whatever you would write 100% chance of jigo as, in the case where both sides can force a draw (or better if oppo makes a mistake). It’s just the nature of perfect information games.
Granted, this is practically impossible to find, as proving a solution means working through the entire game tree of go so as to eliminate all dominated strategies
4 Likes
The main thing to consider is that there is no chance involved, and neither of the players knows anything that the other player could not know.
As a result of this, anything you could think of, is something your opponent could think of as well. Thus, if you make a “losing move”, but hope that your opponent will play a mistake, then your opponent could have exactly the same thoughts as you have: that it is a losing move, and that they shouldn’t make the mistake. This same idea goes equivalently for sequences of moves, so if you’re thinking mathematically, then any possible sequence of moves is a sequence that both you and your opponent can consider. Choosing the best one out of this sequence is then a matter of finding that move so that your opponent cannot prevent you from winning. Because of the nature of the game, one of the players must be able to make such a move.
In practice, this won’t work of course, since practical players cannot consider all possible sequences of moves (there’s too many). But mathematically there’s no problem with practical limitations, and thus the magical function must be either 100% accurately predicting that you are the player with a winning strategy, or 0% if your opponent is the one with the winning strategy.
I’d go a step further, and think that for professionals it probably barely matters if they’re thinking out loud, or playing in silence.
1 Like
Thanks for the explanation. I didn’t consider that the winrate function can only return 2 values 0% and 100% for perfect play (forehead slap). That makes talking about marginally higher or lower winrates for perfect play nonsensical.
If a perfect player is playing a non-perfect player, is there any scenario (corner case) that could cause a perfect player’s winrate to momentarily toggle to 0% ?
Thanks.
I got my head twisted around thinking about calculating probabilities of making non-perfect moves. It’s been a long day.
Thanks for the help.
probably not toggle, but if the perfect player starts out on the disadvantaged side, it will briefly be 0% until the opponent makes a mistake to turn it to 100%, and then by definition there is no way for the imperfect player to force the perfect one back into a 0% state unless the perfect player turns out to not be perfect.
I wouldn’t go that far. Yes, a majority of their reading would be similar, but if they’re thinking out loud, they’re probably mentioning the most interesting parts of reading that are less likely to be noticed by the other, which would influence the other person’s judgement (as they cannot mention literally everything they’re reading unless they’re speaking inhumanly fast)
1 Like
I just got the “nice topic” award for the Go Memes Pedantry thread, which officially confers me the title of Tenured Pedant thank you for your attention
12 Likes
How about a slightly different saying:
The value of your moves depends on how you follow them up.
Just think of how the 9 stone handicap game stones value can be different depending on who wields them, and how the opponent can try for strategies to devalue them 
1 Like
My opinion is that a move’s value is determined by the possibilities that stem from it, with a weight to each possibility depending on how likely its branch is, continuing the exploration until we get to clear-cut, counted, immovable points. That’s basically how we figure out miai values for fuseki and yose, usually without the weight part because (1) it’s tedious and (2) we assume a correct count of the different optimal possibilities by both players. The advantage is that a move is worth the same no matter which player plays it, this solves the issue of “this move is good for a dan player but bad for a ddk” which can be “it’s good but complicated” instead, a solution I and assumedly most people much prefer.
My point is, a gun isn’t worthless just because you later decided to shoot at the ground instead of the zombies. A gun is a spectacular weapon, the later decision is just incredibly terrible. Same with moves imo - a move can be very good, and the follow-ups absolutely horrendous, but that doesn’t devalue the first good move, it’s just the other ones that are very very bad.
1 Like
I think there are different equivalant ways your can look move values. Here’s what we’ve covered (correct me if I’m wrong).
-
Each move has a fixed value at the time it is played, and that value only depends on the current game state. Future moves have their own values (positive or negative) and do not affect the value of previous stones.
-
Moves have a dynamic value that can be affected by other moves.
Lets say you have two state variables called “white_game_value” (WGV) and “black_game_value” (BGV), which represent the total values of all moves played for white, and all moves played for black.
All systems of tracking move values are equally valid if they provide the same difference (in whatever units that may be) between WGV and BGV at each move-number in the game.
The quantity (WGV - BGV) would be a state variable that tells you who’s ahead (in a better position to win, even if only by 0.5 point).
OK, so this last reply was not only long-winded and confusing, but wrong (I had just woke up, shoot me).
Basically the value of a move that I propose is the temperature of the position before you played it, if the opponent had all his normal canonical options, and the move you played was the only canonical option (even if it was not technically canonical in the position before you played it)
Don’t ever let me teach a CGT course 
What’s the probability that White [25k] will play the right move here?
I think about 10%. Surely probabilities depend on the player. So…
This seems like it can’t be true.
It’s definitely not worth as much without the ammo if you’re fighting zombies. In the same way if I play a move but can’t find the right follow ups to make it useful, it’s like having the gun but no ammo 
Anyway it was a meme at the end of the day.
See that’s my issue. You can get a pro to make only bad moves on purpose against a random bot and win. Are those moves good because just in case the random bot plays something threatening the pro will find the correct solution to save things? The move is good or it’s bad, but it’s not “good if you’re good and bad if you’re bad” or a bad player would only EVER make bad moves by definition. There’s no right choice if you’re bad?
2 Likes
You’re ahead of me. I’ve never taken a game theory class. Didn’t have time in school, and I can’t really see myself actually taking a class now. If I want to learn about something, I just buy a cheap used book on the subject and read it on my own time.
1 Like
oh don’t worry, it’s not normal game theory. It’s more a branch of mathematics started by John Conway and a few others.
A couple good intro texts are Winning Ways for your Mathematical Plays and Aaron Siegel’s Combinatorial Game Theory, altho it became relevant to go when Wolfe and Berlekamp published Mathematical Go: Chilling Gets the Last Point (SL link) where a certain very-late endgame position was imagined that “A 9 dan professional from the Nihon Ki-in spent 4 hours trying to solve this problem and failed”, ofc not only that, but the authors could beat the pro from both sides due to their conception of the problem using these tools (Conway apparently heard about this, and was happy that his branch of math which was inspired by go actually made a contribution to go)
6 Likes
In the absolute sense where you assume perfect play and start talking about combinatorial game theory probably not.
But in a realistic sense, we can can all put our own valuations on moves and sequences. Each pro player will have their own style which makes them value certain plays over others. When we review games we often use our own imperfect valuations to try to help other people improve at the game, and I think it works out ok.
Back to this then, we could all say “oh ho ho, perfect play…” or we could look at it as if we were reviewing a game for a friend and say, “Yeah that move was good but…” and it might end “it doesn’t work in this case” or “actually your opponent didn’t play the strongest response and you got a better result than you should of”. Then further one might say things like “oh this was the winning move of the game”, but nobody is saying “oh ho ho, every move up to this point of the game was a mistake assuming perfect play and so in essence calling this a winning move is a fallacy”.
I know we’re in a pedantry thread but still
