[Free Article] Flowchart Thinking

[Vegeta2711]

http://strategy.channelfireball.com/featured-articles/silvestri-says-flowchart-thinking/

A general 'theory' article, but if you play Magic it's probably worth a looksie anyway.

[Marske]

@veggies,
A great read, I enjoyed your examples and it's really something people should be mindful of because lots of players vintage players fall into the same traps you outlined for other formats.

[Elfrago]

Great article, sadly I'm one of those players 

[BruiZar]

Although interesting, I'd like to point out that Sun Tzu has made rules of thumbs for military tactics and could also be considered flowchart thinking. There's nothing wrong with a flow chart. Flow charts can help identify cause and effect. It helps decision making because you eliminate bad choices in a systematic way. Bad choices can be obvious but they can also be  potentially threathening paths with too much uncertainty in the flow chart. Uncertainty would be not knowing what cards your player has in his hand or his deck. I wouldn't call the article "Flowchart" thinking but "Autopilot" instead, even though the classic street fighter flow chart helps get your point across.

[AmbivalentDuck]

For solved games with complete information, aren't flowcharts actually superior?  Even in chess, table/tree-based strategies currently compete solidly with world-champion human players.

Magic (especially, Vintage) will never be solved because of its ever-increasing/changing card pool and enormous amounts of hidden information.  But that doesn't imply that an "ideal" tree is not a superior strategy.  The example in your article only challenges an idiotically unchanging tree that's known to be less than optimal.

[Sextiger]

Flowchart Kens make me money playing Street Fighter 4, I adore them. 

[nineisnoone]

Ideal flowcharts would require absolute knowledge of the circumstances, which in chess is possible because there are no unknowns outside of decisions.  In magic, your opponent's hand is unknown so an ideal flowchart is impossible and thus must be made on assumptions and expectations. 

Flowcharts can be useful in limited or controlled situations.  For a fighting game example, you could have "opponent dragon punched me" 1) did it hit?  Yes - crap.  No - Punish with you most damaging combo.  Extrapolating entire matches is silly though.  There are too many unknowns. 

Basically there are two ways of approaching magic, and generally everything in life, one where you know and one where you don't know.  When you know, you should use flowchart thinking.  If only because if you don't, then there's really no point in knowing anything is there?  When you don't know, you shouldn't because you need a free mind to be able to adapt to the unknown, and flowcharts will encourage your mind to force unknown into familiar patterns, generally ending poorly.  Unless of course, you actually do know.

So then the important thing is to understand when you know and when you just think you know, and be open minded to being wrong one way or the other.  If you have a fountain of knowledge and know it like the back of your hand, by all means, look at the back of your hand.  But if all of the sudden things aren't operating quite like they should, you need to have the discipline to accept that your presumptions were wrong.  On the other hand, if you walk into a situation assuming the unknown and all of the sudden you realize you've been here before, you need to have the confidence to follow that past experience to be able to capitalize on opportunities. 

For every flowchart Ken, there is a non-flowchart Ken who has the flowchart:
Is it a flowchart Ken?
Yes.  -> Bait shoryuken.  Punish shoryuken.  Remember he will shoryuken.
No.  -> Play intelligently. He might not randomly shoryuken all the time.

[Ulthrion]

Very nice article! Although I'm not completely sold on the idea. I think it's very important to think outside of the box, but the flowcharts are not an absolute evil that must be avoided. I've read Playing to Win, and it makes a good case for sort-of flowchart thinking. The main point that stuck out for me was the conservation of mental energy in a tournament. I read this around the time I went to my first Vintage tournament ever, and after 6 rounds, I was mentally exhausted. Even if by some miracle I would have made it into top 8, my concentration (or lack thereof at that point) would have prevented me from reaching much higher.

Tournaments drain mental energy, and flowchart thinking (or autopilot thinking) can help conserve energy for the really important matches.

The biggest point from your article for me would be to always be aware of when you can apply flowcharts, and when not. What I mean is that if you decide to ride out a game on autopilot, you should always be aware when the flowchart is failing, and tighten up your game.

