The role of luck in games like chess

I would have said that luck only comes into a game if it features some kind of randomising element, such as the roll of dice, turn of a card, etc. But there is an interesting take on the role of chance in chess (and by implication other games) in a radio interview I heard with Bill Robertie -
http://www.richardmunchkin.com/2013/09/gambling-with-edge-guest-bill-robertie.html (The bit I'm referring to starts at 35:40.)

He makes a case that it is hard to argue with, essentially that a novice can get lucky against a better player by stumbling upon the best strategy from a given position, even though the novice cannot analyse as many possibilities, nor select which ones to focus on nearly as well as the master can.

I'd never thought of it like that. If we want to identify the randomising element involved, I suppose it is whatever is going on in our brains that makes us focus on one thing over another with no particular reason.

 

Applies to Tournament Play as Well

I would agree with this theory. Given the number of moves available, there is some probability that any one of them will be chosen. These probabilities change with the skill level of the player, but I would think that the probability of a novice making the best move would never be zero. Expand this to a strategy requiring a series of moves and the probability that the novice will play the correct strategy is also then non-zero. This probability would tend to increase with the skill level of the player.

This, of course, would apply to any game involving decision making, including our own beloved blackjack tournaments. Factoring in the skill level of our opponents when betting or playing the cards often enters into our decision making process. We end up with the probabilities that our opponent will choose each of the various actions available to him. The probability that (s)he will make the best decision increases with their skill level. Even vs the most skilled opponent, luck plays a factor however, since there is always the chance that (s)he will overlook something in the heat of battle for no reason at all. I have personally been on both ends of that scenario!

 

That must be true, but I think the point being made is slightly more subtle. I probably gave a bad summary by using the word 'novice'. 'Less skilled player' would be a better term.

The idea is not that the right moves are made by complete chance, though as you say that must always be a remote possibility, but rather that in searching the game tree in order to pick a branch to follow, the more skilled player has an advantage, but the less skilled player can still find something which his opponent misses, since neither of them can analyse anything like all of the possibilities.

Robertie gives a great analogy - they are both using flashlights to hunt for treasure, hidden in a dark forest. The more skilled player has a bigger flashlight, with a wider beam, plus he has a better idea of where to shine it. But still it may be that the lesser player finds the treasure first.

That touches on the one issue I have with what Robertie says. He seems to imply that what he describes is the only mechanism by which an expert can lose to a lesser player. But human beings are not automatons; we can play below our best because we are tired or unwell, or because we have been psychologically affected by something or other (I gather chess players are quite well known for trying to psych out their opponents).

So another element of luck would be to catch your opponent on a bad day, while you yourself are on top form!

 

That is for certain, and I believe it applies for any sport when factoring that the participants are human beings.

But if we speak about chess bots of equal skill, I think the luck consists in who is awarded the white pieces, unless there is a head to head 1 round elimination tournament format where black player advances in case of a draw (or stalemate), in which case is better to be the black player.

This might be interesting: http://en.wikipedia.org/wiki/First-move_advantage_in_chess , and this: http://en.wikipedia.org/wiki/First-move_advantage_in_chess#Tournament_and_match_play

 

Yes, I agree. I wasn't trying to say that the choices are made by random chance. I was trying to say that, associated with each player, and his skill level, is a probability distribution representing the chance that he will choose a given move. For an unskilled player, the distribution will be fairly flat, reflecting that he may not know what he is looking for in a high quality choice. The more skilled the player, the higher the probability that he will select one of the more advantageous moves. Finally for a computer player, the same move will be selected 100% of the time, unless some sort of randomization or learning process is designed into the program.

The notion that there is only a given probability that a skilled player will select a given move reflects the notion that there are external factors at play, including being lucky enough not to overlook something during the decision making process due to some random distraction or state of mind.

I like this analogy and I think it is also reflected by the probability distribution model. The choices on which the light shines are the ones with the higher probability of being selected.

This discussion has piqued my interest, because it could represent a way for me to assign different skill levels to my various bots without making them too rigid or predictable. My software could analyse the effectiveness of various decisions and then assign probabilities to them being selected based on the assigned skill level of the bot. In this way, the more skilled bots will tend to make higher quality decisions, but not always "the best", and the less skilled ones could still have some chance of making the best play.

It reminds me of something my dad likes to say when something lucky happens: "Even a blind squirrel sometimes finds a nut".

 

Drawing lots to see who gets to make the first move is a detail which I conveniently ignored. That's the one element of what you might call 'conventional' luck that applies to chess. But the better player can get the white pieces and still go on to lose, for reasons that can only stem from the processes going on in the two players' brains (or CPUs, since a bot is no more guaranteed to beat a weaker opponent than a human is).

While bots always play their best games, with no errors due to fatigue etc., they must still choose a subset of the tree of possible moves and counter-moves to analyse within the time available, just as a human player must. The bot has the advantage of being able to analyse them much faster, and so tackle a larger subset, but the disadvantage of not being able to spot promising branches and disregard unpromising ones in quite the same way that a human can, utilizing experience from previous games.

So I think a bot-versus-bot contest would be a pure example of the phenomenon Robertie was describing, uncomplicated by any messy human factors.

 

Yes, sorry, on second reading I can see that is what you were saying. I don't know if you have listened to Robertie's interview, but that ties in very well with the sort of language he was using (which I may have slightly added my own spin to, in trying to summarise it).

It is my aim to give you more work to do with every post that I make.

 

Great thread, guys!

As an experienced tournament player with over 250 tournaments under my belt, and several 1st place finishes in Natinoal Open & World Open, I can certainly tell you with great confidence that there is indeed a decent amount of "luck" even in such a skill-based game like Chess!

One is playing a lower rated opponent who plays an opening you are not very familiar with.... he can get a better position as a result, and therefore have an easier transition to the middle game and have an easier game to play! Another way is if a lower rated player is better at strategy vs. tactics and the game happens to be a strategic game so therefore would yield him a better chance than the higher rated player! Even another example is if the lower rated player is better at Endgames; however, having said the above, as the rating difference increases (400 point rating diff. yields ~90% wins for the higher rated player, 800 pt. difference is ~99%!!), that "luck" factor diminishes as well!