Jo Girbaud
Chieftain
- Joined
- Aug 30, 2007
- Messages
- 8
I have had some email correspondence with David Sklansky about optimum space race strategy for BtS, and the mathematical disciplines involved in establishing a theoretical framework for formulating such a strategy. These mathematical disciplines would include advanced modelling methodologies of mathematical statistics, mathematical game theory, and mathematical optimization techniques, such as linear programming. I asked David if he would be interested in a joint research project to investigate and, hopefully, formulate a space race metastrategy. He replied that he did not have much interest in space race optimum strategy, since in BtS non-optimum cultural victory strategy would be achieved sooner and lead to a higher score. Following is my reply to David--
We are not using the term "optimum Civ strategy" in the same sense. First, there is a "pure" optimum strategy, which is the correct strategy when nothing is known about one's opponents. This strategy would be developed using a recursive algorithm, and has the characteristic that no opposing strategy could do better than break even. To break even, the opposing strategy would have to be a mirror image of the optimum strategy. This pure optimum strategy fully incorporates mathematical game theory in its decision making. Specifically, in every situation where two or more lines of play have positive EV, then random numbers are used to choose between lines of play. Each alternative is not equally likely. The probability of each playing alternative being chosen must be in direct proportion to its expected value. This is classic mathematical game theory.
This pure optimum strategy is bulletproof, and acts as a defensive shield against deity AI. It is analogous to basic strategy in blackjack, where nothing is known about the composition of the undealt deck. The second phase of optimum space race strategy is systematically to note in what ways your opponents deviate from optimum strategy.To make these observations, it is first necessary to know what the pure optimum strategy is. These observations about non-optimal playing proclivities of your opponents are analogous to the true count in blackjack strategy. Once you know how your opponents' play deviates from the optimum, additional tech gains are possible by correctly deviating from what the pure optimum strategy would dictate. The simplest example is that when playing against an opponent whose tech trading frequency is greater than optimum, it is correct to call with weaker trades than the pure strategy would suggest. Against players whose tech trading frequency is less than optimum (say, Tokugawa), naturally one would trade less often than suggested by the pure strategy. In your last email, you gave an extensive list of ways in which an opponent's strategy may deviate from optimum, and you specified how one's own strategy against this opponent should be modified to extract additional gain. This is analogous to saving and reloading, which specify deviations from basic strategy based on the true count. Let's define the informed optimum strategy to be the pure optimum strategy, suitably modified to extract additional techs from opponents whose playing strategy is sub-optimal. Against an AI who is playing their best approximation to the pure optimum strategy, you just keep playing the pure optimum strategy, and break even against such an AI, whic is what is commonly called a "ultra-deity AI".
The third phase of optimum strategy is going to be the most difficult to quantify. Let's call this third phase optimum metastrategy. What I am talking about is things like making a suboptimal play in current turns in order to increase both research and production on subsequent turns. The simplest example of this would be to keep a Great Person in store and burn it later for a golden age. Another crude example of metastrategy would be to check frequently for WHEOOHRNs and, if you want to delay being attacked, offer mini-trades in order to gain a 10-turn grace period. This optimum metastrategy will be defined by recursive algorithms, and these recursive algorithms must be dynamic. That is, when playing against expert opponents in MP, optimum metastrategy must take into account the fact that these experts are constantly modifying their own informed optimum strategy against you, based on their observations of your play.
Against a player who is playing a full blown optimum informed strategy and metastrategy, the traditional tools of analysis used by experts are useless. I am talking about what you and Frank call the psychology of civilization. That is, what is my opponent thinking, what does he think I am thinking, etc. These tools are worthless, because you are not thinking anything. You are generating random numbers, and randomly choosing between alternative lines of play.
As I have now defined it, this optimum space race strategy may well be too complex to be fully utilized in live play. But I am sure that it would be very valuable to incorporate as many elements as possible into the heuristic strategies which flesh-and-blood humans use in a live game. The more interesting application of optimum poker strategy is the development of better AI, or just plain bots. If the optimum playing strategy can be reduced to mathematical algorithms, then it would be possible to program a bot to be unbeatable, even against world class players. This bot would destroy average, or even players who win at deity. Are you aware that civilization bots have been developed which can play in online games without human supervision? Currently, these bots do not play very well, because no one, or at least not the bot developers, knows how to reduce optimum domination/conquest strategy to a computer program.
