Game Theory is much like Plato's theory of "Ideal Notions". That is that say a chair is a notion of what you want from a chair and that there is in fact an ideal form of this "chair" and our purpose is to achieve this ideal form through contemplation and trial-and-error. Plato argued that the ideal form would be so profound that all humans would agree "this is the ideal chair". -> The notion that such a thing exists is nothing more than an imperfect notion itself and is therefore incorrect by its own definition because its not in its ideal form.

125ch209, you seem to be arguing from this standpoint and to your credit you're putting up a good effort, but Qi is largely correct. This program that has been beating Poker players for the last 6 months will, without updates, eventually become obsolete because humans adapt. Once a human understands something he begins to manipulate it until he can more or less control it. That is largely what civilization is built upon. Most programmers will tell you that there is no learning AI, once you step outside the parameters of a program's "learning ability" it becomes obsolete. Human minds are much more malleable in that sense, which is why you sometimes run across child prodigies which can play chess or write symphonies that men and women with 20-30 years more experience can't match.

Qi is highlighting that 1. we're not going up against AI, but other human players that can learn and adapt and 2. a map on WarLight is less restrictive than a chessboard with 8x8 squares and 6 different pieces, or a card game with 52 cards. WarLight can change a variety of settings and a player's ability to perform well on one map doesn't mean he's understood the game or is the best.

I make a lot of jokes at Jay's expense, but there's some merit to all his back-row cheerleader shenanigans and bragging. If you're a focused and dedicated player who understands a map and setting well you'll be able to perform well. At the same time a player can become lazy or lack determination and perform terribly at something he was previously good at. Works both ways. However, there is an intrinsic talent that Buddhism refers to as enlightenment. Without pulling religion into this, what I'm getting at is that unlocking a true understanding comes from a long term dedication and practice. Rehashing theory by reading books, going through guides, watching other player's games and a fair share of personal experience (this is meditation, aka contemplation).

This will beat game theory any day, because it is a continued practice that learns and adapts, going through highs and lows, but always a moving force.

First of all i don't deny psychology isn't a big part of today warlight games. Reading about art of war, buddism or plato can make you a better player. Knowing about historical wars can probably make you a better player too. All of this enhence your creativity and thus gives you more material to elaborate winning strategies. Why? because Warlight isn't a "solved" game.

Hauptmann, you are wrong when you say that a program using perfect game theory will become obsolete. Of course the program i was talking about don't use perfect game theory yet, so it will need updates to get close to perfect game theory. I understand how it can be doubtfull a program is able to beat human in a game as "complex" as warlight (tho i think strat 1v1 is actually much simpler in term of variables than no limit holdem poker). For example, chess programs now have pretty much "solved" chess, and no human has the intellectual skills to win against those chess programs on the long run. This is what will happen when poker will be "solved" like chess or for Warlight.

Game theory is a very complex concept, and even tho i looked into it a bit, i don't claim to fully understand it. I will try to explain it the best i can. In order to understand the concept, we can take the example of a simple game: the "cross & circle game" (i don't know how it is called in english)


This game is "solved" and the beauty of it is you don't need a computer to solve it. When your opponent puts a cross in a box, you know where you have to put your circle if you don't want to lose, and if both players knows the game theory, the game ends up as a draw.

Nash game theory states that for every game, it exist an "equilibrium", and a strategy that can't be exploited (the game theory optimal - GTO) by any other strategies, and the only way to not lose against the GTO stategy is to also play GTO. and if 2 players plays perfect GTO, the long term results will be even. So no strategies can beat GTO (i know it is hard to believe, but blame the maths, not me). Still, it doesn't mean GTO is the best strategy against one specific strategy. If i know where my opponent makes mistakes, i'll deviate from the GTO and exploit his mistakes, this is an "exploitive" strategy, not GTO, meaning it works well against a given strategy, but could work bad against another.

To a certain extent, all games are like the "cross&circle" game, but the complexity of a game like Warlight makes it very hard to play or even know what is the optimal strategy, at least for humans.


So back to the point, i do think that, in a vacuum, game theory beats psychology/creativity/whatever. But the beauty of a game like warlight is that it is so complex that everyone makes a lot of mistakes and no-one plays GTO, so other skills like your creativity are crucial (inspired by Sun Zi or Napoleon or whatever you do to sharpen your brain). So Qi, your Art of War is what i call your creativity, but creatives strategies can't compete against game theory by definition.

Edited 3/5/2014 22:31:04

There's one flaw in your thought process..

Warlight is a game much more similar to poker than to chessor tictactoe (or as you called it: cross and circle), simply because:
1) there is luck factor involved
and most important:
2) It's a game with INCOMPLETE information.


So at least to some extent the algorithm is unable to determine enemy's position, enemy's possible moves, furthermore it's unable to decide whether to defend against counters from behind the fog or not etc. It may try to determin best position from those possible, but may easily be surprised half way through >perfectly< playing against a scenario that is not happening..

First of all, GTO is and will always be Great Teacher Onizuka for me, so find a better acronym, like adding an M for math or something.

