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Topic: risk reward? Where are we strategy-wise? (Read 3352 times) |
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ginrunner
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risk reward? Where are we strategy-wise?
« on: Sep 6th, 2011, 12:23am » |
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I apologize, I had a bit of trouble putting my thoughts into words here.
I have noticed recently a sort of pattern in myself (and maybe others in the community have noticed similar things) in regards to strategy. From my understanding when Arimaa first began playing a defensive home strategy was king. I can understand this because playing at home is much much easier than playing away and so everyone was good at it but then people figured out swarming and offensive games became viable (thankfully or else Arimaa would have been a dull game if defense was the only option). Which leads to my observation, I was a defensive player when I first began, out of ease and learning, and then became an extremely offensive player to a fault, out of personality and how I play games. Very recently I have been trying to hold back and play more defensively and in doing so have notice some themes.
1) Most obvious is when playing defensively I can predict my offensive opponent's plan and move accordingly. He-ray for learning!
2) Arimaa has many "tricks" just like chess where if one player can position in a seemingly harmless way can within a few moves dictate a new and deadly position for the opponent. This means just like in chess tables can be created for more positions than just end game.
3) This is sort of an assumption but in a game where absolutely no mistakes are made the more offensive person will win or the game will draw. I base this assumption primarily on my new and slightly less primitive understanding forcing positions, gaining "time", and controlling space. While it is harder to play offense and so therefor more likely to make a mistake, if a player can traverse the board without blundering in the slightest (and the opponent plays a perfect defensive turtle) the offensive player will force the defensive one into ever increasingly tighter position and open up more doors for themselves. Again this is an assumption because I have yet to play a perfect game.
So onto the title. Risk Reward. Since playing a blunderless game is virtually impossible I would think a style of thinking in which a player has an attacking notion in mind and doesn't fall for any "tricks" will win more on average. I sort of have many of the games between Fritz and C&G in mind here. It seems as though each is always pushing forward trying to generate something and they have played each other so many times that they typically don't lose out on any obvious "tricks" or stylistic moves. Also, there are a few positions I have looked at that initially seemed innocuous or even preferable to one player that ended up swinging in the complete opposite direction.
Does anyone else have any thoughts or theories. Is the future of Arimaa just like chess where tables can be used in more positions than one realizes. Is perfect offense better than perfect defense?
Also, could a Deep Blue be made if all of the tables are found and implemented. It would seem that strategy (human dominance) could be turned into extended tactics of maybe 5, 10, 15 forced moves (computer dominance).
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Fritzlein
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Re: risk reward? Where are we strategy-wise?
« Reply #1 on: Sep 6th, 2011, 8:14am » |
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Short answer: I wish I knew.
Long answer: If Arimaa is ever understood to the point where you can make a table that says, "Whenever my opponent tries X, I can stop it with Y," then Arimaa will be dead. If you have such a table in your mind, I sincerely hope it is wrong.
Similarly, if there is nothing left to do when both the players see all the "tricks", then Arimaa is dead. For me, however, that is so far from happening that I don't even think about the possibility. In practice I find that better strategy naturally leads to better positions without requiring anyone to blunder. Sure, most games are decided by blunder, but if there were no blunders the games would nevertheless be decided, or so it seems.
on Sep 6th, 2011, 12:23am, ginrunner wrote:| Is perfect offense better than perfect defense? |
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I am happy that you can't answer this question, in spite of your accumulating a bag of tricks and listing tables of how to respond to which attacks. If you could answer this question, you would be way better at Arimaa than I am. I am getting used to being ranked #3 after a long run of being #2 (and before that #1), but I'm not ready to be #4 just yet!
I hope my answer doesn't sound too flippant. The fact is that your question is too hard. You should expect that it can't be answered. Worse than that, you should expect that even if some super-sentient being told you the answer, you wouldn't be able to understand why the answer is true!
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| « Last Edit: Sep 6th, 2011, 8:17am by Fritzlein » |
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Fritzlein
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Re: risk reward? Where are we strategy-wise?
« Reply #2 on: Sep 6th, 2011, 4:26pm » |
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I imagine that with perfect play, one player will realize he has a forced loss, and that his move that delays the loss for the longest time is to allow a rabbit pull. After the rabbit is exposed, it will have some potential on offense as well as being vulnerable to capture. The way to stave off defeat the longest will be to dart around making threats, but when they are all parried, to give up the rabbit to capture. Then the cycle will begin again, making the length of the optimal game very, very long.