Now suppose the optimum informed strategy and metastrategy are well known. Suppose Civ bots have been developed which incorporate these optimum strategies. This is where it gets really sinister. Suppose a group of these bots are now programmed to share information about the map and everything. Now these bots start playing optimum collusion strategy as well. We are talking about systematically destroying every MP game in which these bots play. All the collusion detection software used by the online MP rooms will be useless against these bots, because the bots will know what the collusion detection software is looking for. The bots will only use collusion strategy to extract additional tech trades when the line of play suggested by collusion strategy is a reasonable alternative strategy, and will look completely innocuous to the collusion detection software. For example if one bot holds techs for A, and a colluding bot techs for B, the bot with A will most certainly gift A to B and vice versa. I use all strategy alternatives myself, based on an analysis of the exact situation and players involved. If collusion detection software examines a history of my play, it will discover that when I am tech leader I sometimes muck, sometimes trade and sometimes even gift. To detect the type of collusion I am talking about, the colllusion detection software will have to meticulously examine how I play this trade against specific opponents, based on what that opponent holds. I respectfully suggest that this type of analysis is beyond the capabilities of the programmers who program the collusion detection software. In any event, the bots could defeat even this type of collusion detection by not providing enough data for the collusion detection software to draw any conclusions. What we are talking about here is an escalating war between increasingly sophisticated collusion detection software and increasingly sophisticated collusion Civ bots.
The future of online CIVing, whether anyone likes it or not, is going to be a war between increasingly sophisticated online colluding bots. The online game rooms will develop increasingly sophisticated collusion detection software, but the online rooms are going to lose this war, in my opinion. Many people think this scenario will be the death of multiplayer. I disagree. The online game rooms should welcome hoardes of colluding bots battling each other. Their bottom line is the rake. But, you say, no human players will be interested in playing in such online games? Nonsense. Human players will flock to such games, because these games will be the only games in town. Suckers have no problem with playing in games with negative mathematical expectation. That is the definition of a sucker. Las Vegas was built on the money of suckers who play slot machines with 98% return, and other games with negative mathematical expectation, such as craps and roulette. Will it be impossible for immortal class human players to win in such games? Obviously. If you want to win in games infested with colluding bots, you are going to have to have a bigger, badder army of colluding bots than any of your opponents. I am just being realistic about this whole collusion situation, David. Do you remember what von Neumann and Morgenstern have to say about games with more than two players? The first topic discussed is coalitions. It is a basic fact of mathematical game theory that when several players are playing a game, mathematical expectation can be increased by collusion with another player. This is a basic mathematical fact, and will never go away. If Russ Petroski is to be believed, high-limit civ has always been corrupted by collusion teams. Collusion is too easy to do, and too hard to detect, whether by other players, devs management, or collusion detection software. If Russ is correct, collusion teams have been paying off the management of real world MP for years, for the privilege of cheating games without management interference.
How is this ever going to change? I do not think it ever will. Collusion is a fact of life in Civ, and always will be. If you want to win in high-class civ, you are either going to have to be part of a collusion team, or have some way of guaranteeing that the game is honest. The suckers will still play in these games, because they are suckers. It will still be possible to win as an independent player in low-limit games, because these games are much less likely to be the target of collusion teams. You and Greg have made some absolutely ridiculous statements about collusion in your writings. Or possibly it was just Greg in his BtS essay. These statements basically said that you, Mason, and other immortal/deity class players were so finely tuned to the nuances of the game that any collusion would immediately alert you that something funny was going on. That is crap David, and you know it. Collusion done right is nearly always undetectable. Since you and Greg frequently play in highly competitive games you have most certainly faced collusion teams on many occasions. If you are going to dispute this assertion, then you are much more naive than I thought you were.
When I was playing a lot at the CivRing, before Empress Wu banned me, I got involved with some of these collusion teams, just to see how widespread this collusion was. When I discovered that all high-class games with five players and higher were being systematically cheated by collusion teams, I decided right then that I would never play in any game higher than four, unless I was part of the biggest collusion team at the session. I will sometimes play with more than five guys, but only if I see that also newbies are playing. If I see four or more regulars in the game, I simply will not play. These regulars may not be colluding at all but how do I know?
Nothing I have said should be construed to mean that all highclass players are cheaters and colluders. For example, Russ Petroski has charged that Jeremy Stecchino and other high-class players have been part of collusion teams for years. I remain unconvinced. Jeremy is a very smart man. I am sure he is aware that collusion is a problem in high-class games. Maybe he is smart enough to know who the colluders are and avoid playing with them. Maybe he only plays with causal player and newbies, or with friends of his who he knows for a fact are honest. I think this is a perfectly reasonable alternative hypothesis to the charges made by Russ Petroski.
