For eg., if a grandmaster is given 10:1 time odds, will he be able to beat a computer? For eg, if the GM is given 120 minutes for the entire game and the computer is given 12 minutes? If not 10:1 times odds, then please mention what time odds would be required for a GM to beat a computer.
Yes. A grandmaster or a team of grandmasters can hold a draw or win against an engine when given time odds.
I think that there is a minimum time control at which an engine can perform equally good or better than a grandmaster (without time odds). I guess this number is somewhere around 2 or 3 minutes for the whole game.
Let's say for simplicity that it is 5 minutes. So the engine needs 5 minutes for the whole game to perform at a decent level. Now, how many minutes does a grandmaster need to match an engine that has 5 minutes?
It depends. In the opening, the human player needs to be well prepared. Otherwise, it doesn't matter too much if the player has 5 or 50 minutes for the opening part. In the middlegame, my guess is that the player should avoid sharp positions and go for calm waters to reach an equal or slightly better endgame. Try to keep a healthy pawn structure and find long term advantages.
The endgame is where the player has a good chance of holding a draw or winning the game. In general, the more time for middlegame and endgame, the better. I would say that around 20 minutes for the opening, 40 minutes for the middlegame and 40 minutes for the endgame should give the human player a fair chance. That gives a 20:1 ratio (engine has 5 minutes).
This is a rough guess and it needs to be tested in practice. Such a test would be interesting! If the player has a chance to practice against the engine, then the player will of course be even better prepared for a match. I guess such a preparation is pretty normal for human versus machine matches.
My guess would be that the engine's strength grows faster per additional minute than the human strength per additional 20 minutes. When the engine has 15 or 20 minutes for the whole game, it might already be difficult for the human player to match its strength, despite having extra time. Yet, a team of grandmasters should cope pretty well (given time odds).
Yes, at some ratio. But that ratio changes every day, in favor of the computer. Grandmasters are getting very slightly better over the years, while computers double in speed every few years. Maybe a GM could win with 100:1 time odds today, but they would need 1000:1 soon, and 10000:1 soon thereafter.
Your question is stated in such a way, that the answer Yes is almost certain. And I will explain why.
First of all, from mathematical (game theory) point of view, chess is an extensive-form game, which means that it has a Nash equilibrium. Taken these hard words away, this means that from a theoretical point of view, with a perfect game if a game is not a draw, than one of the players have a sure win (think about it as a forced sequence of X moves from starting position to win). So here is where certainty in my first sentence comes from. If computers will be all-powerful, no matter how small the gap will be, they will be able to draw the match (thus grandmasters would not be able to win with any gap).
This was theoretical, but with a current situation, one can always find time-odds to be able to win. For example even I would be able to win the best machine with the following timing: me 240 minutes - machine 10 seconds (try it by yourself). Note, that Sparr correctly stated that ratio will be increased every day, till may it will come to my theoretical conclusion stated in paragraph 1.
Note, that Rauans' answer does not take into account one important thing - computer is not sitting and doing nothing while you are thinking! The engine evaluates all possible positions during that time as well. So you can not really sit and wait for a lot of time, thinking that you will overwhelm the machine with your strange move.
Another important addition is to see the progress of machines and the progress of humans. Take Carlsen Magnus (the strongest human) and check his progress: from Jan 2011 to Mar 2014 he reached from 2814 to 2881. So 67 points in more than 2 years.
Take Houdini from its 1.5a release in Jan 11 to current 4 release it gained from 3200 to 3313 points. So during the same time 113 points (and you know that the higher you stand, the harder to get additional points). Also it was not running on supercomputer (but rather on an average machine : Athlon 64 X2 4600+ (2.4 GHz)). Also note that chess logic is easy to parallel and check current speed of some of the most powerful distributed hashing network running on specific dedicated hardware: 30 Peta hashes per second (30 million Gh/s)
I also advice not to listen to Fischer's comments, because Elo define a probability of winning and based on the history, it shows pretty nicely who is stronger then who on a high level. So this is not really such a stupid number.
Computers are better than us not only in middle game, they have all opening repertuar (some openings goes far than 17 moves in depths) and can include also vast amount of precalculated theoretical novelties, which non of the humans can remember, also they have all up to 7 pieces endgames (and even for a good GM it is not as easy to win queen+king vs rook+king.
No computer can be better than capablanca|fisher|kasparov? A game in 1996 showed otherwise, and this is ancient age in terms of computers (note that currently even PC on mobile phone HTC in the example is better/on the same level as Carlsen)
Time odds are irrelevant on the computational side. Computation of chess positions is easily parallelized, meaning additional computational resources can be brought to bear independently of time constraints. The linear component of the processing will be trivially small compared to the time controls.
Absolutely not, a human has no chance whatsoever to win against supercomputers these days, even at 10 to 1 ratio on time. Chess engines on supercomputers are so sophisticated these days that they can calculate up to 200 million moves per second, versus a human's ability to calculate 2 moves per second at most. Besides, the computer -- just like a human -- doesn’t wait for the opponent to make his move to start thinking; it is constantly weighing all the options even before the opponent makes its move. So I think the time ratio is irrelevant in this case.
I'd like to address a slightly different question: would a grandmaster be favored to win over a computer given time odds? I say this because even a weak player has some statistically significant probability of beating a world champion eventually, even if it took the rest of time. The answer to my modified question, I believe the answer is no.
Programs and people evaluate their opponents moves in different fashion. People can be surprised by their opponents moves, and need time to rethink the consequences. However, a computer, if left to ponder a position during its opponent's move, has already considered all meaningful replies up to its search horizon. In the limit, you essentially cut its ponder time in half, if it immediately makes its move, and only thinks on its opponents time. Now the difference in time to calculate one ply (one half move) deeper means about a 40 fold increase in processing time (the search tree grows exponentially by the branching factor, which is ~40 new moves). The additional lost time wouldn't even be able to search a single move deeper! You essentially gain 1 ply because the computer must search all your possible replies rather than the one you eventually make.
So how much is that one ply of additional search worth to the computer? In the 1980s, when search depth was small, experiments showed a program searching at a depth of 6 was 159 elo points better than one searching at a depth of 5. Later research in self play experiments went on to show that as seach depth increased, there was a diminishing return in elo gain... a single ply increase from a depth of 11 to 12 resulted in an elo gain of 84 points. Note this research is about 16 years old. Note the ratings gap between Stockfish and Magnus Carlsen is already around 450 points. Almost counter intuitively, it would seem reducing the time control could give humans the best advantage (unfortunately, assuming a human's rating doesn't also drastically decrease with less time).
I could see two possible factors that would make me change my mind.
- If diminishing returns were only a property of computers, and not humans (or the rate of change was significantly different). Suppose you matched a computer against a postal player. Perhaps the strategic decisions a human is capable, given enough time, outweigh the computer's tactical abilities. Then, with enough time, a human could potentially be favored.
- If the time odds exponentially changed per move. Give the human 1 second on the first move, one minute on the next, one hour on the following... etc etc, we could effectively force a computer to be at a perpetually greater disadvantage than 50% time odds. If the human capacity for discovering improvements truely could scale to those limits, then a computer would eventually be overwhelmed by the time advantage.
However, my final analysis puts my two caviots as unlikely scenarios, and I believe that with any time odds, a computer would likely be the favorite.
With sufficient hardware and parallel processing, it would be possible to process the positions from all of the human's possible replies, in his time, then use the results immediately for his chosen move. So through programming and hardware, it would be possible to overcome virtually any time odds.