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omar
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Increasing the Arimaa Challenge prize
« on: Oct 10th, 2005, 12:51pm »
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I plan to start contacting companies next year to help further increase the Arimaa challenge prize. My goal will be to see if we can pass the $100,000 mark. I know it will be an uphill battle because I will have to convince people who know nothing about Arimaa that it really is difficult for computers and that promoting research in game playing can lead to advances in other seemingly unrelated areas. To make things a bit easier to swallow I will allow the companies to decide not only the amount they want to pledge but also when they want the pledge to expire. For example a company can say they want to pledge $10,000, but only until 2010. I was planning to start contacting companies this year, but instead focused on adjusting the format of the challenge match. Im confident that I won't need to change the format of the challenge match in the future and can focus on other things.
 
I am also very confident that the new challenge match format along with the knowledge we have gained about Arimaa, have made the challenge more difficult for computers now than ever before. I really want to thank the Arimaa community for helping to advance our knowledge of the game and widening the gap between humans and computers. How many games do you know where the top rated players are able to defeat the computer at blitz speeds even after taking on major handicaps?
 
With the increased confidence in Arimaa I am going to personally increase the Arimaa challenge prize further by offering an additional $5,000 until the year 2010. So if someone were to win the prize before 2010 they would get $15,000.
 
I would like to invite the Arimaa community to also show their level of confidence and make a pledge to further increase the Arimaa challenge prize. You can choose the amount you want to pledge and the year when it will expire. You can also do it as multiple pledges with different amounts and different years for each. I know that many of you now have the same level of confidence in Arimaa as I do, so this is your chance to show it. I think having many people supporting the Arimaa challenge will look very good when I approach people who don't know much about Arimaa. So even if you pledge only a small amount it will still help to increase the number of people. Please don't pledge an unrealistic amount like a million dollars; even if it is for a very short term. If you do, then you really better have that amount and be willing to part with if the challenge is unexpectedly met.
 
I've added a link at the bottom of the Arimaa challenge page to instructions on how to submit a pledge.
http://arimaa.com/arimaa/challenge/
 
I don't want to impose a burdon on anyone, but Im sure we can all judicially find an amount and expiration time that we are comfortable with. This is a real test of what others besides myself think about Arimaa. I hope the Arimaa community will step forward to support it. It will provide a lot of encouragment for me when I have to step out next year.
 
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Fritzlein
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Re: Increasing the Arimaa Challenge prize
« Reply #1 on: Oct 11th, 2005, 5:03pm »
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Sign me up for $500 for this year only.  I'll probably pledge next year too, but I think I would prefer not to pledge beyond my active commitment to Arimaa.  It would be weird for me to have a ten-year pledge if I quit playing next year.   I know $500 for one year only isn't much, but I'll feel totally comfortable forking it over if a bot does win this year.
 
Admittedly, it is unlikely someone will be inspired to try for $15500 if they weren't inspired to try for $15000, but I think that's beside the point.  It's a way for me to vote my confidence in this wonderful game of Arimaa that Omar created.
 
I also believe that Omar is dead right about fundraising: big sponsors pay close attention to the behavior of little sponsors with a vested interest.  If he can go around saying that eight of the ten most active players on the server have ponied up money in confidence that Arimaa is hard for computers, the corporate sponsors will get the message loud and clear, no matter what the dollar amount is.  They will understand that there is a community of Arimaa players who believe they can beat the bots and will work together to do it.
 
Finally I don't forget that I paid fifty bucks for my chess set and Omar was nice enough to make his game playable with the same equipment for free.  And I note that a subscription to the Internet Chess Club is fifty bucks per year, whereas Omar lets us play Arimaa on his server for free, and even pays the Player of the Month for playing!  Next year, if my personal financial picture continues to improve, I'll pledge even more.
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PMertens
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Re: Increasing the Arimaa Challenge prize
« Reply #2 on: Oct 11th, 2005, 9:42pm »
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I will add 1500 - but also for this year only at the moment ...
 
I am quite confident the breakthrough is not going to happen this year ... but I got big plans for next time  Wink
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omar
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Re: Increasing the Arimaa Challenge prize
« Reply #3 on: Oct 12th, 2005, 3:19pm »
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Thanks for breaking the ice and showing your support guys. As I mentioned, the amount or time frame will not matter as much as the number of people backing the challenge.
 