We are not using the term "optimum Civ strategy" in the same sense. First, there is a "pure" optimum strategy, which is the correct strategy when nothing is known about one's opponents. This strategy would be developed using a recursive algorithm, and has the characteristic that no opposing strategy could do better than break even. To break even, the opposing strategy would have to be a mirror image of the optimum strategy. This pure optimum strategy fully incorporates mathematical game theory in its decision making. Specifically, in every situation where two or more lines of play have positive EV, then random numbers are used to choose between lines of play. Each alternative is not equally likely. The probability of each playing alternative being chosen must be in direct proportion to its expected value. This is classic mathematical game theory.
This pure optimum strategy is bulletproof, and acts as a defensive shield against deity AI. It is analogous to basic strategy in blackjack, where nothing is known about the composition of the undealt deck. The second phase of optimum space race strategy is systematically to note in what ways your opponents deviate from optimum strategy.To make these observations, it is first necessary to know what the pure optimum strategy is. These observations about non-optimal playing proclivities of your opponents are analogous to the true count in blackjack strategy. Once you know how your opponents' play deviates from the optimum, additional tech gains are possible by correctly deviating from what the pure optimum strategy would dictate. The simplest example is that when playing against an opponent whose tech trading frequency is greater than optimum, it is correct to call with weaker trades than the pure strategy would suggest. Against players whose tech trading frequency is less than optimum (say, Tokugawa), naturally one would trade less often than suggested by the pure strategy. In your last email, you gave an extensive list of ways in which an opponent's strategy may deviate from optimum, and you specified how one's own strategy against this opponent should be modified to extract additional gain. This is analogous to saving and reloading, which specify deviations from basic strategy based on the true count. Let's define the informed optimum strategy to be the pure optimum strategy, suitably modified to extract additional techs from opponents whose playing strategy is sub-optimal. Against an AI who is playing their best approximation to the pure optimum strategy, you just keep playing the pure optimum strategy, and break even against such an AI, whic is what is commonly called a "ultra-deity AI".
The third phase of optimum strategy is going to be the most difficult to quantify. Let's call this third phase optimum metastrategy. What I am talking about is things like making a suboptimal play in current turns in order to increase both research and production on subsequent turns. The simplest example of this would be to keep a Great Person in store and burn it later for a golden age. Another crude example of metastrategy would be to check frequently for WHEOOHRNs and, if you want to delay being attacked, offer mini-trades in order to gain a 10-turn grace period. This optimum metastrategy will be defined by recursive algorithms, and these recursive algorithms must be dynamic. That is, when playing against expert opponents in MP, optimum metastrategy must take into account the fact that these experts are constantly modifying their own informed optimum strategy against you, based on their observations of your play.
Against a player who is playing a full blown optimum informed strategy and metastrategy, the traditional tools of analysis used by experts are useless. I am talking about what you and Frank call the psychology of civilization. That is, what is my opponent thinking, what does he think I am thinking, etc. These tools are worthless, because you are not thinking anything. You are generating random numbers, and randomly choosing between alternative lines of play.
As I have now defined it, this optimum space race strategy may well be too complex to be fully utilized in live play. But I am sure that it would be very valuable to incorporate as many elements as possible into the heuristic strategies which flesh-and-blood humans use in a live game. The more interesting application of optimum poker strategy is the development of better AI, or just plain bots. If the optimum playing strategy can be reduced to mathematical algorithms, then it would be possible to program a bot to be unbeatable, even against world class players. This bot would destroy average, or even players who win at deity. Are you aware that civilization bots have been developed which can play in online games without human supervision? Currently, these bots do not play very well, because no one, or at least not the bot developers, knows how to reduce optimum domination/conquest strategy to a computer program.
