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(Message started by: rozencrantz on Jun 27^th, 2010, 7:53pm)

Title: Psychology
Post by rozencrantz on Jun 27^th, 2010, 7:53pm

On another forum I frequent, we make a big deal of something we call "yomi," a psychological side of strategy that involves figuring out what the opponent plans to do, in situations where an action needs to be countered before it is taken. There is also the corollary that you try to hide your own intentions.

It's a major part of real-time and double-blind games, but I've read some things that make me think it might work in Arimaa. It seems like there is enough uncertainty in a lot of positions that knowing your opponent's strategy would be very valuable, as would concealing your own.

On the other hand, yomi plays the biggest role in games where you can clump your opponent's options into very few groups (usually two) such that you can counter one such group in one way, and the other such group in a different way. I don't know how often this happens in Arimaa, if ever.

I'm not very good at this game, so this is mostly idle speculation. Do deception, information hiding, and knowing your opponent play a role in your play? Could that kind of awareness improve it?

The idea comes from a broader theory of strategy set down by David Sirlin, a Street Fighter champion. I discovered his theories around the same time I discovered Arimaa, so I'm taking the chance to try them out as I learn.

Title: Re: Psychology
Post by Fritzlein on Jun 27^th, 2010, 11:32pm

I think there is a rather limited role for concealing one's intentions in Arimaa. The other player knows where all of your pieces are; if he doesn't know what possibilities you have, then it is equivalent to a strategic mistake on his part. To believe that your opponent will only notice your potential given an obvious move and will overlook your potential on a more subtle move is to count on your opponent to play poorly. This is either lazy (if you are winning) or desperate (if you are losing).

I admit that I have in the past played moves to confuse my opponent, particularly against bots and weak humans, but I don't feel proud of it. I consider it a bad habit, and against a player closer to my own skill it is a recipe for trouble. When my attempted slight of hand fails to be confusing, I always realize afterwards that a more straightforward move on my part would have been stronger. (Incidentally this is an argument in favor of playing more equal matches as opposed to mismatches. Against an equal opponent I know that I can't fart around. When I am looking for the objectively best move on every move, both my opponent and I learn more.)

In games of imperfect information, I can understand the vital importance of concealment and of anticipating your opponent. In Arimaa it simply doesn't apply in the same way. If my opponent has the potential for a strong goal attack, it does not matter whether he is planning that attack or not. I should not try to get into his mind and wonder whether he will be distracted by a threat to his camel on the other wing. I must give him credit for what is available on the board whether or not he sees it. Similarly if I have an attack that will succeed only if my opponent overlooks it, I must not waste time "helping him" overlook it. I must make the best available move instead of weakening myself by underestimating his abilities.

If 99of9 answers this question, I expect you will get a very different perspective. I recall from when he played more actively that he was a master of laying traps and inducing bad moves. He definitely tries to get in the mind of his opponent. However, a key turning point for me to pass him in ability was not to imitate him and get into his mind, but simply to give him more respect. When he played an apparently poor move, I needed to hesitate over the apparently crushing response and wonder if it was as good as it looked. More often than not, when 99of9 would lay a trap it would objectively weaken his position if only I would make the proper response instead of the obvious one. So instead of fighting fire with fire, i.e. instead of "playing the man" like he does, I just needed to be a notch better at "playing the board", i.e. looking for the objectively strongest move regardless of my opponent, and in particular not letting the appearance of a blunder make me move too quickly.

By the way, I put concealment, confusion, and inducing mistakes in a very different category than retaining flexibility. For example, I may be contemplating a swarm on one wing yet only use one leftover step to that purpose. My reason for not making a banzai charge immediately is not that I don't want to tip my hand, it is that I might want to do something else instead, so I don't want to commit myself too soon.

For every single Arimaa strategy, there is a counter-strategy. PMertens punished me many times for committing to one strategy and not being willing to shift gears fast enough. If I had to commit to playing for a narrow objective, a good opponent could thwart me every time. But he can't thwart every objective simultaneously. For example, if my opponent is afraid that I am going to share control of one of his traps, he may advance extra defenders to keep me from invading. If I have played well, I have retained the flexibility to take one of the newly-exposed defenders hostage instead of continuing my own advance. After the game he may say, "I thought you were going to swarm, so I stopped that." Fair enough, maybe I was going to swarm if he had done something different, but his method of stopping my swarm gave me a weakness that I could pick on.

