[Free Podcast] SMIP # 11: The 2011 Year In Review & Optimal Play Discussions

[Smmenen]

http://www.mtgcast.com/?p=22323

Steve and Kevin review the biggest decks, cards and stories of the 2011 Vintage season. Plus, some discussion on the notion of Optimal Play.

Contact us at @ManyInsanePlays on Twitter or e-mail us at SoManyInsanePlaysPodcast@gmail.com

Your Host(s): Kevin Cron , Steve Menendian
Show’s Email: SoManyInsanePlaysPodcast@gmail.com
Show’s Twitter: http://twitter.com/#!/ManyInsanePlays

Enjoy!!!

[Troy_Costisick]

Awesome!  Can't wait to get home from work and listen to it

[evouga]

Flash in the pan.

A particularly weenie-light era of Vintage is just ending, and Delver was well-suited to prey on such an unprepared metagame. But now, with Snapcaster Mage, Goblin Welder, and Delver of Secrets on the rise, people will remember tools like Fire/Ice and Darkblast, and Delver will lose value.

[Stormanimagus]

Hey Stephen,

I am honored that you took my claim and spent nearly the entire podcast dissecting it. I can definitely see the flaw in my assumption that an "optimal" play will always win the game. Sometimes your opponent playing the "long-shot" play can beat your optimal play. There are just too many variables in card interaction and deck construction to consider. I do think that there are MORE optimal plays that can be made by a solid Vintage pilot than by a poor one. One thing I'd like to clarify about my claim. I am also simply implying that "good" players make frequent play mistakes because:

1. Their deck bails them out and they are not conscious of the mistake.

2. They are on autopilot and don't see other possibilities in the heat of the moment.

I'm not putting myself on a pedestal and saying I somehow know better and am a Vintage master, but it does shock me to see seasoned veterans at major events make seemingly obvious and silly mistakes because they are used to playing out a card a certain way (it is more possible for me to see such mistakes with the increase in popularity of Vintage videos of top 8s).

A perfect example was at the Vintage champs. It was Oath vs. Dredge and the Oath pilot had mana crypt out and Time Vault. He tutored for Voltaic Key instead of Tinker and lost to his own Crypt instead of just winning. I see mistakes like this one an alarming amount and it doesn't lend credence to me thinking highly of the play skill of Vintage players. Is it possible that decks with the game-turning bombs that Vintage decks run spoil players and make them soft to tight play? I am typically a fish pilot and that deck does not tend to reward anything other than mistake-free play. Anyway, just food for thought.

Are Vintage players critical Magic players who don't just like to be lazy and go on autopilot? I think there is a danger of that because the card pool changes at a glacial pace. What do you, the reader, think?

-Storm

[chrispikula]

Your post is too long and fancy.  The players who do well at Vintage are not as good at Magic as the players who do well in other competitive tourneys.  The player pool is much smaller so this should not be a surprising reality.  The best Magic players in the world like LSV and Kibler make boneheaded errors from time to time. The best vintage players will make these much more often. 

[Smmenen]

Context for other listeners:

The second discussion issue in this podcast is the Issue of Optimal Play.   It's derived from a question Stormanigus asked here: http://www.themanadrain.com/index.php?topic=43455.0

I would have to say that I am more in the camp of your teammate Kevin on this one. I never assume that my opponent will play any less than optimally. Why would you? If you assume they will play optimally and you then play to beat that shouldn't you also beat a player who makes mistakes?

There are several different questions here we tried to tease out.   Certainly, the question of whether an opponent will always play optimally is a problematic one, since Vintage players, as a practical matter, make mistake all the time (myself included).  The answer to Storm's question "Why would you?" Is exceedingly simple: because they do.  

However, there is a broader and more interesting question lurking within this discussion that we tried to tease out.

It's taken pretty much as an article of faith in the Magic community that in every single situation there is an optimal play.   This play may not always be knowable -- either given the information available or the time constraints of tournament play -- but it is taken as a given that there is one.