Perhaps making a pledge for a year at a time is probably the best way to go for individuals.  
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PMertens
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Re: Increasing the Arimaa Challenge prize
« Reply #4 on: Oct 12th, 2005, 5:52pm »
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I sure hope that "breaking the ice" does help ... the pledge/views ratio is still a little disappointing  Roll Eyes
 
Cmon guys ...  
Higher stakes means better bot-opponents !
And we really could need some - even if that means we cannot wash the dishes while playing :-P
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99of9
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Re: Increasing the Arimaa Challenge prize
« Reply #5 on: Oct 13th, 2005, 1:05am »
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I am in a little bit of a dilemma here.  Here's a bunch of random thoughts.
 
on Oct 10th, 2005, 12:51pm, omar wrote:
I will have to convince people who know nothing about Arimaa that it really is difficult for computers
 
Part of my difficulty is that I don't necessarily believe this as strongly as you do Omar.  I think the odds are that a programmer putting in the arimaa_bot hours as a serious hobby will succeed in the challenge before 2010.  If a team or coporation decides to attack it, in my mind it would be almost certain to fall.  That is of course not to diminish the challenge, there is certainly research and work required, it's just that I think this research is achievable.  What is more, the research would not get done without the challenge, so I certainly admire you committing to the challenge in the first place Omar.
 
(as a side note, if the challenge details are now finalised, I'm planning to open a claim at www.ideosphere.com so that a market-based agglomeration of opinions can give an estimate of the probability of the challenge being won, and if so, the length of time it might take)
 
On the other hand, I am as confident as Karl and Paul that it won't go off this year.
 
Should I then make an offer each year I think it is a near certainty the bots will lose, and then pull out when I think it will go off?  That seems a bit disingeneous - even if it will win bigger sponsors.
 
Or should I view it like Karl's last point - write it off as an entertainment expense like I might if I subscribed to the Internet Chess Club?
 
Or like Paul's last point - as a bot-bashing entertainment expense?
 
... but how do these convince the corporate sponsors?  That just proves that I like arimaa and am willing to pay for it.
 
On one hand I make a reasonable offer, but if my judgement is good/conservative, am highly unlikely to pay it.  On the other hand, I make a small contribution, set my year to 2020, and basically commit to giving it away.
 
Perhaps I should go for something in between, something that I believe is indeed challenging?  Something that I think has a 50% probability of coming off??  That way, if my expectations are similar to a bot-programmers, it might inspire him/her to try to be that quick.
 
Anyway, obviously I need to think more.  Please tell me if any of this reasoning is silly.
 
Ah, I've thought of one more possibility.  If I'm really confident that it will go off before say 2012, perhaps I should offer to pay Omar $$$ if it doesn't go off before then.  That way he'd be able to increase the prize pool by that amount of $$$ between 2012 and 2020, but not before then.  How's that for strange??  Would that help or hinder sponsorshipHuh
 
Quote:
and that promoting research in game playing can lead to advances in other seemingly unrelated areas.

This I can certainly help you with.  You are welcome to publicise my example of this from a long-previous forum thread (I think it was "Research Arising From Arimaa").
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PMertens
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Re: Increasing the Arimaa Challenge prize
« Reply #6 on: Oct 13th, 2005, 1:31am »
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Hmmmm .....
 
Maybe just making it for one year in a timeframe where it is absolutely impossible to make something work is really not that great ...
 
Herewith I change my pledge a little bit:
 
2006: 2000 (this year)
2007: 1500
2008: 1000
2009: 500
2010: 250
 
This also reflects the timeframe I expect to be finished with my bot and win the challenge Smiley
 
 
Anyway ... I think it proves not only that you are willing to pay, but also that you think the risk is minimal ...
While I can certainly afford the money I really would prefer to keep it :-P
« Last Edit: Oct 13th, 2005, 1:35am by PMertens » IP Logged
Janzert
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Re: Increasing the Arimaa Challenge prize
« Reply #7 on: Oct 13th, 2005, 3:35am »
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on Oct 13th, 2005, 1:05am, 99of9 wrote:

Ah, I've thought of one more possibility.  If I'm really confident that it will go off before say 2012, perhaps I should offer to pay Omar $$$ if it doesn't go off before then.  That way he'd be able to increase the prize pool by that amount of $$$ between 2012 and 2020, but not before then.  How's that for strange??  Would that help or hinder sponsorshipHuh

 
Hmm, sounds like "selling short".
 