Secondly, you pointed out a key difference I should highlight. In WarLight there is fog, so unlike Chess and Tic-Tac-Toe, you can only respond to what you see and if that isn't the whole picture then you can't be sure.

However, like Texas Holdem you can know what your opponent doesn't have and use that knowledge to aid your game.

Also, when I talked about Plato I should have added this. The ideal form is always changing because of the definition and demand is always changing. Just like maps and minor settings in the Seasonal Ladder are always changing. You can say that at one point at the "end of history/time" there will be the optimal form, but that perspective can impact your ability to take new changes into account.

Perfect Game Theory may render a game redundant, but the way to change that is simply add in new variables or make a new game altogether. It's true though, you can't beat the program in the long run, but our brains don't have the GHz to process information on the level of a modern computer and we're playing against other players not the computer.

Doubtless, should this game become successful enough, Fizzer would implement something like that to rank top players, but until that day comes (or doesn't), Qi's definition works rather well.

the problem with GTO is very vivid when an experienced good player meets somebody who is above average in terms of gameplay, but noobish in terms of picks. Often the top player plays a perfect strategy, but is very vulnerable, cause he does not take into consideration completely inefficient opponent's position.. This leads to surprise attacks from unexpected regions, and wasting troops sneaking to reasonable positions, which may turn out being unocuppied.. In the long run this may lead to the pro player losing.

Of course in the long run the pro player will win more often than not, and eventually will win all games against the noob, but he's got that tiny little feature the algorithm would lack - which is human nature - ability to adapt. Where GTO would lose, a human will win by playing other strategy (of course it will be also a GTO but for variables verifiable only for a real human player)

Fridge is intentionally spiting me at this point, possibly for my previous comment on Poland...

Fridge, you made some very interesting points, and it shows why game theory is so complex.
what you call luck factor and incomplete information, i call that probabilities. As Hauptmann said, you know what your opponnent doesn't have, and with this information, you can know the probabilities for everything you opponent CAN have. GTO is not a strategy that will allow you to win every single game, it is a strategy that will allow you to win against any other strategies ON THE LONG RUN. For example, if i tell you that you have 99% chance of winning double of what you bet on a game, and ask you if you want to bet money on it. You would be a fool not to bet, the correct decision GTO-wise is to bet. It doesn't mean it is the right decision if you are result-oriented, because you still have 1% chance of losing your money.

Now I'll take your analogy of a good player playing against a weak player. GTO is NOT the best strategy against this player. He is a weak player so he is going to make big mistakes, the best strategy against him is a strategy that is going to exploit those mistakes. For example, playing safe/defensive against an overly aggressive oppenent is better than GTO, you exploit the fact that he is over agressive. But playing too defensive against another player with another strategy can be a bad. GTO is the perfect balance, "equilibrium", that no strategy can exploit. GTO is unexploitable, but it is not an "exploiting" strategy. Against a given human, GTO is not the best strategy, but overall, no strategy can beat GTO. And to answer to Hauptmann i also like Great Teacher Onizuka way better than Nash and his fucking game theory ;)

btw, if you have seen the movie "A beautiful Mind", it relate the life of Nash, this skizophrenic genius whose work on game theory earned him a nobel prize...

edit: here is an abstract of wikipedia's page about game theory:
"The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome. (Rasmusen refers to these four "essential elements" by the acronym PAPI.)[3] A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability."

Edited 3/5/2014 22:03:19

for chess it is possible to calculate the best move

for warlight, no.
At some situations for WL, it is like rock paper scissors, where within a single turn,
1. if your opponent defend territory A, then it will be best for you to attack territory B
2. if your opponent defend territory B, then it is best for you to attack territory A
3. if your opponent attack you, you stall and defend it off will be best

this is simple because, unlike chess, warlight carries out the moves of both side together. The best move is simply based on the best counter of your opponent move. In that case, the best AI of warlight MUST include the full analyze of a player battle history and take in the consideration of a player habit as a part of the decision making, and then calculate the chance of each of the player option.

An AI who do rock paper scissors without analyzing the opponent's pattern, simply doing pure random moves.

I am not saying warlight is always in a rock paper scissors situation, and i am not saying in warlight each of the "rock" "paper" "scissors" are equal, generally in warlight they have different "weight". But still, at many of the situations you need to correctly predict your opponent in order to make the "best" move.

Edited 3/6/2014 01:14:06

That's true, with random turn order the calculations that a computer AI takes into consideration could be nullified by an opponent getting the first/last move. Not to mention the use of cards. Complex wouldn't begin to describe the process, though if it's cyclical and no cards then it would still be difficult to accomplish.

Considering the nature of this thread I was hoping Riya would be more excited to contribute :P

Edited 3/6/2014 01:13:54

Without realizing it, you are actually making my point, rock paper scissor is a great example for game theory. The Nash equilibrium for this game is this:
chose randomly rock/paper/cissors 1/3 of the time (33%/33%/33%). This is an unexploitable strategy, no strategy can make you win if your opponent is using the 33/33/33 strategy. Even if Rock/paper/scissors have differents weighs, it exists an equilirium that can't lose against any strategy. Rock/paper/scissors is a very particular game because if your opponent plays the Nash equilibrium, you won't win, but you won't lose either. For more complex games, this is not the case.