Thus, the question of an optimal play is largely understood as an epistemological question: there is an optimal play, but practical limitations/contraints prevent us from calculating it at this time.  In this podcast, we are actually positing something far more radical: that there isn't always an optimal play.  We are taking an ontological position, not an epistemological one.  

Note, I am not saying that there is never an optimal play.  Rather, I'm saying the inverse: that there isn't always an optimal play.  That it is not true 100% of the time that there is, in fact, an optimal play.  The dueling Demonic Tutor example is a good one, but here is the hypothetical I posed on my team forums that I felt illustrated this idea best:

Suppose the opponent can do two things: A or B.  Suppose A is the generally presumed optimal play.

Suppose you have three possible responses: X, Y, or Z

X is the best answer to A, but loses to B.  Y is the best answer to B, but loses to A.  Z is the worst answer to either A or B, but neither loses to A or B.

Which is the best line of play?   I would likely choose Z.

A player who assumes that his or her opponent always plays optimally would choose X, and lose if they played Y.  

This is a simplified example that could benefit from some clarification of terms, but I think the principle is evident.

As I said to my team, when people wondered if this was MERELY a leveled thinking discussion, I said that it's more than that:

This isn't about mind games (or being a jedi) -- it's about heuristics for play -- what kind of assumptions we tend to make and the validity of the grounds for them.   My basic claim is that assuming the opponent will always make the best play may actually lead to suboptimal plays on your part.  

It's really a modest claim: that opponents won't always play optimally, and that there isn't always an optimal play.  

But again, people who aren't reading carefully may mistake what I'm saying and think that I'm arguing that there is never an optimal play.   This is one of those instances were subtle but significant distinctions can trip people up.  

[nataz]

So, how familiar are you with formal game theory? There is a ton of literature devoted to exactly these types of questions.

[Smmenen]

Studied it briefly in college in both economics and philosophy classes.  Let's try to keep the discussion focused on the podcast discussion though. 

[Troy_Costisick]

Stephen,

Would you say that part of the strategy of bringing a rogue deck to a tournament is to capitalize on sub-optimal play?  You're counting on it, aren't you?

Peace,

-Troy

[DubDub]

Suppose the opponent can do two things: A or B.  Suppose A is the generally presumed optimal play.

Suppose you have three possible responses: X, Y, or Z

X is the best answer to A, but loses to B.  Y is the best answer to B, but loses to A.  Z is the worst answer to either A or B, but neither loses to A or B.

Which is the best line of play?   I would likely choose Z.

A player who assumes that his or her opponent always plays optimally would choose X, and lose if they played Y.

Why is A the 'generally presumed optimal play' if there's a response that's better against A than against B?  That seems like an outright contradiction.

Edit: Okay I won't wait for a response before I go on.

A game of Magic is a series of 'states' achieved in turn as determined by the actions of the players or by (when instructed) random events.  What are these states?

Tell me something about the gamestate: whether or not you have a Tropical Island in your hand, whether or not you have a Tarmogoyf in play, whose turn it is, who has priority, whether or not Yawgmoth's Will is in your library or graveyard or exile, etc.  Now, tell me EVERYTHING about the gamestate: all public information, all derived information, all private information that you know (i.e. the contents of your library, even if you don't know what order it's in).  All of that knowledge, and the remaining uncertainty (information private to your opponent or unknown by both players), constitutes a single 'state' in the chain (these are called Markov Chains for those interested in finding out more).  Magic is a ridiculously complex game in the sense that it takes an enormous number of variables to fully describe each state.

When you cast Tarmogoyf by your action the game has moved from a state where you had access to at least  and a Tarmogoyf in your hand, to one where you no longer have access to that mana and Tarmogoyf has moved from your hand to the stack.  When you draw a card during your drawstep (unless it was already known) the game is moving from one state to another randomly as controlled by which card of the actual possibilities you end up drawing.

Some of these states are at the end of the game.  One player has zero or less life and no mitigating circumstance (like Lich or Platinum Angel), etc.  For each pair of potential gamestates we can calculate the probability that one state will progress to become the other in one step.  By compounding these probabilities we can find out the probability that from a certain state another particular state can be reached ever.  I.E. you cannot go from not having Yawgmoth's Will in your deck to having it in your deck with no other changes, because deck selection is static.  In comparison, the probability of moving states by casting Tarmogoyf is very high, because Tarmogoyf is very good (assume that you don't have any opportunity cost to casting Tarmogoyf).