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Arimanator
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Re: Increasing the Arimaa Challenge prize
« Reply #8 on: Oct 13th, 2005, 4:21am »
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on Oct 13th, 2005, 1:05am, 99of9 wrote:
I...If a team or coporation decides to attack it, in my mind it would be almost certain to fall...

I sincerely doubt that any corporation would bother to put a team in the hopes of winning $100 000 which as you know is petty change when it comes to finance at team of well paid researchers plus the material plus the infra structures. I mean the naked rooms housing your researchers alone would cost you dozens of thousands dollars a month.
 
So I wouldn't worry about corporate involvement unless the prize goes up to 10 million or so.
« Last Edit: Oct 13th, 2005, 4:23am by Arimanator » IP Logged
Arimanator
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Re: Increasing the Arimaa Challenge prize
« Reply #9 on: Oct 13th, 2005, 4:28am »
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on Oct 13th, 2005, 1:31am, PMertens wrote:
...This also reflects the timeframe I expect to be finished with my bot and win the challenge Smiley...

 
Then why don't you pledge big money on it since you're assured to get it back, in other terms you won't have to actually fork it over?  Wink (joke)
« Last Edit: Oct 13th, 2005, 4:29am by Arimanator » IP Logged
99of9
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Re: Increasing the Arimaa Challenge prize
« Reply #10 on: Oct 13th, 2005, 5:48am »
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on Oct 13th, 2005, 4:21am, Arimanator wrote:
So I wouldn't worry about corporate involvement unless the prize goes up to 10 million or so.

Yes, you're probably right.  Unless some bigwig company decided to do it for the kudos... but I guess Arimaa's not popular enough for the kudos to be big enough either yet.
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Fritzlein
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Re: Increasing the Arimaa Challenge prize
« Reply #11 on: Oct 13th, 2005, 6:33am »
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on Oct 13th, 2005, 1:05am, 99of9 wrote:

Part of my difficulty is that I don't necessarily believe this as strongly as you do Omar.  I think the odds are that a programmer putting in the arimaa_bot hours as a serious hobby will succeed in the challenge before 2010.

 
Ah, this would be a deterrent to pledging prize money.  Obviously the chance of humans losing is cumulative, so if you think bots have a 5% chance of winning each year, then bots have a 54% chance of winning sometime in the next 15 years, so one should bet accordingly.  That I fully understand.
 
Yet I'm quite surprised that both you and PMertens predict that the chances of humans losing will increase each year, i.e. a higher chance in 2008 than in 2007, assuming it isn't won in 2007.  I don't foresee this at all.  So far the bots had the best chance of winning in 2004, less chance in 2005, and 2006 offers bots the worst prospects yet.  In my estimation, by 2010 human dominance will make the challenge a joke, an annual bot-bashing festival.
 
My reasoning, of course, is that humans are still rapidly getting better at Arimaa.  I don't yet see a plateau in how good humans can get.  Of course, there will be a point of diminishing returns when increased strategic understanding weighs less than failing to see every move, and at that point computers will start inexorably gaining, if only due to speed improvements.  But I'm stunned that you two foresee this happening sooner rather than later.
 
I guess I am just going from subjective impressions, but I feel that I am still learning every game, particularly from postal games.  Pardon me for tooting my own horn, but I don't feel I am undefeated postally due to doing the same thing that everyone else does, only doing it more carefully and more accurately.  Rather I feel that I absorbed some strategic ideas sooner and/or at a deeper level than they are widely understood.  Furthermore, I feel that there are large classes of positions that I don't understand well, but I feel some of them gradually seeping into my consciousness to the point that I will be able express them in some future Wikipedia article.
 
Do you both feel you know most of what there is to know about Arimaa strategy?  Do you think you'll evaluate Arimaa positions five years from now essentially the same as you do now?  If so, I'd like to hear a good rule of thumb as to when the E+H attack is strategically advantageous, a rule will still be generally accepted in 2010.
 
