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Topic: Drawing (Read 5081 times) |
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99of9
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Re: Drawing
« Reply #15 on: Mar 26th, 2008, 7:33am » |
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on Mar 25th, 2008, 7:17pm, omar wrote:Actually Wayne Schmittberger had also suggested this to me shortly after seeing Arimaa back in 2003. I like this option as well since it would be much easier to adopt. In fact if it turns out that Gold has the advantage, I would prefer to try this option first.
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Great - it is way more elegant than your complicated scheme!
I would just like to note that it does not have to be 2 steps for gold, it could be 1 or 3 depending on how much advantage you think gold had with 4 steps - it just gives you a little more flexibility to correct any imbalance.
(I personally still maintain that with 4 steps gold has a small but significant advantage.)
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jdb
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Re: Drawing
« Reply #16 on: Mar 26th, 2008, 8:37am » |
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If it turns out gold has an advantage, another way to equalize is to use the "swap rule".
Gold places his pieces and then silver has the option of placing his pieces as normal, or playing the gold pieces.
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lightvector
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Re: Drawing
« Reply #17 on: Mar 26th, 2008, 9:32am » |
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If Gold takes 2 steps, then tempo-wise, the game is even. Silver and Gold each alternate between having taken 2 steps more than the opponent.
Except that Silver gets the advantage of the second setup, which means Silver should have a slight advantage if Gold gets only 2 steps on the first turn.
How much do people think the second setup is worth?
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Fritzlein
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Re: Drawing
« Reply #18 on: Mar 26th, 2008, 11:09am » |
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on Mar 25th, 2008, 1:31am, omar wrote:| In the future if we find conclusively that Arimaa is favored towards one side or the other by more than 2%, I want to reserve the right to try a significant rule change to the setup which I think may help to make it more balanced. |
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If we have set the threshold for considering a rule change at Gold winning 52% of games between even players (which is equivalent to Gold being worth 14 rating points) then odds are we will be fine keeping the current rules forever. See the latest statistics here:
http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;nu m=1163650023;start=15#21
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Fritzlein
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Re: Drawing
« Reply #19 on: Mar 26th, 2008, 11:26am » |
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on Mar 26th, 2008, 9:32am, lightvector wrote:| How much do people think the second setup is worth? |
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My current thought is that the second setup is worth nothing to Silver, because I will balance my horses no matter what. Also I will always centralize my camel for defense against an EH attack on either wing, unless Gold set up unbalanced horses, which never happens these days. The fact that I don't use the second setup to adapt to what my opponent does is the reason I think Gold must have an advantage due to the first move.
However, there is a real possibility that we are wrong about opening theory. It may be that swarming attacks including the camel are good. It may be that one should attack with EH on one wing and MH on the other, in which case decentralizing the elephant and camel could be a net gain of time. Alternatively it may be that it is good to have EHH on one wing and MD on the other. It may be that only Silver can take advantage of the decentralization of the camel, because if Gold decentralizes the camel, Silver can place both horses on the opposite wing and gain advantage. Contrariwise, it may be that only Silver can gain from having unbalanced horses, because if Gold sets up with unbalanced horses, Silver can nullify it by setting up the camel on the same wing. If one is trying to measure the setup advantage in steps (i.e. does it offset a two-step tempo for Gold) it could easily be worth more than two steps. For example putting the camel two steps from where it would have been and putting a horse four steps from where it would have been could mean the second setup was worth six steps!
In short, if opening theory changes to favor swarming attacks, it could easily change my conviction that Gold has an advantage into a conviction that Silver has an advantage.
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| « Last Edit: Mar 26th, 2008, 11:37am by Fritzlein » |
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aaaa
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Re: Drawing
« Reply #20 on: Mar 26th, 2008, 1:47pm » |
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on Mar 26th, 2008, 8:37am, jdb wrote:If it turns out gold has an advantage, another way to equalize is to use the "swap rule".
Gold places his pieces and then silver has the option of placing his pieces as normal, or playing the gold pieces. |
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I don't like it except as a last resort, because it would mean you would have to deliberately play suboptimally with respect to the game at the "object level".
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omar
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Re: Drawing
« Reply #21 on: Mar 26th, 2008, 11:49pm » |
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I would also prefer not to use the pie rule. In some games it can't be avoided, but in Arimaa I think we can use other means to compensate.
If we find that Gold has an advantage then reducing the number of steps Gold may take in the first move, might be enough to fix it. Though we could reduce by 1, 2 or 3 steps depending on how much compensation is need, it would be nice to use 2.
If we find that Silver has an advantage then using the interlaced setup might be the way to fix it.
Hopefully the difference stays below 2% and we never have to worry about it.
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aaaa
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Re: Drawing
« Reply #22 on: Apr 2nd, 2008, 10:51am » |
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I realized that there is yet another advantage of a consistent rabbit extermination rule: There could never be a superfluous move after total annihilation.
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gatsby
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I have recently discovered Arimaa, and I think it is a major effort in creating a game difficult for computers, as well as an entertaining challenge for humans. My congratulations to you, Omar.