So what do we do with this information?  Well we sum up the probabilities from each gamestate of reaching, eventually, any 'end' state in which Player A has won.  Ignoring the unlikely outcome of a draw the probabilities we find for Player A and Player B (Player A's opponent) winning from a given state must sum to 1.

When decisions are made based primarily on knowns (like, I have the mana to cast Tarmogoyf and no reason not to) the probabilities of changing states will be very high, and correspondingly the probabilities of a player eventually winning from either position will be very close.  When decisions are made based on uncertainties (like, do I think my opponent has a Mana Drain to use on my Goyf?  If so, does my opponent have a Fact or Fiction to sink the mana into?) the probabilities of changing states will be more evenly distributed over the range of potential options.  We  won't see large changes in probabilities until the uncertainty is resolved: either "yay, Tarmogoyf resolved!" or "crap, Goyf got drained."

Anyway, the definition of 'optimal play' in this framework is simple: the play feasible in the current state that maximizes probability of winning in the next state for the player considered the protagonist.

Optimal plays then always exist, though they can be unknowable in the face of uncertainty.

[Smmenen]

Listen to the podcast.

[Smmenen]

Suppose the opponent can do two things: A or B.  Suppose A is the generally presumed optimal play.

Suppose you have three possible responses: X, Y, or Z

X is the best answer to A, but loses to B.  Y is the best answer to B, but loses to A.  Z is the worst answer to either A or B, but neither loses to A or B.

Which is the best line of play?   I would likely choose Z.

A player who assumes that his or her opponent always plays optimally would choose X, and lose if they played Y.

Why is A the 'generally presumed optimal play' if there's a response that's better against A than against B?  That seems like an outright contradiction.

There are any number of reasons why A might be considered the optimal play, and I could come up with a dozen explanations, but it's all irrelevant.

Whether A is considered optimal or not according to conventional wisdom is irrelevant to the hypothetical.  I included it merely for context, given Storm's points.

The subpoint here is that not every play beats every other play.  Hurkyl's Recall or Red Elemental Blastl doesn't beat Yawgmoth's Will any more than Tormod's Crypt beats Tinker.   Yet, they defeat the other.   One of Storm's points is that doesn't your best play beat all of their optimal plays, etc.  The answer is no. 

Anyway, the definition of 'optimal play' in this framework is simple: the play feasible in the current state that maximizes probability of winning in the next state for the player considered the protagonist.

Optimal plays then always exist, though they can be unknowable in the face of uncertainty.

Too wonkish.  Optimal play is the play that maximizes your chances for winning the game.  We go over this in the podcast.    If folks wish to weigh in, please listen to the podcast first, as it addresses the issues in far more detail.   Then, I'll be happy to follow up.  

[DubDub]

I have finished listening.  I still feel like, as was explicitly said in the podcast, option A for the opponent is only considered 'optimal' because of some external authority.  You're talking about assuming they're going to make the 'optimal' play when what you've described is not in fact optimal.

In that example, the opponent's optimal play is to be unpredictable, because being predictable allows the protagonist player to make an informed choice of response.  Since always choosing the play you've described as 'optimal' causes A-X to be the paired selection the opponent is worse off than if they instead choose to be unpredictable.  Both A-Z and B-Z are preferable for the opponent to A-X so their goal should be to get the protagonist to select Z.

There are any number of reasons why A might be considered the optimal play, and I could come up with a dozen explanations, but it's all irrelevant.

Whether A is considered optimal or not according to conventional wisdom is irrelevant to the hypothetical.  I included it merely for context, given Storm's points.

I mean, the example was meant to illustrate a case where:

Note, I am not saying that there is never an optimal play.  Rather, I'm saying the inverse: that there isn't always an optimal play.  That it is not true 100% of the time that there is, in fact, an optimal play.  The dueling Demonic Tutor example is a good one, but here is the hypothetical I posed on my team forums that I felt illustrated this idea best:

Example. 