Just to be perfectly clear about my pledge, I do not intend to decrease it each year, and I don't intend to pull out because loss looks inevitable.  On the contrary, I intend to keep my pledge steady, and even increase it every year if I feel I can afford it.  The reason I keep my timeline short is purely because I can't predict my personal involvement in Arimaa.  I may find a job or another hobby that is more absorbing and takes me away from Arimaa, and I have no desire to pledge when I'm not part of the community of defenders.  But for as long as I'm around playing actively, (OK, with a 2020 cutoff Smiley) I'll at least pledge my $500 every year.
« Last Edit: Oct 13th, 2005, 1:22pm by Fritzlein » IP Logged

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Re: Increasing the Arimaa Challenge prize
« Reply #12 on: Oct 13th, 2005, 8:00am »
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I think the reason bots are currently behind is that arimaa strategy is still rapidly evolving. These new strategies are being used on bots that were written before the strategies existed, so any conclusions should be made with care.
 
However, I think, the strategies developed this year are more difficult for a bot to understand, than the older strategies. Taking a camel hostage is easier to understand, than say flooding rabbits. It will depend on what new strategies are developed in the future.
 
The current strategies look difficult to implement, but not impossible. My guess is that 99of9's opinion will prove accurate.
 
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Re: Increasing the Arimaa Challenge prize
« Reply #13 on: Oct 13th, 2005, 11:00am »
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on Oct 13th, 2005, 8:00am, jdb wrote:
These new strategies are being used on bots that were written before the strategies existed, so any conclusions should be made with care.

 
That's a good point.  Bots haven't had a chance to catch up with the present year of advances in human strategic understanding.  The "widening gap" I keep talking about is between humans who are actively learning and bots which aren't being actively developed, so it's not quite a fair comparison.
 
Some new strategic knowledge can be expected to benefit bots more than it benefits humans, i.e. the gap will be narrower when both sides know X than it is when neither side knows X.  For example in chess knowing that KQ vs. KBB is won and KQ vs. KNN is a draw (not the other way around as humans had believed) makes humans stronger players, but helps computers more, since compters can play such endgames perfectly while humans still blunder even after learning the technique.
 
One example I can think of for Arimaa is a good material evaluation scheme.  If there is an accurate formula for material advantage, then it will benefit bots more than humans, since bots will be able to calculate it accurately and quickly.
 
That said, I think it is reasonable to draw conclusions about the tractability of certain problems judging by progress (or lack thereof) in solving them so far.  The oldest strategies should be handled best by the bots if it is only a matter of encoding catching up to what is known, right?  Yet so far "camel hostage" is the only strategy that Bomb has more or less solved, and even there Omar found a loophole to exploit.  No other bot adequately avoids camel hostages, despite the age of the strategy.  The next oldest and most solved is "elephant blockade".  Bomb has more loopholes there, but existing progress suggests that full blockade possibilities will eventually be a net advantage to bots, not humans as they are now.
 
Apart from these two areas of progress, the third-oldest strategy, namely "nickel-and-dime" with the lone elephant, which Omar rode to an 8-0 victory in 2003, hasn't been solved yet either, at least not by Bomb.  When the new entrants for the 2006 computer championship come on-line for human play, testing this strategy is my second priority (after camel hostage).  Bots that can't beat a strategy more than two years old need an excuse in addition to recent advancement of human understanding.
 
This year should give us some good new information about the difficulty of encoding an evaluation of a multi-piece attack, because the E+H attack is now a full year old.  Fotland was definitely trying to adjust to the E+H last year, for example putting horses next to traps rather than dogs, and activating the camel after getting a horse hostage, but these were only stopgaps.  Last year one might have said that the E+H attack was too new to be responded to properly, but after Belbo pummeled Bomb with it 7-1, it has to be addressed this year.
 
What is the time frame in which unsolved problems go from "We haven't tried yet," to "The year after next we'll think of something for sure," to "It's actually quite a hard problem."?
 
Quote:

It will depend on what new strategies are developed in the future.

 
I quite agree that each new strategy affects the balance of power.  Humans will always get a temporary advantage by thinking of it first, but in the long run the advantage may be nullified or turn into outright disadvantage as computers understand it too.
 
(Now that I think about it, developers might be first to roll out some new strategies too, for a temporary advantage on their side.  How much room to humans have to adapt?  If a bot suddenly did something to shoot its rating to 2300 would humans be able to learn from playing it and get up to 2500?)
 
The strategies of the future will, I believe, depend much more on the nature of the game of Arimaa than on how assiduously human players or bot developers are applying themselves.  We can only guess whether or not there are machine-understandable ideas that will bust the game and win the challenge.
 