I have being reading your recent post proposing your solution to an eventual problem of Gold-Silver imbalance. It is a good idea, but too complicated. I would like to post here my personal proposal, which would, by the way, elliminate every possibility of opening preparation. Current rules already make it difficult, but the setup phase can be simply considered as one more move, and consecuently standarized. My solution overcomes this, and it is as follows:
At the start of the game, every player places his eight rabbits in his nearest row of the board. The rest of the pieces will be placed randomly in the second nearest row, in such a way that Silver pieces are centrally symmetrical to Gold ones (i.e., the same setup as Gold but rotated 180∫). This is to avoid the possibility of elephant confrontation in the same file, and gives us a total of 2520 possible initial positions, a number large enough to make opening preparation impractical. After the pieces setup -and this is the important thing-, Gold starts the game by making one step. Silver then replays with two steps, and Gold, subsecuently, makes three steps. Then every side gets four steps per turn as usual. As you will observe, both Gold and Silver gets an advantage of one step right after making the first move of the game, and a two steps advantage for every move since. I think that this progressive method is fairer than an initial two steps for Gold followed by four steps for every side since then.
Lastly, I would like to join the people who thinks that threefold repetition should be declared simply illegal, and not an instant loss as it is now.
I would be glad to read your answer. Congratulations again for having created such a wonderful game!
P.D.: I write this from Leon (Spain). Please excuse me if my English is not fully correct.
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omar
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Re: Drawing
« Reply #24 on: Apr 8th, 2008, 1:19pm » |
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Thanks for the suggestion gatsby and also for the nice comments about Arimaa.
I'm really hoping that the setup advantage of silver balances out the first move advantage of gold and that we never see a statistically significant imbalance of more than 2% for one side or the other. So if that never happens, we will never have to consider changing the setup.
If it turns out that gold has the advantage then the least disruptive solution would be to reduce the number of steps gold gets on the first move. Perhaps 2 steps or perhaps the gradually increasing number of steps for both sides as you suggested. The actual choice will probably depend on how much advantage gold has.
If it turns out that silver has the advantage then I think fixing it will require changing the setup stage. But I think we will find ourselves in a strange predicament. We will have various proposals on how to fix it, but how will we know which one to chose. We really should try out those various proposals experimentally and pick the one which balances both sides the best. But that of course will require a lot of games to determine and probably won't be possible. Also the current rules will probably be so entrenched by then that there will be a large resistance to change even if it could make things better.
What would really be great is if we could find a method to somehow compute the imbalance for a given set of rules. This would allow us to try and determine if we are headed for disaster with the current Arimaa setup and if so allow us to test different proposals to fix it. I remember seeing some thread where Fritzlein suggested trying to run a lot of games between random bots to see if there is any imbalance in such games; but can't seem to find that posting now. Anyways, I would be interested to hear any suggestions on this.
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Fritzlein
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Re: Drawing
« Reply #25 on: Apr 8th, 2008, 2:08pm » |
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We don't yet suffer from standardized openings. If some day in the far future Arimaa loses its freshness due to stereotyped openings, then it would be an attractive solution to give the two sides random but equal setups, and balance tempo by reducing steps in the initial move(s). But if we do that, why put all the rabbits on the back row? I think it would be much more interesting to randomize the entire setup.
For the present, I would strongly object to enforcing random but equal setups, because we don't yet know whether Silver can use the second setup to advantage. If Silver can gain tempo from the setup, a very interesting dynamic will be created that I would like to see played out. Let's not try to fix the opening when so far is it not broken; first let's try to figure out how to play this game.
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| « Last Edit: Apr 8th, 2008, 2:09pm by Fritzlein » |
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aaaa
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Re: Drawing
« Reply #26 on: Apr 8th, 2008, 2:14pm » |
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If a random element were to be added to Arimaa, it would, for me personally at least, seriously detract from its attractiveness.
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gatsby
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I quote Fritzlein: "If some day in the far future Arimaa loses its freshness due to stereotyped openings, then it would be an attractive solution to give the two sides random but equal setups, and balance tempo by reducing steps in the initial move(s). But if we do that, why put all the rabbits on the back row? I think it would be much more interesting to randomize the entire setup."
Simply because a rabbit placed in front of another piece would obstruct it and force the player to advance the rabbit, which could be inconvenient in the early stages of the game. Also, I think it is more elegant to place in the first row the pieces whose objective is to step through the entire board to goal.
But all of this is, of course, hyphotetical.
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99of9
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Re: Drawing
« Reply #28 on: Apr 9th, 2008, 10:09pm » |
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on Apr 8th, 2008, 2:14pm, aaaa wrote:| If a random element were to be added to Arimaa, it would, for me personally at least, seriously detract from its attractiveness. |
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Me too. Particularly because we know that some setups are better than others, this would be like giving a player a random handicap.
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Arimabuff
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Re: Drawing
« Reply #29 on: Apr 10th, 2008, 2:41am » |
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on Apr 8th, 2008, 2:14pm, aaaa wrote:| If a random element were to be added to Arimaa, it would, for me personally at least, seriously detract from its attractiveness. |
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I agree as well, Arimaa would stop being a game like Chess, Go or Checkers and enter into that category of any game where you have to roll the dice to know what to do next (like Monopoly for instance).
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