This is a simplified example that could benefit from some clarification of terms, but I think the principle is evident.

Was it not?

There wasn't a succinct argument made in the podcast or yet in this thread that it's possible no optimal play exist.  I would appreciate a straightforward statement of the ontological case you're making.  Another abstract example is fine, provided that it actually works and that the 'optimal play' posited is not in reality clearly suboptimal.

[Smmenen]

Another abstract example is fine, provided that it actually works and that the 'optimal play' posited is not in reality clearly suboptimal.

The example works without the caveat of which is 'optimal.'    Your opponent has two options: A or B.  Let's say A is the most likely play and B is very unlikely (like the chance of them having drawn a 1-outer or make several unlikely coin flips)

You have three possible responses.  If you play X, you will defeat A, and have a 95+% chance to win the game, but lose if they do B.  If you play Y, you will defeat B, and very likely win the game, but lose to A.  If you do Z, you will not lose to either A or B, but you're chances of winning the game are about 50-50 (or, return to what they were before the threat of A or B arose).  Which is the correct play?  

You can manipulate this hypothetical in any number of ways to illustrate different points.  Ultimately, it's illustrating a kind of rock-paper-scissors dynamic that does exist in some scenarios.  

In some situations, you can have perfect information over everything that can possibly be known at that time: 1) the contents of your opponent's library, 2) the contents of your opponent's hand, and 3) their proper role.   Given all of that information, you can still come into scenarios where an optimal play does not exist because what is unknown is your opponent's future behavior.

This is never knowable with complete certainty.  There will be times when it doesn't matter.  You can select lines of play where their behavior does not change what your optimal play is.  But there are times where this does matter.   You can describe uncertainty as to the opponent's future behavior as an epistemological limitation.  But that's not typically how we understand future behavior.  

The issue or debate over making an optimal play in the context of Rock, Paper or Scissors, or in my example, A or B, is not an epistemological question, it's an ontological one.   The case of Rock, Paper, Scissors, there is no optimal play that gives you a best chance of winning.  You know what all of their options are, and you know what your possible responses are.  But what you don't know is which option they will ultimately select.

I'm positing that there are magic scenarios that can arise that resemble that dynamic.  Not necessarily in the strict sense of equal probable outcomes, but of different decisions for which one answer fails and another succeeds, and for which, given another play, mutually exclusive responses are required from the other answer.  R,P,S need not each have a 33% chance of occurrence, you could give Rock 40%, and P and S 30% each, and the basic point I'm illustrating would still apply.  The dueling tutor play is a good example.  It's resolution may turn, not on optimal play theory, but leveled thinking, or something resembling it.  

  

[MaximumCDawg]

It's taken pretty much as an article of faith in the Magic community that in every single situation there is an optimal play.   This play may not always be knowable -- either given the information available or the time constraints of tournament play -- but it is taken as a given that there is one.

Thus, the question of an optimal play is largely understood as an epistemological question: there is an optimal play, but practical limitations/contraints prevent us from calculating it at this time.  In this podcast, we are actually positing something far more radical: that there isn't always an optimal play.  We are taking an ontological position, not an epistemological one.  

There is always at least one optimal play.  That's the better way to put it.  You can be in a situation where, due to a large lack of information, even given infinite time to calculate you could not determine which of two plays is the best.  In your examples, if you find yourself in a rock-paper-scissors situation and you evaluate that all of the possible results of your actions are equally probable, then you have several indistinguishably optimal plays.

If, as you put in your example here, you can choose an option that is "less bad" in total, one that doesn't lose to both paper and scissors but also doesn't straight up win against rock, then I think you're out of this situation.  You can calculate the optimal play.  30% chance to win (+1) with a 70% chance to lose (-1) works out to a negative value.  100% chance to not lose or win (0) is optimal here.  Of course, my weighted values are arbitrary as all get out, but you get the point - you can adjust them if you like and still do the math.  This seems to fit perfectly well with your statement that:

Optimal play is the play that maximizes your chances for winning the game.  We go over this in the podcast.  