But since we live in a suboptimal world, the player whose rabbit is exposed will not give it up. He will increase the temperature of the position, trying to make the game into a swarm or a capture race or a goal race. This is suboptimal in the sense of bringing on defeat earlier if the opponent plays perfectly, but a good strategy in the real world because it creates a chance for the opponent to make a mistake. Perhaps it is easier to play defense than offense, but mistakes when attacking lose a little bit, whereas mistakes when being attacked lose a lot.
I speculate that the arc of a perfect game involves the eventual winner playing a home game at first. In imperfect games, I speculate that the player who attacks first (in the sense of committing to an away game) will win more often.
But all of this is pure fantasy. Next week/month/year I will have a different imagination.
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| « Last Edit: Sep 6th, 2011, 10:06pm by Fritzlein » |
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ginrunner
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Re: risk reward? Where are we strategy-wise?
« Reply #3 on: Sep 6th, 2011, 5:07pm » |
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Thank you for your input.
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chessandgo
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Re: risk reward? Where are we strategy-wise?
« Reply #4 on: Sep 13th, 2011, 5:22pm » |
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on Sep 6th, 2011, 12:23am, ginrunner wrote:Does anyone else have any thoughts or theories. Is the future of Arimaa just like chess where tables can be used in more positions than one realizes. Is perfect offense better than perfect defense?
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If your question is whether a perfect player waiting patiently on his/her home ranks can lose, then the answer is yes, sure. If that's not what you meant... well then I'm not sure what you meant  When it's a matter of attacks vs counterattacks vs ..., the distinction between offense and defense becomes a gray area.
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ginrunner
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Re: risk reward? Where are we strategy-wise?
« Reply #5 on: Sep 13th, 2011, 8:26pm » |
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It kind of is. The same question in reverse would be can a player playing patiently and perfectly only in their home ranks beat a player that is attacking perfectly. Is that a possibility? If it is I, understand less than I think I do (quite possible :-P). If it is not then the postulate that offensive play is the way to win in the future holds firm.
Another possibility is would that perfect defense be able to draw with the perfect offense with nothing being exchanged (or even exchanges while still not allowing the advanced player the ability to goal) and still creating enough possibilities to move and not be blocked in. This almost represents a win for the defensive side. If they can't be goaled against and not forced to be repetitive in their moves then my thinking is wrong.
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Fritzlein
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Re: risk reward? Where are we strategy-wise?
« Reply #6 on: Sep 13th, 2011, 8:30pm » |
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on Sep 13th, 2011, 8:26pm, ginrunner wrote:| It kind of is. The same question in reverse would be can a player playing patiently and perfectly only in their home ranks beat a player that is attacking perfectly. Is that a possibility? |
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You need to define attacking a little better. Does it count as an attack if I cross the midline only to pull out a rabbit that I pull back to my side to capture/hostage/frame?
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ginrunner
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Re: risk reward? Where are we strategy-wise?
« Reply #7 on: Sep 14th, 2011, 12:59am » |
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good question. I would probably consider that defensive in nature. Though it is creating a threat you are doing so in a defensive position (hypothetically). I am assuming though that the offensive player wouldn't mind though as they are probably swarming in that area anyways if the option presented itself (again hypothetically). I may even go as far to say that a lone elephant attack with the intention of flipping pieces back for capture could be considered defensive but that is pushing it in the theory. Offense and defense seems to be thought of in terms of which traps a person wants to control most. Could this thinking be wrong as well? I am just trying to pick peoples brains here to figure out where we are heading. Obviously I am oriented in a more offensive position 
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Boo
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Re: risk reward? Where are we strategy-wise?
« Reply #8 on: Sep 14th, 2011, 5:24am » |
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For me 'attacking' is forcing an opponent to waste some of his quarter-moves on something he would not waste on without my 'attacking' move. It does not matter on which side of the board that happens. I can control my 1 home trap, the opp can control the remaining 3, and I still can consider my position as 'attacking', if I threaten to trap his camel, and opp doesn't threaten anything.
I guess I was talking about initiative here Well for me it is synonyms.
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Hippo
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Re: risk reward? Where are we strategy-wise?
« Reply #9 on: Sep 14th, 2011, 3:33pm » |
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on Sep 14th, 2011, 5:24am, Boo wrote:For me 'attacking' is forcing an opponent to waste some of his quarter-moves on something he would not waste on without my 'attacking' move. It does not matter on which side of the board that happens. I can control my 1 home trap, the opp can control the remaining 3, and I still can consider my position as 'attacking', if I threaten to trap his camel, and opp doesn't threaten anything.
