None of the things you describe above make any significant difference in international tournament chess.
In any case, provided you use DSYoungEsq definition of “luck”, in the millieu of board/card games as “random chance”, rather than “bad opposition”, then chess is 100% pure skill. (The plus of having White is taken care of by playing each opponent twice, once with each colour).
I think there are several levels in chess, where each level will beat the next lower 100% of the time.
Call them:
beginner
club player
state player
international player
world-class player
Chronos,
why can’t I use a dice to play fully random paper-rock-scissors?
Someone skillful at a game is lucky to have that skill, so luck is always a factor.
How you define what percentage of a game is luck is not clear. As implied in the orginal question, maybe comparing winning percentage of an average player against an expert gives some indication. But doesn’t an average player possess some skill? If there is a game where an expert always breaks even with a novice, this game could be 100% luck. It could also be that the game is 100% skill, but the strategy is so simple that anyone can play at an expert level.
Chronos:
Maybe you trusted that your sister didn’t stack the deck, but with 25 matches and one mismatch she was definitely not using a regulation deck of cards.
Chronos said about rock-paper-scissors:
"Now, if I’m deciding my moves based on some non-random algorithm, it’s theoretically possible for my opponent to figure out what that algorithm is, and therefore beat me every time. This is why it’s not good from a game theory point of view. However, if I can make that algorithm complicated enough, then my (human) opponent won’t figure it out, so I’ll win despite what game theory says. "
Zzzt! Simply having a complicated strategy that the other guy can’t figure out does not in any way improve your chance of winning. After all, given what the other guy is doing, your complicated, inscrutable strategy might simply be a complicated way to lose.
To actually win consistently more than 50% of the time, your strategy has to incorporate what the other guy is going to do. This is the part you’ve left out of your analysis, and this is the part that leads to randomization: given I know that the other guy is trying to figure out my strategy, and given the payoffs in the game, my best defense is to randomize. That way, my opponent can’t second guess me, and regardless of what he does, I’m still going to win 50% of the time (ignoring draws).
(Yes, humans are lousy at randomization, but they’re also lousy at detecting statistical patterns, so it evens out. And yes, a smart player can usually beat a stupid player for a while. But you don’t need a lot of fancy math to show that. What you need the fancy math for is to examine two players of equal skill playing at their best. Or, to put it another way, the original purpose of game theory was to examine the properties of the game, not the limitations of the players. Nowadays, of course, game theory studies limitations of the players as well, but that’s another story…)
One word about the problem of producing random sequences: One way I heard of that can do this is simply to take a short glance at your watch before doing your move: If it’s an even number of seconds, you take alternative #1, with an odd number of seconds #2 (for P-R-S you have to develop a three-alternatives-scheme). Let your eyes rest on the watch several seconds, so your opponent can’t know which one of those seconds was the “decisive” one, and he can’t use his own watch to predict your next random move.
Or you prepare for the game: You do a series of coin flips or dice rolls, memorize the results, and when playing, you choose your alternatives according to that series. This will produce a perfect random sequence, and change the game into pure luck.
Of course it will. But everything else will, if your opponent detects your pattern, cause you win less than half the games, so the only sensible tactical advice in P-R-S is: Choose your moves by random; it will set your winning chances at exactly 50 %, more than every other possible plan.
I think this a fair assessment of how luck and skill combine fairly equally in backgammon. A player cannot control the dice (legally), but the skillful player can make moves based on the probability of subsequent rolls (both his and his opponent’s). This is why a more skillful player will often dominate the neophyte utterly. In just a few rolls, he can set up his blocking or completely immobilize his opponent on the bar, all the while putting his own backboard in order. I’ve done it (and seen it done) in only three or four rolls.
That said, I’ve also seen a newbie, through nothing more than the luck of the dice, totally take apart a more experienced player. Heck, it’s happened to me more than once. I’ve been beaten by someone who I know couldn’t play as well as I (based on the time it took them to make their moves, missed opportunities, and just poor choices).
Still, I think with backgammon, skill will win out over luck more often than not. But the luck factor is there just enough to make it extremely interesting.