EDIT: I suppose you could quibble with what I'm saying if you don't agree that one should assign equally likely probabilities to events that can happen in several ways where you lack information to the contrary.  I am making that basic probability assumption.

Also: YAY NEW PODCAST!  I'll load it up and listen to it on the plane this weekend.

[Smmenen]

It's taken pretty much as an article of faith in the Magic community that in every single situation there is an optimal play.   This play may not always be knowable -- either given the information available or the time constraints of tournament play -- but it is taken as a given that there is one.

Thus, the question of an optimal play is largely understood as an epistemological question: there is an optimal play, but practical limitations/contraints prevent us from calculating it at this time.  In this podcast, we are actually positing something far more radical: that there isn't always an optimal play.  We are taking an ontological position, not an epistemological one.  

There is always at least one optimal play.  That's the better way to put it.  You can be in a situation where, due to a large lack of information, even given infinite time to calculate you could not determine which of two plays is the best.  In your examples, if you find yourself in a rock-paper-scissors situation and you evaluate that all of the possible results of your actions are equally probable, then you have several indistinguishably optimal plays.

As I tried to explain, RPS is useful but misleading because I'm not trying to suggest that the possible options are equally probable.  Rather, I'm using RPS to illustrate the idea that a winning response to one possible action is a losing response to another.   Just as tutoring for Hurkyl's Recall loses to Yawgmoth's Will as tutoring for Tormod's Crypt loses to Tinker, but each defeats the other.  

Storm's assumption was that choosing the best play should beat all other plays an opponent can make.  Not so.  The probabilistically optimal play is not necessarily the one that beats all plays.   We can rejigger RPS to show this.   

[DubDub]

Another abstract example is fine, provided that it actually works and that the 'optimal play' posited is not in reality clearly suboptimal.

The example works without the caveat of which is 'optimal.'    Your opponent has two options: A or B.  Let's say A is the most likely play and B is very unlikely (like the chance of them having drawn a 1-outer or make several unlikely coin flips)

You have three possible responses.  If you play X, you will defeat A, and have a 95+% chance to win the game, but lose if they do B.  If you play Y, you will defeat B, and very likely win the game, but lose to A.  If you do Z, you will not lose to either A or B, but you're chances of winning the game are about 50-50 (or, return to what they were before the threat of A or B arose).  Which is the correct play?  

You can manipulate this hypothetical in any number of ways to illustrate different points.  Ultimately, it's illustrating a kind of rock-paper-scissors dynamic that does exist in some scenarios.

Let's just be rigorous about this:
I'm trying to maximize a value associated with a paired outcome.  My opponent is trying to minimize it.  Here are the values for the six possible outcome pairs:

f(A,X) = 9
f(A,Y) = 1
f(A,Z) = 6
f(B,X) = 1
f(B,Y) = 9
f(B,Z) = 6

Now, you say that option A is for whatever reason more likely.  Let's say it's 80% likely (so B is 20% likely).  Are you really saying you're not going to choose response X?  With that probability static for the opponent here's what we get:

Our option X
0.8*f(A,X) + 0.2*f(B,X) = 0.8*9 + 0.2*1 = 7.4

Our option Y
0.8*f(A,Y) + 0.2*f(B,Y) = 0.8*1 + 0.2*9 = 2.6

Our option Z
0.8*f(A,Z) + 0.2*f(B,Z) = 0.8*6 + 0.2*6 = 6.0

Do the math for the opponent varying the probability they select A.  The more unpredictable they get, the closer to 50% of selecting A or B, the better it is for them because the fixed option Z appeals more and more.  As I said above, their optimal strategy is to force a response of Z because they can't do any better than that without getting lucky.

In some situations, you can have perfect information over everything that can possibly be known at that time: 1) the contents of your opponent's library, 2) the contents of your opponent's hand, and 3) their proper role.   Given all of that information, you can still come into scenarios where an optimal play does not exist because what is unknown is your opponent's future behavior.

OK, first of all, you're saying as much, but I want to make it explicit.  'Role' is external to the game state.  Being the 'Control' role doesn't mean I hold back with Bob or Vendilion Clique instead of just trying to end the game anyway I can when I can.  'Role' is a term meaning that a certain range of possible actions one can take is more likely in the abstract than others.