I think that flowcharts/autopilot can be weapon in winning a tournament, but you always need to be careful when applying it.

Ideal flowcharts would require absolute knowledge of the circumstances, which in chess is possible because there are no unknowns outside of decisions.  In magic, your opponent's hand is unknown so an ideal flowchart is impossible and thus must be made on assumptions and expectations. 

Just for nitpicking purposes: In magic, even though a hand might be unknown, each card represents a few thousand possible plays, but nothing infinite. Therefore it is possible to create an ideal flowchart like in Chess. For mathematical purposes, Magic is still a finite game at any given point in time.

[nineisnoone]

i never said finite, i said known.  it's entirely possible to have known infinites.
in chess the entire game state is visible on the board. in magic the entire game state is not visible on the board. you cannot create an "ideal" flowchart because of that.

when i say an "ideal" flowchart, i mean to say to create the "perfect" move for any situation.  it is logically possible in chess (perhaps not strategically, i suck at chess).  but it is not in magic. you have to make some set of assumptions when you enter into an unknown game state.  

for instance a chess flowchart could look like (simplified as hell):
1) does he have a Queen?
Yes - > move Knight
No -> move Rook

but a magic flowchart dealing with unknowns would look like (against simplified as hell):
1) does he have FoW?
Yes -> bait FoW
No -> just play whatever

the difference is that you can look to the board and see the Queen, but you cannot see if they have a FoW in their hand in magic.  your flowchart is made on presumptions of game state rather than knowledge of game state. that is what i mean by the fact that magic cannot have an "ideal" flowchart.

[Harlequin]

I can't read the article at work but I intend to when I get home.

Reading the comments here, you can "Solve" games that have random or unknown information based on sets of possible results.  For example there -is- a solution to Backgammon.  Dispite every turn being based on a roll, you can only roll 21 unque combinations of two dice.  Knowing that bascailly you look at all possible future rolls for you and your opponent.  You work your way backwards from all possible futures to know the optimal move based on the set of all possible rolls, and optimal moves.

If you look at Backgammon on Wikipedia about 2/3s of the way down it talks about the history of computer opponent's as well as general theory of "bearoff" points to make optimal plays.  Here's a quote:

TD-Gammon's [the computer program's] play was at or above the level of the top human players in the world.  Woolsey said of the program that "There is no question in my mind that its positional judgment is far better than mine."

This idea could be ported over to MTG, however your decission tree's and possible futures (while finite) are much more expansive than you would think.  Because you have to not only analyze what -is- in thier deck, you have to analyze what -could be- in thier deck.  So you're tree would including things like  "If they are running only 3 force of wills."  You could even transpose that with the probability that "If they are running 1 force of will, there is a 95% chance they are running 4 forces"  And we can sorta fuzz out all the "If they are running 4 Feral Thalids then..."  Because there is very low probability of that.

Anyway, I like to think of magic this way, at least in the abstract.  Where at any given point in the game there is an array of all possible futures for this game of magic.  Not bound concretely by what the run, but bound by the probability they run cetain cards.  This idea makes those dicussions about "the right choice" versus "what happened" a little eaiser.

[Ulthrion]

I was going to make a reply here, but Harlequin said it better than I could.

The point that there is unknown information is not of concern, because the number of possible direct futures (i.e. game state when you regrain priority in Magic, or when it's your next turn in chess) is finitely bounded. In a sense, the problem of there being unknown information is the same as the unknown decision making process you opponent uses to make their moves. In both cases, you can't predict the outcome 100% each time, but you can calculate all possible outcomes.

[Harlequin]

Well Chess is a different story.  With perfect computation, you could derive a move in chess that would Win* the game with 100% certainty.  By setting up a chain of If my opponent does this, I do this.  And eventually you get to the end.  This is unique to games like chess because at any point there are a finite and static set of possible moves.

In games like Backgammon or MTG, there is veriance.  So your immediate goal in any choice is not nessiarily to ~win~ the game... but instead to possision youself to have better odds of eventually winning the game based on all possible futures weighed against the probability of those futures.