Suppose we have a r-p-s round-robin, and the contestants are Schnitte, Lucwarm, and Bart Simpson. Each player plays 100 games against each other player, so each player will accumulate between 0 and 200 wins. (“ties” are replayed)
Since Schnitte plays randomly, he will win approximately 100 games. (50 against Bart Simpson, and 50 against Lucwarm).
Lucwarm wins approximately 150 games - 50 against Schnitte and 100 against Bart Simpson.
Bart Simpson wins a mere 50 games.
Thus, Schnitte ends up in the middle, and Lucwarm comes out on top.
How does Lucwarm win every game against Bart Simpson? By playing “paper” each and every time. (Remember, Bart Simpson’s strategy is very simple: “Good ol’ rock.”)
Now you may object and say that Bart Simpson should have played differently. And maybe he should have. But you can’t decide what strategies others should play. And as soon as a few players think (reasonably or not) that they can gain an advantage by playing non-randomly, the door is open for other players to attempt to take advantage of that non-randomness by also playing non-randomly. And so on.
Anyway, there’s no need to debate over the theory involved, because I have been speaking on the basis of experience. There happens to be a computerized r-p-s competition, and the best programs do not always play randomly – they may play randomly at times, but they also try to detect and take advantage of non-randomness on the part of their opponents.
I believe that the first competition was won by an incredibly subtle program known as “iocaine powder.”
This is true. But (as in your example) half the players who play non-randomly will come below the random guy. You can only ‘play well’ if the other guy is playing badly.
Unlike chess where you can play reasonably well and still be outplayed.
‘incredibly subtle’? No. Well designed to take advantage of opponents misplaced optimism, but still unable to beat a simple random strategy. (Of course that’s the fault of the game).
Big Blue (IBM chess program that played Kasparov) was incredibly subtle.
First of all, Deep Blue was not in the least subtle. It plays by pure brute force.
In Paper-Rock-Scissors: Suppose I’m playing in a manner I call “smart”, that is to say, I’m trying to find the pattern in my opponent’s moves. If I’m bad at this, it’ll be much the same as just moving randomly, so let’s suppose I’m good at it. Now, let’s look at my possible opponents: Opponent one tries to play randomly, but isn’t very good a it. it probably isn’t anything as simple as “good ol’ rock”, but it’s simple enough that I can analyze it. I win. Opponent two rolls a die before each move, and hence plays truly randomly. I win, lose, and draw with a 1/3 chance for each, just like I would if I were playing randomly, too. Opponents three and four are also playing “smart”. Opponent three isn’t as good at it as I am, so I’m figuring out his algorithm and foiling his prediction efforts, and beating him. Opponent four is better than I am, so he’s foiling my efforts, and he beats me.
In other words, if I’m playing smart, then the only way that someone can beat me is to do the same thing that I’m doing, but better. As Wumpus points out, an experienced player will beat an inexperienced player for a while, but that’s the defining characteristic of a game of (at least partly) skill.
Quoth manlob:
You’re right, it wasn’t actually 25 matches. We always played that after a match, you played three cards face down, to add to the spoils.
This applies if I am in the incredibly lucky position to meet a player like Bart (anywhay, it could still be a trap: Bart could have done rock 20 times, but it doesn’t necessarily mean he’ll do so the 21[sup]st[/sup] time; he wants me to think so, so I choose paper, and he smashes me away with his scissors. After I’ve seen he chose rock once again, I have no proof for the theory he’s going to do rocks the 22[sup]nd[/sup] time, and so on… )
But the interesting thing is: Every pattern, however complicated, will push me below 50 % if detected by my opponent. I agree completetly with Glee: You can only ‘play well’ if the other guy is playing badly. And “badly” means : Everything except random, because those sophisticated software players will detect every pattern in my thoughts. I don’t doubt Iocaine Powder will win against me if I do NOT play random, so what shall I do? Play random. Trying to detect Iocaine Powder’s pattern would be useless, since it doesn’t have one.
If two experienced players meet, it will maybe always end up in pure random, since both expect the other one will detect every pattern. If my opponent has a pattern, I will of course not play random but the appropriate answers to my oppononet’s customs. But I do not expect to find such an opponent.