Secondly, while your opponent's specific future behavior is unknown, you can make estimates based on their likely behavior in certain situations weighted by the likelihood of those situations arising.  An optimal play does still exist where you're maximizing the probability of winning over the set of possible future states as weighted by the likelihood of those states.  Fundamentally, the future behavior of your opponent can be lumped in with all other uncertainties (the order of your deck, i.e. what you will topdeck next).  And moreover it is only useful to assume that your opponent will play optimally in each of those potential future states when evaluating which state you like best.  Any deviation from optimality by the opponent is a welcome bonus for you, but wouldn't you want a bonus stacked on top of a high salary versus a bonus stacked on top of a low salary?  I know I would.

This is never knowable with complete certainty.  There will be times when it doesn't matter.  You can select lines of play where their behavior does not change what your optimal play is.  But there are times where this does matter.   You can describe uncertainty as to the opponent's future behavior as an epistemological limitation.  But that's not typically how we understand future behavior.

What?  Why not?  My opponent is acting based on imperfect information too, it's perfectly reasonable to say that they're trying their best in the face of uncertainty as well.  

The issue or debate over making an optimal play in the context of Rock, Paper or Scissors, or in my example, A or B, is not an epistemological question, it's an ontological one.   The case of Rock, Paper, Scissors, there is no optimal play that gives you a best chance of winning.  You know what all of their options are, and you know what your possible responses are.  But what you don't know is which option they will ultimately select.

I'm positing that there are magic scenarios that can arise that resemble that dynamic.  Not necessarily in the strict sense of equal probable outcomes, but of different decisions for which one answer fails and another succeeds, and for which, given another play, mutually exclusive responses are required from the other answer.  R,P,S need not each have a 33% chance of occurrence, you could give Rock 40%, and P and S 30% each, and the basic point I'm illustrating would still apply.  The dueling tutor play is a good example.  It's resolution may turn, not on optimal play theory, but leveled thinking, or something resembling it.

An optimal line of play can still be described as: be unpredictable, because whomsoever is predictable is the player that can be beaten.
I think you're too focused on the concept that playing optimally means selecting a specific play, when it can mean "flip a coin (weighted, if necessary), and then do what the coin says."

[evouga]

Hmm. "There is no optimal play" strikes me as a bit of a cop-out. Sure, I agree that there is no "absolute" optimal play. But there is always an optimal play conditional on the information you have at the time.

If you don't know your opponent's deck, from your knowledge of Vintage, the metagame, cards you've already seen, etc you can still assign likelihoods to the various decklists he could be playing. And once you have these likelihoods, you could, in theory, find the mathematically optimal play in the sense of maximizing your expected probability of winning.

"Role is more than information" : I completely disagree. If you don't know your role in the matchup, you can again draw from metagame statistics, your opponent's demeanor, past match records (if the opponent is known), average behavior (if the opponent is unknown), etc. and calculate the role that maximizes your expectation of winning. Doing so is of course completely impractical -- players will use crude heuristics and intuition instead -- but that doesn't mean there's "no optimal play," or that some lines of play are above being meaningfully reasoned about.

[Smmenen]

As I said above, their optimal strategy is to force a response of Z because they can't do any better than that without getting lucky.

I think you missed the point.  My preference is for Z as well.   However, if someone assumes that their opponent will play optimally, and further assumes that A is the optimal play, they would would exclude the possibility of B, and play X.   

That's what I'm critiquing.  Your math supports my argument vis-a-vis Storm.

In some situations, you can have perfect information over everything that can possibly be known at that time: 1) the contents of your opponent's library, 2) the contents of your opponent's hand, and 3) their proper role.   Given all of that information, you can still come into scenarios where an optimal play does not exist because what is unknown is your opponent's future behavior.

while your opponent's specific future behavior is unknown, you can make estimates based on their likely behavior in certain situations weighted by the likelihood of those situations arising. 

I disagree.   Perhaps in some situations, but definitely not all. 