My current guess is that we will see more and more games in which multiple traps are contested.  I recently played my first game (against Robinson) in which all four traps were simultaneously contested, and I see Belbo vs. Robinson postal is another example with four contested traps.  The key strategic decision is deciding whether to shift the elephant (or other forces), conceding disadvantage in one area to gain advantage elsewhere.  I expect computers to stink at that decision-making when it is strategic, i.e. when no immediate captures are available.  A secondary strategic decision is choosing which trap one should spend time playing at if one isn't going to shift forces.  I also expect computers to be bad at that.
 
I further predict we will see more congested games with multiple advances by both players long before capturing clarifies the situation.  In the past a lack of captures has usually indicated defensive play by both sides, but in the future we will see a lack of captures also in games with aggressive play and rabbit advances.  Belbo vs. Robinson postal is an example of this phenomenon as well.  Congested games will probably favor humans too, because the positions take longer to change (for example it takes two or three moves for an elephant to cross sides instead of one move in an open position) so long-term planning is more important.  
 
In the long run, the intentional anti-computer features such a high branching factor and variable initial setup will pale in comparison to  emergent features of excellent play.  From my present understanding, emergent features are favoring humans more and more.   That is to say, the better we play, the more the positions are becoming difficult for computers to understand.  This is quite different than chess, in which best play is quite often tactical and creates positions favorable to computers.
 
Admittedly this could change.  For example, it could turn out that one can be forced into a race game, i.e. either you race or you accept a disadvantage.  If this were true, then computers might turn out to be better at racing than humans, and humans would have the handicap of having to prevent races.  This would definitely tilt the scales.  But at the moment E+M attacking still looks bad most of the time, so E+H is the closest we get to "forcing" a race, and the defender has so many resources against E+H we're not even sure when it is an advantage and when it is a disadvatage.  At present bots can bungle it from either side, losing both when they attack with E+H and when they defend against an E+H attack.  (Of course, at present bots also lose races Wink but that seems potentially easier to correct.)
 
Quote:

The current strategies look difficult to implement, but not impossible.

 
Given that statement, JDB, I'm very curious to see what Clueless does about E+H this year.  At the moment Clueless handles it better than Bomb, because Clueless will go nuts with its camel.  This often results in Clueless losing camel for horse, which is better than losing the whole game slowly and surely like Bomb does, but still isn't much of a solution.  In fact, it doesn't even look close to a solution.
 
I guess it is in the nature of the Arimaa Challenge that non-programmers will be skeptical of what bots can do, because they don't know enough to know what is possible.  When I say "It can't be done," I really mean "I don't understand how it can be done," which reflects more on my poor understanding than on the reality of the situation.
 
On the other hand, it is probably equally natural for programmers to be overconfident.  When you have an idea that hasn't been tried yet, it is easy to suppose that it will work.  And if it doesn't work, you can always generate another idea.
 
This chasm in expectations is well and good.  After all, if all bot developers were as pessimistic as I am about their chances, they would all give up and go home.  Tongue  
« Last Edit: Oct 13th, 2005, 1:24pm by Fritzlein » IP Logged

omar
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Re: Increasing the Arimaa Challenge prize
« Reply #14 on: Oct 15th, 2005, 12:32pm »
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Wow, you triggered an avalanche of discussion here Toby. Thanks for livening up this topic.
 
on Oct 13th, 2005, 1:05am, 99of9 wrote:

I think the odds are that a programmer putting in the arimaa_bot hours as a serious hobby will succeed in the challenge before 2010.  

If Arimaa continues to have the kind of players that it already has now there is no way this is possible. Im the kind of person that is ready to put my money where my mouth is in things I beleive in strongly. I would be ready to take you up on this at whatever stakes you chose. But I think you should reconsider this. 2010 is only 5 years away. Hardware speeds might quadruple by then, but that will hardly effect things. So you would really be betting that there is going to be a software breakthrough or that incremental improvements in the evaluation functions will significantly surpass human players. If the first happens then you deserve to win for calling that, but I don't think that's what you are counting on. What are the chances of the second happening. I think we can look at Chess, Go and Shogi for guidance. In all these games the best programs are ones that have highly tuned (usually hand tweeked) evaluation functions. Only in chess are computers now starting to surpass the best players. In the other two, computers are way behind. The nature of chess is so tactics oriented that it amazes me we still have some humans that can stand up to computers. The other two games are more strategy oriented; there are tactics, but they don't dominate the nature of the game. I think Arimaa fits firmly into the second catagory and so by its very nature will be resisent to computers. But what about the possibility that due to the small human player population and limited knowledge about the game, computers will supass the humans. If Naveed and I were the only human Arimaa players I think this would be possible Smiley However, we now have some players (like Karl, Frank, Pat, Paul, yourself and more)  who don't seem to have an upper limit in their potential especially when it comes to playing computers. If the computers start winning humans will analyze the games, figure out what went wrong, develop counter strategies and learn to crush it especially in slow time control games. If you remember the early days of Arimaa we didn't even know the concept of taking a camel hostage until Claude stumbled on it. After that all the humans suddenly became better against bot_Bomb. Or when Ceejay stumbled on Bait and Tackle. That allowed me to consistently win against bot_Speedy; and you know how terrible I am at fast speeds Smiley Humans will learn from the computers faster than they will learn from us. That I think is the key which will allow humans to stay ahead of the computers well beyond 2010.
 