Thus while I am not trying to deceive my opponent, I am definitely trying to remain dynamic and retain ways to hurt him no matter what he does. I am pleased whenever I make a move my opponent wasn't counting on, but I don't want the reason for surprise to be that I fooled him. I want to surprise my opponent because I saw the inherent possibilities in the position that he could have seen but didn't. I try to win by superior understanding, not by misdirection. That mindset works pretty well in Arimaa, even though I imagine it would work abysmally in imperfect information games.

Title: Re: Psychology
Post by chessandgo on Jun 28^th, 2010, 12:28pm

from a mathematical perspective, "concealing one's strategy" is not mandatory even in a game such as poker, as there always exist a Nash equilibrium (ie a strategy which is unbeatable even when the opponent knows it). So I don't expect concealing one's strategy could play an important role in arimaa (but maybe other psychological aspects could?).

Title: Re: Psychology
Post by rbarreira on Jun 28^th, 2010, 12:44pm

I liked the detailed response that Fritzlein wrote (as always), but there's one psychology aspect he didn't cover (edit - granted it was not really asked by the OP) -- the timing of moves. I read somewhere that chess players often start playing faster when they want to cause an opponent mistake. Apparently players move faster when their opponent moves fast.

Maybe this does not work well over the Internet though?

Title: Re: Psychology
Post by Fritzlein on Jun 28^th, 2010, 2:10pm

on 06/28/10 at 12:28:17, chessandgo wrote:

from a mathematical perspective, "concealing one's strategy" is not mandatory even in a game such as poker

Well, that's true in the mathematical sense of "strategy", whereby you self-randomize and the opponent doesn't know which course you have chosen. But in a practical sense of course you have to conceal (until he has called or folded) whether your all-in bet was a bluff.

Also, even in the mathematical sense of strategy, a suboptimal strategy can benefit from being unknown.

Title: Re: Psychology
Post by Fritzlein on Jun 28^th, 2010, 2:18pm

on 06/28/10 at 12:44:33, rbarreira wrote:

I read somewhere that chess players often start playing faster when they want to cause an opponent mistake. Apparently players move faster when their opponent moves fast.

I have done this too, and also generally regretted it. I have come believe that for time management, one should completely ignore the opponent's clock. Sometimes managing your own time poorly can induce your opponent to manage his time poorly, but you can't count on it. Why play worse yourself in hope of making the opponent play worse, when you can just play well?

Title: Re: Psychology
Post by Sconibulus on Jun 28^th, 2010, 3:18pm

Psychology does seem to be important, at least at lower levels of play. I've noticed that most of the time, if I can block off a sizeable chunk of the board my opponent starts playing more desperately. (if he's human, after I'd been doing that for a while Bomb and Clueless started biting me) I think that's how I won my game against Nevermind in the World League.

I've also noticed that playing to the opponent's clock is only useful in HvH games with move times of 45s per move or less, and they're already below 20-30s of reserve, otherwise it doesn't seem to do much other than get you in trouble. An exception to this, is that every once in a while if you correctly predict an opponent's move, (a non-obvious one) it can be useful to make your planned counter rapidly, as it sometimes seems to induce fear in your opponent, and can cause them to play tentatively for a few turns.

Title: Re: Psychology
Post by rozencrantz on Jun 28^th, 2010, 11:19pm

Thank you all, Fritzlein especially, you've raised some good points. It seems like both you and chessandgo are espousing a philosophy that brought me a lot of criticism when I suggested it, "assume your opponent is Capablanca, even when they aren't."

I tried some of these tactics out today, I can't say much other than that I won. As Sconibulus said, it may have only worked because of the low level of play (1100-ish). It might not have worked at all, and I just played well/got lucky in other areas.

Thanks for bringing up time. In the Go match chronicled in "The Master of Go" ("Meijin"), the challenger abused time controls and may have made the master angry enough to make his fatal blunder.

'course, in a modern match with komi, the master would have won by 1.5. I'll keep exploring.

Title: Re: Psychology
Post by 99of9 on Jun 29^th, 2010, 3:55am

Quote:

Do deception, information hiding, and knowing your opponent play a role in your play? Could that kind of awareness improve it?

Yes, yes, yes, and yes!

Knowing your opponent: The very fact that Fritz suddenly started talking about me means that he is in fact a master of this art. I don't know how much his knowledge changes his game play (apart from pausing after my blunders to wonder if I'm trying to trap him!) But it certainly changes mine - my preparation before a tournament game is usually about exactly this - trying to figure out what my opponent's usual objectives are. What does he overvalue or undervalue (in my opinion)? In the game, if you just pay a little extra attention than you think is necessary to frustrating those objectives, he will go to great extra lengths to achieve them. Meanwhile, you can do something good with the spare time.