I guess I was talking about initiative here Well for me it is synonyms. |
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So allowing capture is attack as well?
The difference between weak bots and stronger ones is weak bots often went to situation they cannot find a plan and they just suffle pieces. Stronger bot usually finds a plan requiring some (long term) reaction.
Humans rarely play with no plan. (Except the cases the plan is to play reactive game )
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Fritzlein
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Re: risk reward? Where are we strategy-wise?
« Reply #10 on: Sep 14th, 2011, 7:04pm » |
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on Sep 13th, 2011, 8:26pm, ginrunner wrote:| can a player playing patiently and perfectly only in their home ranks beat a player that is attacking perfectly. |
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OK, now that you have included pulling out rabbits and other hostages in your definition of defense, and now that you have limited the definition of attacking to be an attempt to control an opposing trap (or two), then I think it is entirely possible that perfect defense beats a perfect offense. If I had to bet, I would take the side of the defense. I think a perfect offense beating a perfect defense is less likely to be true.
But what is more likely than either of these two scenarios is that we are asking a question that misses the point. For example, imagine someone asking whether the player who has both cats on the same side will beat the player who has one cat on each side. It would be a mistake to answer the question as asked, no matter whether you said "split cats" or "unified cats", because the cat alignment isn't fundamentally what makes one position better than another. Taking sides on the cat alignment issue would expose your ignorance no matter which side you chose.
Similarly, I suspect that a higher caliber of player than me would laugh at me for taking the "defense" side of your question, not because "offense" is the correct answer, but because the question is missing something.
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| « Last Edit: Sep 14th, 2011, 7:04pm by Fritzlein » |
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ginrunner
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Re: risk reward? Where are we strategy-wise?
« Reply #11 on: Sep 15th, 2011, 2:22am » |
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That is indeed very possible. With my current understanding I clearly (and maybe wrongly lol) see games and determine who is the offensive player or defensive in any given situation. My mindset is usually on attack and defend but there are aspects that don't fit into that scenario like for example when I say to myself "His elephant is going to move in on the east so get your camel to the west" This is neither offensive nor defensive in nature.
If I were to rank play styles i would say from worst to best would be a bad offense, bad defense, good defense, good offense. The problem is it is much harder to play a good offense than it is a good defense. Positioning is the main determinant of who wins and loses (my elephant on the east side versus your camel on the east side should give me the advantage in that area). My argument stems from the fact that if both players are trying to maintain the best possible positioning for their pieces the offensive player will have more options with what they can do and more opportunities to take options away from the opponent, or at least I believe that to be the case. Eventually the person with less and less options has zero.
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| « Last Edit: Sep 15th, 2011, 2:23am by ginrunner » |
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Fritzlein
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Re: risk reward? Where are we strategy-wise?
« Reply #12 on: Sep 15th, 2011, 7:45am » |
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on Sep 15th, 2011, 2:22am, ginrunner wrote:| My argument stems from the fact that if both players are trying to maintain the best possible positioning for their pieces the offensive player will have more options with what they can do and more opportunities to take options away from the opponent, or at least I believe that to be the case. Eventually the person with less and less options has zero. |
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That's a plausible argument, but also the player whose pieces are framed or hostaged should have fewer options than the player with no pieces in immediate danger of capture.
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chessandgo
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Re: risk reward? Where are we strategy-wise?
« Reply #13 on: Sep 16th, 2011, 12:57pm » |
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I was going to say: Since the game has no draw and the only player you have forbidden something to is the defensive player, then the other player must have a winning strategy But well, if you forbid pulling pieces to the attacking player... To me pulling is part of the attacking repertoire. It makes your horse attacks more powerful if the opponent has both to defend his hometrap and prevent his dogs/cats from being dragged back.
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chessandgo
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Re: risk reward? Where are we strategy-wise?
« Reply #14 on: Sep 16th, 2011, 1:10pm » |
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Maybe another way to express the problem would be: Defense (silver) is forbidden to move a piece to the 3rd rank, but wins if Offense doesn't win in n=200 moves or less. I think it's clear that when n-> infinity Offense wins, but I wonder where the threshold is. Maybe that'd be a "fun" variant with n=80 or something (in a boring way ^^).
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