The "problem" with chess is that we just dont have that computation power.  Because each possible move has hundreds of possible 'next' moves, and each of those children have hundreds of children after that.  With Backgammon you have the luxiory of knowing that there are only 21 different sets of numbers you could possibly roll.  So 21, 441, 9261... it gets up to like 32 million or so before the game is over.  In chess you're looking at adding two additional powre of ten each move you make.

*- Ok maybe not win, but you could at least force a draw...

[AmbivalentDuck]

In games like Backgammon or MTG, there is veriance.  So your immediate goal in any choice is not nessiarily to ~win~ the game... but instead to possision youself to have better odds of eventually winning the game based on all possible futures weighed against the probability of those futures.

Not necessarily true, it's probably possible to build a post-Duress tree for various storm builds.  The number of hand-library combinations is suddenly finite.  And you only care about a handful of cards that your opponent can have in hand.

[Harlequin]

Oh sure, you can get to a point where it was not possible for your opponent to win.  You don't even need duress.  If youre opponent is at one with no cards in play and you have city of solitude in play and attack with your mons goblin raiders.  We know now know with certain the outcome of this game.  But you still have to get to that point, and getting to that point involves making choices with unknown futures.  What if they counter duress?  What if you duress them and they have Tripple force with 3 blue cards? 

[BruiZar]

Good players can fill in the blanks when it comes to decklists as soon as a player reveals his first card. That eliminates alot of chance right there. Reveal hand cards such as Duress and cabal therapy and permission cards such as mana drains and Force of Wills remove even more chance.

I especially believe Cabal Therapy is a very important learning tool for people to become good in magic. Because your decision is based on incomplete data and the result of your decision is shown immediately after resolving the Therapy. Meddling Mage is the same thing but sometimes it's hard to know if you really named the right stuff because there's no built-in check like you have with Therapy.

[nineisnoone]

Well Chess is a different story.  With perfect computation, you could derive a move in chess that would Win* the game with 100% certainty.  By setting up a chain of If my opponent does this, I do this.  And eventually you get to the end.  This is unique to games like chess because at any point there are a finite and static set of possible moves.

In games like Backgammon or MTG, there is variance.  So your immediate goal in any choice is not necessarily to ~win~ the game... but instead to position yourself to have better odds of eventually winning the game based on all possible futures weighed against the probability of those futures.

I'm not sure if you were intending that as a comment on my post or not, but that is exactly what I'm am trying to distinguish between "ideal" flowcharts that are logically possible in Chess, but not in Magic.  

Playing "odds are they have a FoW," is not the same as knowing they do or do not.  Good players will see that you are playing that probability, and leverage it against you. Magic, imo, is closer to Poker than anything else.  You can look at the flop, and look at the best, and play the probabilities.  And at certain levels, you will dominate.  But at higher levels, you're just another Flowchart Ken.

Chess (and I'm guessing Backgammon) are more like competitive puzzle games.  There is another player, but to a certain extent you are not playing the player, you are playing the board state.  Opposing players have no hidden knowledge or powers that they can leverage.  Dice rolls are irrelevant because despite being random, opposing players cannot leverage them so they are equal to both of them.  

And while there are puzzle aspects to Magic, because there's more to it.  Making choice based on opponents probabilities, means your opponents get to make choices on 100% certainty.  Think about it this way, there is no flowchart that you could give to an opponent, and he will not be able to beat you.  In Chess (and maybe backgammon) it doesn't really matter. If the flowchart is "ideal", i.e. perfect, then it will win regardless.  Strategically, it's probably not exactly possible, but logically it's sound.

The only time where a flowchart in magic or a fighting game can be ideal is when the game or the deck is unbalanced, where there is simply no way that the deck can lose and all you need to do is solve that puzzle.  But that's why fighting games get re-balanced and magic has banned/restricted lists.

[Harlequin]

It's very interesting that you bring up Poker.  If you wrote a "prefect" program for poker that made bets proportionally equal to its odds of winning the hand, It would likely lose all the time.  Poker is an extremely interesting example because if you play by a flow-chart it ends up being easier for a player to read you and basically guess your hand based on your bet. 

