Game Theory - Perfect Strategy?

Sort:
u0110001101101000

If chess were no longer competitive I wouldn't play it.

Elroch

Chess will always be competitive for humans, if they can be bothered to play it, like running will always permit racing. happy.png

u0110001101101000

Yeah, and I agree with your post #83 happy.png

Kevin-J-Yuan_06
AndTheLittleOneSaid wrote:

Can't we just ask Magnus?

Bro,he never goes on chess.com only like 1 or 2 times a year

bbeltkyle89
philidor_position wrote:

It's obviously a draw with perfect play, but how does that make it exactly the same with tic tac toe? Why the rush to reach so quick conclusions? Basketball is exactly the same as football, except that it's completely different.

Is it so obvious? i like to hope that black has the ultimate zugzwang, where any move white makes is a "mistake".

u0110001101101000
bbeltkyle89 wrote:
philidor_position wrote:

It's obviously a draw with perfect play, but how does that make it exactly the same with tic tac toe? Why the rush to reach so quick conclusions? Basketball is exactly the same as football, except that it's completely different.

Is it so obvious? i like to hope that black has the ultimate zugzwang, where any move white makes is a "mistake".

I've said this a few times in the past, but I like the ideas, so I'll repeat them.

What can we say observationally about zugzwang? The chance of zugzwang is inversely proportional to the number of pieces on the board and the number of legal moves. We see in the starting position maximum pieces, and many legal moves.

What can we say observationally about drawn positions? They're proportional to symmetry and inversely proportional to threats/forcing moves (or we could say contact between the two forces). Again, we see in the starting position perfect symmetry and no threats (no contact).

So based on experience, and at a glance, it certainly seem chess is a draw.

Elubas

Something I never thought about before is that it's funny how some people like to be all sceptical about chess being a draw (like "maybe there is some insane computer-esque win here even though the position is symmetrical"), yet that same idealism is bashed mercilessly when it comes to resigning. If someone thinks there might be something outrageous in a totally lost position, that's totally unacceptable and mentally insane, but if they think a drawn position can be outright won out of nowhere, that's "sophisticated."

Elubas

Double standards: They exist in chess, too.

Elubas
0110001101101000 wrote:
Bur_Oak wrote:
Memorizing [the solution to chess] would likely be vastly more difficult than memorizing MCO.

I know this is 5 year old, but holy crap. This is like saying the sun is likely bigger than a tennis ball.

I guess his thought might have been that there is just one big solution line and you can just go down that and ignore everything else. Though that gets broken down quickly since the solution must cover every reply :)

u0110001101101000

Whenever it's the nameless faceless "them" vs the other "them" then yeah, there tends to be crazy contradictions wink.png

u0110001101101000
Elubas wrote:
0110001101101000 wrote:
Bur_Oak wrote:
Memorizing [the solution to chess] would likely be vastly more difficult than memorizing MCO.

I know this is 5 year old, but holy crap. This is like saying the sun is likely bigger than a tennis ball.

I guess his thought might have been that there is just one big solution line and you can just go down that and ignore everything else. Though that gets broken down quickly since the solution must cover every reply :)

Yeah, but anyone who's ever tried to learn... just about anything in chess... should realize that knowing 1 line amounts to nothing as soon as the opponent deviates.

I realize not everyone has though.

bbeltkyle89
0110001101101000 wrote:
bbeltkyle89 wrote:
philidor_position wrote:

It's obviously a draw with perfect play, but how does that make it exactly the same with tic tac toe? Why the rush to reach so quick conclusions? Basketball is exactly the same as football, except that it's completely different.

Is it so obvious? i like to hope that black has the ultimate zugzwang, where any move white makes is a "mistake".

I've said this a few times in the past, but I like the ideas, so I'll repeat them.

What can we say observationally about zugzwang? The chance of zugzwang is inversely proportional to the number of pieces on the board and the number of legal moves. We see in the starting position maximum pieces, and many legal moves.

What can we say observationally about drawn positions? They're proportional to symmetry and inversely proportional to threats/forcing moves (or we could say contact between the two forces). Again, we see in the starting position perfect symmetry and no threats (no contact).

So based on experience, and at a glance, it certainly seem chess is a draw.

Honestly, yes i think it might "seem" that chess is a draw.  I just dont think it is obvious....or worth finding out for that matter.