Deception: As you can see from Fritz's answer, apparent blunders are a little too obvious. The best form of deception is where it seems that are pushing for one tactical outcome, but when there are actually two available to you (sort of like a meta-fork). Humans are not mathematics, and the raw fact is that we all overlook things. Some moves stick out to us more than others. If you take the pure mathematical view, games like arimaa are a game of playing perfectly and waiting until your opponent makes a mistake - so lets try to still play perfectly, but take the equally good options that allow more chance for an opponent error.

Information hiding: So how do we hide the surprise tactical option? One important observation is that when making four non-dependent steps, the natural human choice is to make the most important ones first. So, to hide your ploy, play its setup step last, especially if you can make it look like a regular general development step. There are other methods that pop up occasionally, but I'll stop here for now.

Title: Re: Psychology
Post by leo on Jun 29^th, 2010, 1:41pm

on 06/29/10 at 03:55:41, 99of9 wrote:

So, to hide your ploy, play its setup step last, especially if you can make it look like a regular general development step.

How sly of you :D I occasionaly ponder about step order, although rather from an esthetic point of view.

Title: Re: Psychology
Post by Fritzlein on Jun 29^th, 2010, 8:06pm

on 06/29/10 at 03:55:41, 99of9 wrote:

Knowing your opponent: The very fact that Fritz suddenly started talking about me means that he is in fact a master of this art.

There is a subtle distinction to be made here. On one level, yes, I am admitting that deception and misdirection do work, because I acknowledge that they have worked against me in the past and probably will work against me in the future. That's why I am talking about you. As you say, there are effective forms of getting into the opponent's head beyond faux blunders, such as:

Quote:

trying to figure out what my opponent's usual objectives are. What does he overvalue or undervalue (in my opinion)? In the game, if you just pay a little extra attention than you think is necessary to frustrating those objectives, he will go to great extra lengths to achieve them. Meanwhile, you can do something good with the spare time.

Indeed I have hurt myself by pursuing a plan that my opponent has stopped in advance, so your scheming does work. Sometimes. The reason I downplay the importance of such mind games is that I do not have to play along. I have a counter-measure that does not involve getting into your mind. Specifically, I can become aware of when a certain plan of operation is not objectively worthwhile, and learn to do something else in those circumstances. I don't have to realize what you are scheming in order to rise above it. As I phrased it before, your strategy of "playing the man" can be neutralized by my getting better at "playing the board". If I need anything in addition to knowledge of the game (and I am not sure I do), then self-knowledge will suffice. You I can ignore.

I quite disagree that I am a master of knowing my opponent. In your case, I am positive that I never got a step ahead of you in thinking things like, "OK, I can tell that 99of9 wants me to do Plan A, so it will really throw him off if I do Plan B." That's not my strength. What I got better at was sensing, "Given the board position, Plan A is just going to waste time. I need to change gears." Perhaps that gives the impression that I can tell what you are thinking and that I am trying to outfox you, but I'm not. I'm just trying to let go of rigid ideas so that I can play what is called for by each position.

Quote:

Humans are not mathematics, and the raw fact is that we all overlook things.

True, but given that we are all mistake-prone, what line of thought offers the best payout? Looking for mistakes that my opponent might make if I invite them? Or looking for mistakes that I might prevent myself from making if I pay better attention? For me the answer is clearly the latter.

Quote:

If you take the pure mathematical view, games like arimaa are a game of playing perfectly and waiting until your opponent makes a mistake - so lets try to still play perfectly, but take the equally good options that allow more chance for an opponent error.

It's news to me that you would reject a tricky move that might induce an error if you think the move is objectively weak. I rather got the impression that you would, at least some of the time, weight the probability of an opposing error high enough to offset the probability that your opponent might see a weakness you have unnecessarily exposed.

I may be wrong about that. Perhaps you will reject laying a trap whenever it is a trap that will hurt you if your opponent sees through it. Perhaps you will not try to induce the opponent to waste time on a strategy you have stopped in advance if you realize that stopping it in advance is actually a waste of time for you if your opponent changes gears in time. If that's how you feel, then we are actually agreeing, because what you call "good options that allow more chance for an opponent error" are just what I call retaining flexibility and having multiple threats.

