51–60 of 81 posts
Some of the contests, you just cannot win, and all you can do is to try to minimise the damage. Some, you are almost sure to win, and is no fun playing. Close contests are thrilling, and upsets are exhilarating...
Earlier quoted context omitted.
I don't think that's a very convincing argument, in game theory you are not supposed to be helping your opponent out, except in some very specific scenarios that usually involve zero and/or one probabilities or infinities, so they don't apply to real life. Using minimax in a non-infinite iterated game like chess, with the standard goal function, I don't think it ever happens. Winning is the optimal strategy every sin…
> All iterated games in the real world have a first game as well not really. Any opponent you face in a serious tournament has played before. If he's played in major matches, you have his games to study, so he's not "helping" you. Experiment: A plays B, in two different scenarios, one where A knows all of B's prior games, and the other where he doesn't even know it's B. in which scenario would A do better?
Earlier quoted context omitted.
> All iterated games in the real world have a first game as well not really. Any opponent you face in a serious tournament has played before. If he's played in major matches, you have his games to study, so he's not "helping" you. Experiment: A plays B, in two different scenarios, one where A knows all of B's prior games, and the other where he doesn't even know it's B. in which scenario would A do better?
Right, but if not playing before or playing differently before increases the chance of victory, that's a good thing in the utility function. For example, even in a non-infinitely iterated true prisoner's dilemma, defecting is the right move. In an infinitely iterated one it's probably not, but that requires pretty sophisticated decision theory, including acausal or backwards looking analysis. In a standard forward lo…
"That's interesting. It works in practice, but will it work in theory?"
the other one, since you wondered, is:
Two economists are walking on the sidewalk and spot a $100 bill. One bends down to pick it up, but the other stops him and says, "That can't be a $100 bill. If it were, someone would have picked it up already."
Earlier quoted context omitted.
Right, but if not playing before or playing differently before increases the chance of victory, that's a good thing in the utility function. For example, even in a non-infinitely iterated true prisoner's dilemma, defecting is the right move. In an infinitely iterated one it's probably not, but that requires pretty sophisticated decision theory, including acausal or backwards looking analysis. In a standard forward lo…
You know, this reminds me of one of the few Economist Jokes I know, where the economist hears of a previously-unknown real world phenomenon: "That's interesting. It works in practice, but will it work in theory?" the other one, since you wondered, is: Two economists are walking on the sidewalk and spot a $100 bill. One bends down to pick it up, but the other stops him and says, "That can't be a $100 bill. If it were,…
In practice, Chess is not a game of perfect information, since you generally don't know which lines your opponent has prepared beforehand.
In theory, chess is a game of perfect information.
But in practice, this is only true for ~6-piece endgames: every outcome has been / can be computed. But for any middle- or early-game position, the amount of finite information greatly exceeds any person's or computer's capacity, practically speaking.
In concrete terms, the tablebase for 6-piece endgames is ~150 GiB. For 7-piece, it's 16 TiB.
I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively. This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well? But in both cases, there is perhaps still some state… At least if you’re playing a human. You might…
I find it fascinating how Chess is, in a way, stateless. Other than whether some rules like castling are still valid, you don’t need to have played the previous moves to be able to play the next moves effectively. This got me thinking: is that common in games? If I take someone’s place at a Risk board, can I play well? But in both cases, there is perhaps still some state… At least if you’re playing a human. You might…
I don't believe stockfish cares about past moves at all besides castling/en passant. It's able to evaluate a board so effectivly that it doesn't need it.
A standard optimization in chess engines is to treat a single repetition as a draw, while in competitive rules the position must be repeated twice in order for either player to claim a draw.
This works fine for playing against an infinitely good opponent, or against a clone of itself, which is how engines are usually tuned, because the repetition will be made if and only if the best evaluation under minimax is a draw, in which case a second repetition will also be optimal.
But it's not maximally exploitative against a weaker opponent. It's possible in some positions to give the opponent the choice between repeating moves and making a mistake: you can do this "for free" by giving the opponent this choice and then playing a different continuation if the opponent correctly chooses to repeat. And when annotating a human game, this bug will cause the engine to scream that the human blundered if he allows a single repetition in a winning position, whether for this reason or to gain time on the clock.
Time is also a factor - in speed chess you only uncover as much as there is time to.
Chess belongs to a class of games that are particularly interesting to study: it is a finite extensive form game which basically means the game can be modeled as a tree and requires only shared knowledge among participants, all the participants have complete shared knowledge, it’s sequential, has perfect recall (nothing prevents looking backwards at the game state), and a simple payoff function (you win if you checkm…
My thought here is that perhaps the hidden information on a chess board is in the mind of the player. Time is also a factor - in speed chess you only uncover as much as there is time to.