Quote:

If a team or coporation decides to attack it, in my mind it would be almost certain to fall.

No way. If the Arimaa challenge attracted a corporation and became a high profile topic, it would also attract a lot of human players which would help increase our knowledge of the game and the level of the highest players would continue to rise even faster. So it would balance itself out to the first senerio.
 
Quote:

(as a side note, if the challenge details are now finalised, I'm planning to open a claim at www.ideosphere.com so that a market-based agglomeration of opinions can give an estimate of the probability of the challenge being won, and if so, the length of time it might take)

Unless I am not able to find three humans players for the challenge match, I don't think there would be any need to change it. Go ahead with the posting, it will be interesting to see what the general public thinks.
 
Quote:

Should I then make an offer each year I think it is a near certainty the bots will lose, and then pull out when I think it will go off?  That seems a bit disingeneous - even if it will win bigger sponsors.
 
Or should I view it like Karl's last point - write it off as an entertainment expense like I might if I subscribed to the Internet Chess Club?
 
Or like Paul's last point - as a bot-bashing entertainment expense?
 
... but how do these convince the corporate sponsors?  That just proves that I like arimaa and am willing to pay for it.

I don't think corporate sponsors care about the details of what others motivation for sponsorship might be; they usually only look at the big picture. Their main concern is going to be: how risky is this and what do we get out of it. If I go to a corporate sponsor and say "look I created this game and put out a challenge, would you like to join me in increasing the challenge prize" they are going to think Im nuts. On the other hand if I can say "there's twenty other sponsors supporting the challenge, would you like to join" it gives them more confidence to do it.
 
So my suggestion would be to pledge year to year if that's what you feel comfortable with. But do pledge so that there will be more total sponsors.
 
Also taking a stance on the Arimaa challenge will end up making this long term adventure more interesting and entertaining for yourself.
 
Quote:

On one hand I make a reasonable offer, but if my judgement is good/conservative, am highly unlikely to pay it.  On the other hand, I make a small contribution, set my year to 2020, and basically commit to giving it away.
 
Perhaps I should go for something in between, something that I believe is indeed challenging?  Something that I think has a 50% probability of coming off??  That way, if my expectations are similar to a bot-programmers, it might inspire him/her to try to be that quick.

You can make multiple pledges with different time frames. So you don't have to acheive everything with just one pledge. So you could make one pledge with a large amount for a short time frame and another pledge with a small amount for a long time frame.  
 
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Ah, I've thought of one more possibility.  If I'm really confident that it will go off before say 2012, perhaps I should offer to pay Omar $$$ if it doesn't go off before then.  That way he'd be able to increase the prize pool by that amount of $$$ between 2012 and 2020, but not before then.  How's that for strange??  Would that help or hinder sponsorshipHuh

Interesting twist. This would help to attract more bot developers by providing a more constant prize through the life of the challenge, but would not help with attracting corporate sponsors; might actually hinder sponsorship. But then again if I can't get them to do a forward sponsorship maybe they would be willing to do such a reverse sponsorship. What Im worried about is that corporate sponsors won't want to take any stance at all; they worry too much about stuff like, corporate image, risk managment, return on investment, etc. But if you want to do it this way, that would be fine with me.
 
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This I can certainly help you with.  You are welcome to publicise my example of this from a long-previous forum thread (I think it was "Research Arising From Arimaa").

Yes I remember you posted about this earlier. If you have a paper about the research and it mentions Arimaa, game playing, etc. then it would definitely help.
« Last Edit: Oct 15th, 2005, 1:26pm by omar » IP Logged
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