Phil Hellmuth won most of his bracelets before the internet boom aka when texas hold'em was not nearly as popular as now. Nowadays it is practically impossible to win WSOP main event twice in a row (10 times more contestants, most of them pretty strong). He gets great tournament performance, because his playstyle is extremely effective against weak players, but anyone who was watching "Poker after dark" or similar regular events will quickly understand how he was outplay by Phil Ivey, Tom Dwan and the rest of the pack. Phil Hellmuth is a bit like Impaller had Impaller continued playing and not improved. Also, he has a much bigger ego than mine which says something. Ending with a simple questions, Phil Ivey won all his 9 bracelets after 2002, how many bracelets did Hellmuth win since then?

actually Phil Hellmuth is continuing to have a lot of success in tournament, he won 6 bracelet after 2002, including WSOPE main event in 2012 for 1.3M$, and finished 3 times runner-up in 2011. Everyone says that he only won that much bracelet because at the time no one knew how to play, but his results proves the critics wrong. He is a great nlhe tournament player, but he can't compete if you throw him against the top pros in cash game or any game that isn't nlhe

Impaller was better than Teddy. Teddy came back and dominated.

Impaller could come back and beat Gnuff in a best of series on 1v1 ME. When Impaller came back the last time, his level of play was at least as good as Gnuff's record breaking run. Did you watch Gnuff's six losses? Gnuff said.

Boxing analogy. Think in terms of rounds. If you compare WL games to boxing rounds, it makes more sense. Boxing has strategy and risk taking very similar to WL.

Game theory: All the programmers, mathematicians, and statisticians are good or great players. But the best players have backgrounds in social sciences. To make a computer beat top WL players, you need the computer to use intuition, to read the language of troop movements and deployments, and to play the player as well as the board. Sze, your strength is game theory. Understanding it helped you become a top player. But it also is your weakness: an overreliance on any theory means you are less able to rely on intuition and random guessing (which should throw off game theory calculations).

If game theory were so powerful, our head to head record would be different: you would have my winning record and I would have your losing record.

Edited 3/5/2014 15:12:33

I dont agree with this Qi, perfect game theory will always prevail against "feeling" players. I started with the poker analogy because poker and WL are very similar in lots of ways. Both have mathematical and psycological aspects. 10 years ago, everyone said poker was a game of adaptation, where you have to play the players as much as the cards & the board. Everyone said no computer could ever win long terme against top pros. A few months ago was released a program based solely on game theory optimal (GTO,based on Nash game theories) , and it has been crushing everyone for the past 6 months (of course a lot of people says it is rigged). Same thing happened with chess and backgammon programs, every masters were saying a computer can't beat the best humans, because of the psychological part of the game. Today people skills are measured through those programs. WL hasn't reach this level in term of game theory (and probably won't) so great "feeling" players can still be the bests. But in a vaccum game theory beats psychology

My "feelings" are based on reading hundreds of books on history and philosophy. War evolves in time and place. I see certain situations in games and think of Alexander the Great or Napoleon or certain historical battles. The strategies we use in WL are historical strategies. You can use game theory to innovate (in your own mind, because the strategies are new to you) or you can have a database of historically successful strategies and adopt and adapt them to WL (and the particularities of the board you are playing any given turn). Most of this I have internalozed to the point where most of my moves are based more on intuition and less on thought. If you want to consider this "feelings," I don't mind.

But the notion that game theory is the best approach to WL is not wise. How do you program a computer to read different maps and understand where is best to pick? At some point patterns from past games have to be used I assume. And that is no different than using actual history as a guide to WL. Patterns from past games is history, or art of war, not game theory.

The art of war is a science too. If a WL-playing computer were developed that could beat every player every time, I would say it mastered the art of war, not game theory.

Edited 3/5/2014 16:12:47

warlight has absolutely nothing to do with the "art of war". conquering a territory is determined on probability, not on your troops healthiness, spirit, the quality of equipment, their leadership, the resilience of the natives, weather, alliances shifts or any other factor real war have. The board is set at the begining of the game, and from this point every scenario can calculated and anticipated in theory. The thing is it is impossible for a human to play optimal game theory, human makes mistakes. And because human make mistakes, it is exploitable. And thit is where the psychological part of the game is important, to exploit your opponent mistakes. Game theory doesn't makes mistakes,it only choses the best theoretical moves for a given board. Of course an optimal game theory for Warlight doesn't exist yet, probably won't ever, but i can't see why there wouldn't be one in theory.

edit: by "feeling" i don't mean that in a bad way, what i mean by feeling is trying to get in the head of your opponent.

Edited 3/5/2014 16:33:31

Read 孫子兵法 in the original classical Chinese. Be open to not only what is explicitly mentioned but also pay attention to the Daoist and other strands of Chinese philosophy that Sunzi gets his words from. Next, keep these ideas in mind and apply them as best you can to your readings on war in other times and places. Lastly, try to apply these ideas to WL. If you did all that, you would disagree with your assessment of what the art of war is. Art of war is game theory plus military science, history, psychology, sociology and philosophy.

If you understand game theory so well, apply it to your games and win more. If you have the secret to winning, why sell yourself short?

Edited 3/5/2014 16:41:09

well i knew at some point my results would come up, that's what happens when someone lacks arguments for an abstract conversation.I guess you have trouble understanding the things i said, so i'll try to say it again so that you can understand. Human makes mistake, human are not machines. But human can understand how the machine works and can make the machine. Does it mean the programmer of said machine is better than the machine he has created? NO. Because the programmer is human and doesn't have the calculation capability of his machine. Human can get better by experience,by putting a lot of work into his game and try to get closer to optimal game theory, wich he will never be able to reach.

So of course you are eager to speak about me as a player and not about my ideas, because you are the great Qi, you've been around forever and think that your reputation gives you authority for everything you say. I'll respond this to you: No i don't know the optimal game theory for WL nor have the skills to creat it, and even if the optimal game theory for WL already existed, i don't have the time to try to master it. Try to humble yourself, nobody cares that your read the art of war in fucking chinese, or that you know all about Napoleon, especially because it isn't relevent to the conversation.

I've been playing warlight for 3 months, and the ladder for 2 months, so no i'm probably not as good as you are yet. There you go, you are the best Qi!

Edited 3/5/2014 17:32:59

I am the Great Qi. I have existed since time immemorial! Heed my words, little man! Bow before me!

I don't know who you are or your results/stats, and frankly I don't care. I was being facetious. Sze says he plays using game theory. I think it is simply a logical theory among many influences that give order and clarity to his thought process. Since I doubt anybody can apply pure game theory to WL, I jokingly asked you to do so, knowing full well nobody can.

Art of war is all encompassing. Machines require a man made brain, which requires a special language. Sure, game theory could be that language. But when you apply it to WL it is art of war. There is no pure game theory in WL. There can be pure art of war.

Chinese is relative to the conversation. If you read Art of War in Chinese and English, you would be amazed at how profound the Chinese is compared to the English. The translation loses so much. There is no strategic equivalent in the English language. But, since you seem to prefer cussing and simple assumptions about me, my ideas, my jokes, etc., I don't think foreign ideas especially suit your intellect.

So, let's go back to your first assumption: art of war does not exist, only game theory exists, and therefore game theory is the greatest way to win in WL, because WL is a game and game theory has the theory.

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