Title: Re: Psychology
Post by 99of9 on Jun 30^th, 2010, 5:40am

on 06/29/10 at 20:06:09, Fritzlein wrote:

Usually I would reject it if I saw a significant weakness. The exception to this is if I consider my position to already be in serious trouble. At that stage an orderly and controlled board is obviously to my disadvantage, so I may play weak moves if they have the chance to shift the dynamics with an opponent mistake.

However, I don't usually consider it to cause a significant weakness when I spend a step or two of over-defence against a particular opponent's overvalued offence. Even if he is nimble enough to adapt and change plan, it should get him into a strategy-space he is less familiar with (but obviously it depends on the opportunity cost of that step).

Finally, calling you a master of the art was a little tongue in cheek. But you do take interest in following people's styles and games, so even if you don't take to it naturally, I think you have the necessary data available in that big brain of yours :).

Title: Re: Psychology
Post by Hippo on Jun 30^th, 2010, 2:49pm

I agree it could help to study game style of your opponent.
I did it especially against neveed in preparation for the 2nd WC round.
My plan was not to give up camel hostage and horse hostage as well ..., I just was not prepared for hostage prevention.
On the contrary I was prepared to swarm as fast as possible as it seemed to me he was not used to such positions.
I was more lucky at the end than good.

I also try to pay attention to opponent's reserve time.
When he is out of reserve time I am trying not to simplify the situation. I am trying to think on opponennts time as well and I usually improve my time reserve when he plays move I was expecting.

Title: Re: Psychology
Post by omar on Jun 30^th, 2010, 8:50pm

I tend to agree with Karl that there is no psychology involved if you are playing against an optimal player or one that strictly ignores what your intentions might be (like a bot). So psychology comes into play only if your opponent is prone to it. Most humans are quite prone to it. So I also agree with 99of9's argument. In particular "so lets try to still play perfectly, but take the equally good options that allow more chance for an opponent error". We had a discussion once about what the rating of a perfect chess player would be. 99of9 pointed out that even among perfect chess players one which tried to induce mistakes against suboptimal opponents would have a higher rating than other perfect players.

Maybe psychology would come into play more if Arimaa was played a bit like poker. On each turn the player to move has to add some fixed amount to the pot in order to make the move and continue playing; otherwise resign. The winner gets the pot. If you are much stronger than your opponent you don't want to beat them in a quick crushing way, but rather engage them in a long close game and win at the end. Sometimes you might want to let them win, but rather quickly. And of course you want to conceal your true rating by losing quickly to weak players once in a while. It would certainly lead to some spectacular games :-)

Title: Re: Psychology
Post by 99of9 on Jul 1^st, 2010, 4:59am

Even against a bot knowing your opponent helps. Deception and information hiding aren't very useful though.

Title: Re: Psychology
Post by Fritzlein on Jul 1^st, 2010, 6:09am

on 07/01/10 at 04:59:02, 99of9 wrote:

Even against a bot knowing your opponent helps. Deception and information hiding aren't very useful though.

It's funny you should say that, because it is against bots that I am most tempted to use deception. Or is deception the wrong word? If I am aware that a certain action on my part will trigger a good response from the bot, I try not to trigger that response until it is too late. I'm thinking in particular of Bomb and trap defense. Occasionally I am even aware that I can trigger a bad response, for example inducing Clueless to attack a wing that appears weak so that I can swoop in and take the attackers hostage.

I'm aware when I do this that I am probably forming bad habits, but it is made more tempting by the fact that bots are easier to manipulate into error than humans.

Title: Re: Psychology
Post by 99of9 on Jul 1^st, 2010, 4:16pm

I'm also a little confused on the exact definition of deception in a game like arimaa. But I agree with you that your "psychological" method works well against bots :).

Title: Re: Psychology
Post by aozeba on Jul 30^th, 2010, 10:43pm

I think psychology definitely helps, especially as a beginning player. Once a player has enough experience to know what to do, it may matter less.

BTW I think in my last postal mixer game with rosencrantz it seemed like he knew what I was about to do before I did it, so at least in that game it mattered!

(I timed out of that game because I didn't have internet access for a while, sorry about that rose!)

Title: Re: Psychology
Post by Fritzlein on Jul 31^st, 2010, 9:23am

The return of PMertens makes me want to recant my skepticism about the effectiveness of psychology. Apparently he knows exactly how I think, and lays traps for me knowing that I won't be able to avoid stepping in them. I don't know how else to explain that his head-to-head record against me is so much better than our respective records against the rest of the playing population would predict. He must have discovered a psychological vulnerability to exploit.