In poker, everyone is going to get equally good hands in the long run.  The players who bet the -best- win, and this is almost exactly opposite of people who make "the best bets" (ie bet big on every good hand, and fold every bad hand)  Sometimes you have to bet big on bad hands, and fold good ones.  Actually thats what makes me an awful poker player, I play too much like the computer.

I would say that Chess is really off in its own world when it comes to trying to group Chess, MTG, Backgammon, and Poker.  As you pointed out about the perfect ideal chart.  While all games have a point at which you could conceivible say "Mate in 4" only chess has the theoretical turn 1 "Mate in 247" We just haven't solved it yet.  The differance is that as soon as you set up the chess board, the set of all futures is 'known' at least in the abstract.  Take a similer game like Tic-Tac-Toe or Connect 4.  These games have true ideal right from turn 1 flow charts to winning (or tieing).  Chess has one too, we just don't know it.

In Backgammon there is a set of all -possible- rolls, as well as poker, there is a set of all -possible- hands, and in magic as set of all -possible- gamestates.  But at the end of the day, at some point in the game, your opponent will have a chance to win.   So every choice up until the end is about putting yourself in an advantage in the eyes of probability.

[AmbivalentDuck]

It's no different than backgammon, you go all Bayesian on the problem and maximize the expected value of something.  You're just saying that the problem space is large.  Wasn't the backgammon AI trained by just playing against itself?  Based on MTGO's existance, we know that the rules of magic are codable.  It should be possible to go game by game and have an AI explore the full tree of legal decisions.  Maybe a support vector machine?

[Harlequin]

Its an interesting idea, however I think it would be orders of magnitude greater than that of the chess solution.  In order to find "the best deck" and essentially code a primer of "best plays" lets say even for an 18 person event.  You'd take the 18 decklist and have the computer play out tournements with all possible pairings, sideboard options, and plays considered.  To then say "who is most likely to win, given everyone is playing 'optimally'." 

That would only tell you the best deck of those 18.  If you really wanted to -build- a deck, you would have to go through the set of all vintage legal cards, and build a deck to beat that 18 person metagame. 

Then of course you could add that deck to the meta and build another deck to beat that 19 person meta.  And so on...

Interesting idea though.

[AmbivalentDuck]

Actually, the minute I'm unlazy enough, I'm doing the parsing on morphling.de, which turns out to be trivial because all decks on there are available like this.  Then we can use PCA to find/build optimal decks.

With PCA we can decompose decks into components with variable winningness and use the winningness of components to build optimal decks since that's just simple linear regression after the heavier matrix factorization is done.

[TopSecret]

The main problem with this "flowchart thinking" is that it is based on what you think you know,
and what people think they know can be wrong.
This is especially true for noobs because of their lack of experience, among other things.

Flowchart thinking is more or less human habit
so it isn't effective to shun it. It's the most efficient method for most humans to do work.
Players just have to realize that they are always forming habits of play,
realize how they form these habits,
and then use this information to purposefully form habits that lead to reaching their goal.

The trick is to use the mental energy saved by having a flowchart
on other things that matter for in-game play,
and then when you do lose, try your hardest to figure out your mistakes.
Unlike everything else, we know that in game mistakes effect what happens in the game,
which then directly influences who wins,
so in game mistakes should be given the highest priority in understanding why they happen.
It's all a balancing act that redirects all the individual's energy toward winning.

Once you have constructed a flowchart of behavior that reaches a reasonable threshold of accuracy in making the optimal play,
you can then use the mental energy saved elsewhere,
like learning how to read the opponent.

[bluemage55]

It's very interesting that you bring up Poker.  If you wrote a "prefect" program for poker that made bets proportionally equal to its odds of winning the hand, It would likely lose all the time.  Poker is an extremely interesting example because if you play by a flow-chart it ends up being easier for a player to read you and basically guess your hand based on your bet.  