Elubas

If you watch top level chess and how hard it is for either side to take any control of the game, you'll much better understand why the opinion of chess being a draw is so strong and popular. And as I said before, the analogy to resigning applies. Let's say you lose a queen in the opening for no compensation. It's "clearly lost," but it would be impossible to prove just by listing all possible variations, because there are too many. But that's not a reason to have serious doubt about the theoretical result.

u0110001101101000

Yeah, or if you realize what the drawing margin for practically 100% of endgames is... you can't just be a little ahead and win a game of chess (with best play).

Elroch

There is sort of a race with imperfect knowledge (always the case until chess is solved). One side has a slight practical advantage (eg as assessed by a top engine, or traditionally by GM assessment), which gives it a better chance to get the opponent into a corner where it eventually turns out to be losing. But there is a contrasting effect that small advantages become increasingly likely to turn into dead draws in endgame positions because effectively there is a time limit kicking in - the practical number of moves in which an advantage might be turned into a win.

Encouragement for the majority view that chess is a draw is given by the fact that the large majority of opening lines reach a position which is considered equal, rather than leaving white with an advantage. This suggests that there is a tendency for small practical advantages present early on in most high quality openings to dissipate as black has sufficient resources to hold the position.

u0110001101101000
Elroch wrote:

Small advantages become increasingly likely to turn into dead draws in endgame positions because . . . the practical number of moves in which an advantage might be turned into a win.

What? I read this a few times and I don't understand what you're saying. Are you talking about the 50 move rule?

When I say a small advantage isn't enough to win a game, I mean like being a pawn down but the tablebase says draw. (And a pawn down is of course massive compared to usual advantages.)

Elroch

No, I am referring to the situation where a win is beyond your horizon but you know you have a practical advantage, and it turns out that as both players play apparently accurately, the advantage grows eventually into a winning one. This phenomenon happens with both strong players and computers.

The practical chance for an advantage to have time to "grow" into a win is more limited the more towards the endgame you are.

xman720
JG27Pyth wrote:

Chess may be a devilishly difficult endgame study composed by God... "White is in Zugzwang! 0-1 "

TheIronDuke
0110001101101000 wrote:
bbeltkyle89 wrote:
philidor_position wrote:

It's obviously a draw with perfect play, but how does that make it exactly the same with tic tac toe? Why the rush to reach so quick conclusions? Basketball is exactly the same as football, except that it's completely different.

Is it so obvious? i like to hope that black has the ultimate zugzwang, where any move white makes is a "mistake".

I've said this a few times in the past, but I like the ideas, so I'll repeat them.

What can we say observationally about zugzwang? The chance of zugzwang is inversely proportional to the number of pieces on the board and the number of legal moves. We see in the starting position maximum pieces, and many legal moves.

What can we say observationally about drawn positions? They're proportional to symmetry and inversely proportional to threats/forcing moves (or we could say contact between the two forces). Again, we see in the starting position perfect symmetry and no threats (no contact).

So based on experience, and at a glance, it certainly seem chess is a draw.

 

Chess doesn't have perfect symmetry, the position of the king and queen are switched for black and white, which is why if you both castle kingside you are both on the same side of the board, instead of opposite.

bbeltkyle89
TheIronDuke wrote:
0110001101101000 wrote:
bbeltkyle89 wrote:
philidor_position wrote:

It's obviously a draw with perfect play, but how does that make it exactly the same with tic tac toe? Why the rush to reach so quick conclusions? Basketball is exactly the same as football, except that it's completely different.

Is it so obvious? i like to hope that black has the ultimate zugzwang, where any move white makes is a "mistake".

I've said this a few times in the past, but I like the ideas, so I'll repeat them.

What can we say observationally about zugzwang? The chance of zugzwang is inversely proportional to the number of pieces on the board and the number of legal moves. We see in the starting position maximum pieces, and many legal moves.

What can we say observationally about drawn positions? They're proportional to symmetry and inversely proportional to threats/forcing moves (or we could say contact between the two forces). Again, we see in the starting position perfect symmetry and no threats (no contact).

So based on experience, and at a glance, it certainly seem chess is a draw.

 

Chess doesn't have perfect symmetry, the position of the king and queen are switched for black and white, which is why if you both castle kingside you are both on the same side of the board, instead of opposite.

wat? 

https://en.wikipedia.org/wiki/Reflection_symmetry