Now suppose the optimum informed strategy and metastrategy are well known. Suppose Civ bots have been developed which incorporate these optimum strategies. This is where it gets really sinister. Suppose a group of these bots are now programmed to share information about the map and everything. Now these bots start playing optimum collusion strategy as well. We are talking about systematically destroying every MP game in which these bots play. All the collusion detection software used by the online MP rooms will be useless against these bots, because the bots will know what the collusion detection software is looking for. The bots will only use collusion strategy to extract additional tech trades when the line of play suggested by collusion strategy is a reasonable alternative strategy, and will look completely innocuous to the collusion detection software. For example if one bot holds techs for A, and a colluding bot techs for B, the bot with A will most certainly gift A to B and vice versa. I use all strategy alternatives myself, based on an analysis of the exact situation and players involved. If collusion detection software examines a history of my play, it will discover that when I am tech leader I sometimes muck, sometimes trade and sometimes even gift. To detect the type of collusion I am talking about, the colllusion detection software will have to meticulously examine how I play this trade against specific opponents, based on what that opponent holds. I respectfully suggest that this type of analysis is beyond the capabilities of the programmers who program the collusion detection software. In any event, the bots could defeat even this type of collusion detection by not providing enough data for the collusion detection software to draw any conclusions. What we are talking about here is an escalating war between increasingly sophisticated collusion detection software and increasingly sophisticated collusion Civ bots.
The future of online CIVing, whether anyone likes it or not, is going to be a war between increasingly sophisticated online colluding bots. The online game rooms will develop increasingly sophisticated collusion detection software, but the online rooms are going to lose this war, in my opinion. Many people think this scenario will be the death of multiplayer. I disagree. The online game rooms should welcome hoardes of colluding bots battling each other. Their bottom line is the rake. But, you say, no human players will be interested in playing in such online games? Nonsense. Human players will flock to such games, because these games will be the only games in town. Suckers have no problem with playing in games with negative mathematical expectation. That is the definition of a sucker. Las Vegas was built on the money of suckers who play slot machines with 98% return, and other games with negative mathematical expectation, such as craps and roulette. Will it be impossible for immortal class human players to win in such games? Obviously. If you want to win in games infested with colluding bots, you are going to have to have a bigger, badder army of colluding bots than any of your opponents. I am just being realistic about this whole collusion situation, David. Do you remember what von Neumann and Morgenstern have to say about games with more than two players? The first topic discussed is coalitions. It is a basic fact of mathematical game theory that when several players are playing a game, mathematical expectation can be increased by collusion with another player. This is a basic mathematical fact, and will never go away. If Russ Petroski is to be believed, high-limit civ has always been corrupted by collusion teams. Collusion is too easy to do, and too hard to detect, whether by other players, devs management, or collusion detection software. If Russ is correct, collusion teams have been paying off the management of real world MP for years, for the privilege of cheating games without management interference.
How is this ever going to change? I do not think it ever will. Collusion is a fact of life in Civ, and always will be. If you want to win in high-class civ, you are either going to have to be part of a collusion team, or have some way of guaranteeing that the game is honest. The suckers will still play in these games, because they are suckers. It will still be possible to win as an independent player in low-limit games, because these games are much less likely to be the target of collusion teams. You and Greg have made some absolutely ridiculous statements about collusion in your writings. Or possibly it was just Greg in his BtS essay. These statements basically said that you, Mason, and other immortal/deity class players were so finely tuned to the nuances of the game that any collusion would immediately alert you that something funny was going on. That is crap David, and you know it. Collusion done right is nearly always undetectable. Since you and Greg frequently play in highly competitive games you have most certainly faced collusion teams on many occasions. If you are going to dispute this assertion, then you are much more naive than I thought you were.
When I was playing a lot at the CivRing, before Empress Wu banned me, I got involved with some of these collusion teams, just to see how widespread this collusion was. When I discovered that all high-class games with five players and higher were being systematically cheated by collusion teams, I decided right then that I would never play in any game higher than four, unless I was part of the biggest collusion team at the session. I will sometimes play with more than five guys, but only if I see that also newbies are playing. If I see four or more regulars in the game, I simply will not play. These regulars may not be colluding at all but how do I know?
Nothing I have said should be construed to mean that all highclass players are cheaters and colluders. For example, Russ Petroski has charged that Jeremy Stecchino and other high-class players have been part of collusion teams for years. I remain unconvinced. Jeremy is a very smart man. I am sure he is aware that collusion is a problem in high-class games. Maybe he is smart enough to know who the colluders are and avoid playing with them. Maybe he only plays with causal player and newbies, or with friends of his who he knows for a fact are honest. I think this is a perfectly reasonable alternative hypothesis to the charges made by Russ Petroski.
Unfortunately the important topic of metastrategy is not commonly discussed in these forums, hence the understandable bewilderment from those posters who are unfamiliar with game theory.