I'm an online poker player, and this is patently false.  You can design a computer program that makes game-theory optimal decisions; that is, it the program will balance its ranges and play in such a way that you cannot read it.

For example, I can program a computer to check/raise with both monster hands (for value) and with strong draws (to semibluff).  Because the optimal counterstrategy against each of these hands is very different (e.g. if you have top pair you want to fold to the monsters and reraise the draws), it is impossible to correctly counter this strategy unless you have discerned from other points in the hand what the computer's hand is.  Additionally, optimal bluffing frequencies can be mathematically calculated (you should bluff so that the odds that you are bluffing are directly equal to the pot odds your opponent is getting) to make it impossible to choose a proper response to such a check/raise in a vacuum (forcing the opponent to instead make the play according to the strength of their own hand).

The real drawback of computer programs is that the state of technology as it exists today is insuffiicent to allow for learning AIs.  While computers can play optimally (that is, they can play in such a way that reading them is impossible while still building large pots with a majority their big hands and pot controlling with a majority of their medium hands),  they cannot play exploitatively to take advantage of holes in the opponents' strategy.  You can design a program to recognize cues that the opponent is exploitable (e.g. they bluff too much, or play too passively, or always bluffs on paired boards, etc.), it is very difficult to give the computer the intuition that most poker players use to determine exploitable opponents.  Even online players who utilize HUDs to track exact betting frequencies must make judgment calls due to the limited sample sizes that you will have available before the opponent leaves or changes strategies.  You would also be hard pressed to design an AI today that can determine the level of thinking the opponent is on; plays that may fool a thinking player may fail against an idiot and vice versa.

[bluemage55]

the difference is that you can look to the board and see the Queen, but you cannot see if they have a FoW in their hand in magic.  your flowchart is made on presumptions of game state rather than knowledge of game state. that is what i mean by the fact that magic cannot have an "ideal" flowchart.

You can, however, calculate your optimal decision by considering the likelihood that the opponent holds a FoW and statistically calculate your average expectation.

For example, if playing Yawg will yield an expectation of (using arbitrary numbers) +12 towards winning the game if they lack FoW, and -4 towards winning the game if they do, then you should cast Yawg if the likelihood the opponent holds FoW is less than 75%.  This is because your average expectation = (odds that opponent lacks FoW) * (expecation from sucessfully casting Yawg) + (odds opponent has FoW) * (expectation from getting Yawg countered).

[AmbivalentDuck]

it is very difficult to give the computer the intuition that most poker players use to determine exploitable opponents.  Even online players who utilize HUDs to track exact betting frequencies must make judgment calls due to the limited sample sizes that you will have available before the opponent leaves or changes strategies.  You would also be hard pressed to design an AI today that can determine the level of thinking the opponent is on; plays that may fool a thinking player may fail against an idiot and vice versa.

The 'learning to learn'/coadaptation problem kills us in both haptics and brain-machine interface design    All of our advances involve making the human side handle the coadaptation problem.

[nineisnoone]

the difference is that you can look to the board and see the Queen, but you cannot see if they have a FoW in their hand in magic.  your flowchart is made on presumptions of game state rather than knowledge of game state. that is what i mean by the fact that magic cannot have an "ideal" flowchart.

You can, however, calculate your optimal decision by considering the likelihood that the opponent holds a FoW and statistically calculate your average expectation.

For example, if playing Yawg will yield an expectation of (using arbitrary numbers) +12 towards winning the game if they lack FoW, and -4 towards winning the game if they do, then you should cast Yawg if the likelihood the opponent holds FoW is less than 75%.  This is because your average expectation = (odds that opponent lacks FoW) * (expecation from sucessfully casting Yawg) + (odds opponent has FoW) * (expectation from getting Yawg countered).

Seem to be missing my point completely.  Shoryuken!

[BruiZar]

I advise you to read up some stuff on Information Asymmetry. It's an important factor in business. For example, if it wasn't for the concept of information asymmetry, the SEC wouldn't be against insider trading.
http://en.wikipedia.org/wiki/Information_asymmetry