Well, I suppose we shouldn’t get into a debate over this, since it’s GQ, but, let me just say that when I first heard (on slashdot) that there was a computerized rock-paper-scissors competition, my initial reaction was pretty similar to what I’m hearing here: “What’s the big deal? Just play randomly.”
But, after reading the web page set up for the competition; looking at the results; and reading the description of “Iocaine Powder,” I came to the conclusion that rock-paper-scissors is a much more complicated and subtle game than it seems, and that “Iocaine Powder” is a brilliant program.
As far as whether playing non-randomly necessarily constitutes “playing badly,” consider the following example:
You play randomly the first 80 rounds. Each of those rounds, your opponent plays “rock.” Would it be “playing badly” to intentionally play “paper” on the 81st round, and then switch back to random play?
Iocaine’s basic strategy is pretty simple: 1) If Iocaine Powder detects a pattern in the opponent’s play, it attempts to exploit it. (This is where all the subtlety comes in.) 2) If Iocaine Powder is getting whupped by the opponent, it plays randomly.
So the fancy strategizing is only used against poor players. Against a good player, Iocaine Powder plays randomly, just as in the classical game-theoretic analysis. As Scnitte suggests, this it why there is no professional Rock-Paper-Scissors–a match between an amateur and a grandmaster is more interesting than watching two grandmasters play against each other randomly!
Of course, some people disagree. For some laughs, check out:
Ahh, but how do you know whether you are playing a good player or a poor player? And how do you know whether you are about to take advantage of your opponent’s weak play or if you are walking into a trap? Moreover, even if you know for a fact that your opponent is poor, how do you take full advantage of his weaknesses?
The answers to these questions are non-trivial. Iocaine powder embodies elegant, but not necessarily optimal, solutions to these problems.
It’s worth noting that at a more recent r-s-p round-robin competition, iocaine powder was soundly defeated by another program.
Anyway, I agree that playing randomly is the game-theoretic “minimax” strategy - the best strategy to play if your opponent knows your strategy in advance.
Just as an interjection, if anyone here believes that Poker is a game of luck, please send them to my house for a chance to “try their luck” at my dining room table.
lucwarm said: If you don’t know whether your opponent is smart or dumb, your comments about detecting and exploiting an opponent’s weaknesses are spot-on.
However, there are lots of situations where you know perfectly well that your opponent is smart. Ranked chess players playing each other is one example. If one grandmaster is playing another, it’s no use for one to pretend that this is the first time he’s ever played the game!
The round-robin computer program tournament we’ve been referring to didn’t consist only of bots submitted by contestants. Various suboptimal pattern-based bots were also part of the tournament as dummy players. In other words, the tournament was padded with stupid players to give pattern-detection programs something to chew on. See:
I think you’re confusing Deep Blue with a $50 chess program!
Deep Blue was an 7 year IBM project which cost hundreds of millions of dollars, involving a team of full-time programmers and a US Grandmaster. It used 256 parallel processors (not bad for 1996), and the team undoubtedly analysed all of Kasparov’s published games before selecting their opening strategy. Deep Blue also had the Thompson database for all 5 piece endings, so would play perfectly in all those positions.
Yes, the heart of any chess computer program is an attempt to analyse ahead, then assess the resulting positions, but I don’t think this deserves the epithet of pure brute force.
Suppose a Paper-Rock-Scissors computer met the same opening sequence of 10 moves by each side. Wouldn’t it **always **predict the same move?
I don’t see how this is ‘incredibly subtle’.
As you know, my problem with the Paper-Rock-Scissors game is that a ‘World Champion’ can be held to a draw by any beginner with a dice.
I agree that a program that attempts to detect patterns is extremely interesting, but perhaps we need a better framework to see how good the programming is.
True, but also the only way you can drop below 50% is to use a ‘strategy’.
Chronos,
have you looked at my thread in IMHO about random chess moves?
It’s called chess test, but I don’t know how to reference it better than this:
And yes, a smart player can usually beat a stupid player for a while. But you don’t need a lot of fancy math to show that. What you need the fancy math for is to examine two players of equal skill playing at their best. Or, to put it another way, the original purpose of game theory was to examine the properties of the game, not the limitations of the players. Nowadays, of course, game theory studies limitations of the players as well, but that’s another story…)