For example, in poker:
lets say you have only 2 options: going all-in or fold if it is your turn, or calling/folding if your opponent goes all-in. It exist a Nash equilibrium (depending on player's chips stack and the blinds) saying that you should go all in with x% of your cards, and folding the rest. Same with the defender, it exist an equilibrium saying that he should call with z% of his card and fold the rest.
-If the defender plays the equilibrium and call exactly with z% of his cards, deviating from your equilibrium, meaning you go all-in with more than x%, or less that x%, will make you lose money on the long run
-If the oponnent goes all in with exactly x% of his card, calling him with more that z%, or less than z% will make you lose money

Now for warlight: when the attack factor is 60% and defender 70%, it is easy to understand that if both players have equal incomes, both should defend more often than attack, the equilibrium is more toward defending than attacking. This is a mistake a lot a new players makes, attacking too much, thus loosing more troops than the defender,and allowing him to use the extra troop he has to expand. This is a simple situation, but for any situation in a finite game (finite number of players, finite number of moves), how complex it might be, a Nash equilibrium always exists. (Nash's Existence Theorem)

edit: Hauptmann, the randnomness of the moves orders can very well be taken into account in the calculation. the computer calculate the outcome if he gets first move or last moven and choses the right strategy accordingly

Edited 3/6/2014 02:38:44

Just dropping in to say chess isn't solved and most likely never will be. Also, there are still positions in chess where people are superior to machines.

There is no such thing as "pretty much solved". It either is or it isn't.

um.. what made u think it most likely never will be?

of course it isn't solved, what i meant by "pretty much solved" is that for "pretty much" any positions (especially late positions, given the limited number of pieces in play), we know with a reasonable degree of certainty what move is the perfect next move and we know the outcome if both players plays perfectly.But no, computers didn't solved every situations yet, so chess isn't solved. will it be solved one day? i don't see why not, maybe it will require 24/7 calculations during 100 years until all possibilities have run out.

Edited 3/6/2014 14:42:05

On solving chess:

If you consider the possible positions of all pieces except for any pawns and assume you can consider a billion of those positions every second, it will still take you about a billion millenia to consider all these positions. Now multiply this by a number somewhere in between 33 and 64 for every pawn of every player and multiply this number with another huge number (not even bothering estimating that one) for all pieces that you can theoretically change all pawns into.

Then, take into account that "solving" chess means that what I previously called "considering a position" actually requires writing a recursive/iterative script in which all possible follow up positions are searched for an optimum.

So unless some brilliant mind finds an unexpected way to reduce the dimensionality of this problem any time soon, I agree with Ace Windu: it probably won't ever be solved. ;-)

At least we'll have an almost-solved version for the alien archaeologists to dig up when they visit our planet a couple thousand years from now.

Hopefully they won't find this forum.

both theory about being able to solve chess are argued and defended by game theorists. I'm not a game theorist so i don't see the point in arguing. You don't know what technology we will have in 50 years, but yes todays computers are incapable of completetly solving chess (tho chess is partially solved). The point is that chess IS solvable in theory, and there is no arguing that

edit: what i meant by "solved" earlier is that no human can have an edge over today chess programs

Edited 3/6/2014 18:39:54

Practically ANYTHING is possible in theory.
And there is no arguing with theory since it is only theory and thus can't be refuted.

well, i don't know what you guys were arguing about, but i was talking about game THEORY...so sorry if it involves theory. And no, not anything is possible in theory

I am not saying warlight is always in a rock paper scissors situation, and i am not saying in warlight each of the "rock" "paper" "scissors" are equal, generally in warlight they have different "weight". But still, at many of the situations you need to correctly predict your opponent in order to make the "best" move.

Warlight, like any simultaneous-move game, is almost always in a "rock" "paper" "scissors" mode, thus the GTO strategy is almost always a mixed strategy. The GTO solution is almost always 80% move A + 15% move B + 5% move C. The percentages come from calculating the payoff matrix for each pair of move/response and solving minimax. This procedure automatically parses away dominated strategies, and assigns the percentages to non-dominated strategies.

On occasion, when completely lost as to what to do, I would select 6-7 options that I had, 6-7 options that my opponent had, estimate payoffs for each combo of actions, apply minimax to that matrix, and make my options much more clear. You could call that my form of meditation :)

On occasion, when completely lost as to what to do, I would select 6-7 options that I had, 6-7 options that my opponent had, estimate payoffs for each combo of actions, apply minimax to that matrix, and make my options much more clear. You could call that my form of meditation :)

that's the spirit :)
I don't know how you do it tho, analysing 6*6 situations to find each payoff, rank payoff and defining the best mixed strategy...sounds like harcore meditation :D