And I'm talking about those situations where there is no basis for making a prediction or such an estimation.  Your opponent can do A or B.   How are you supposed to guess pr estimate which it will be?  The card you need to tutor for changes depending on which they play.  Your response to A or B is mutually exclusive.   It's just rock paper scissors, at that point. 
You could just say the possibilities are equally likely. Or, it could be that even though the possibilities are not equal, you need to make a judgment call based upon weighing risk and reward.   

This is never knowable with complete certainty.  There will be times when it doesn't matter.  You can select lines of play where their behavior does not change what your optimal play is.  But there are times where this does matter.   You can describe uncertainty as to the opponent's future behavior as an epistemological limitation.  But that's not typically how we understand future behavior.

What?  Why not? 

The same reason that there isn't an optimal play in Rock Paper Scissors (as we've defined optimal).  You know what your opponent's range of options are, but the optimal play doesn't exist because you can't know which play they will make.  When facing the RPS scenario, there simply isn't an optimal play -- a play that maximizes your chances for winning the game compared to other scenarios. 

The idea of calculating optimal plays, as in chess, assumes the full range of possibilities that the opponent might make.   Optimal play theory generally does not care what the opponent does.   We don't need to know their behavior because we can foresee -- and plan for - every eventuality.   

In the case of a situation in which there are options you can foresee, but cannot predict or estimate OR which are equally likely, then no optimal play can be calculated.  There are simply different options, none of which can be described as optimal.

If you consider the uncertainty about opponent's future behavior an epistemological limitation rather than an ontological one, then we are simply disagreeing on terminology. 

That is, if you consider the inability to calculate an optimal play in RPS is an epistemological problem, not an ontological one, then I think you've missed the point of RPS.   

The issue or debate over making an optimal play in the context of Rock, Paper or Scissors, or in my example, A or B, is not an epistemological question, it's an ontological one.   The case of Rock, Paper, Scissors, there is no optimal play that gives you a best chance of winning.  You know what all of their options are, and you know what your possible responses are.  But what you don't know is which option they will ultimately select.

I'm positing that there are magic scenarios that can arise that resemble that dynamic.  Not necessarily in the strict sense of equal probable outcomes, but of different decisions for which one answer fails and another succeeds, and for which, given another play, mutually exclusive responses are required from the other answer.  R,P,S need not each have a 33% chance of occurrence, you could give Rock 40%, and P and S 30% each, and the basic point I'm illustrating would still apply.  The dueling tutor play is a good example.  It's resolution may turn, not on optimal play theory, but leveled thinking, or something resembling it.

An optimal line of play can still be described as: be unpredictable, because whomsoever is predictable is the player that can be beaten.

As I said, the problem's resolution turns on something OTHER than optimal play theory.  I suggested leveled thinking as one possibility.  Your solution, be unpredictable, is precisely that.  See: http://www.starcitygames.com/php/news/print.php?Article=23167

I think you're too focused on the concept that playing optimally means selecting a specific play,

Of course it does.  That's exactly what it means.  The optimal play is a discrete play among all of the options generated to maximize your chances for winning.

Hmm. "There is no optimal play" strikes me as a bit of a cop-out.

You need to re-read the thread and listen to the podcast more carefully.  No one is claiming there is no such thing as optimal play.  Rather, what we are saying is that there isn't *always* an optimal play.   

Given that, isn't it more of a cop-out to say that there is always an optimal play?  Isn't it more of a philosophically nuanced position and less hyperbolic position to say: sometimes there are optimal plays, sometimes there are not? 

Doesn't always assuming there is an optimal play seem like more of a cop-out since it allows people to disclaim responsibility for the fact that sometimes there are just judgment calls? Or other things at work?

Sure, I agree that there is no "absolute" optimal play. But there is always an optimal play conditional on the information you have at the time.

See my response to Dubdub

[voltron00x]

Catching up on these...

Interesting to hear you guys talk about Dredge, even if I disagree with a lot of what was said (I know, surprising).

Most specifically - Kevin, I think you underestimate the changes that went into morphing Dredge from the build in early 2010 (slower build, Chalice, Leyline, Petrified Field, maindeck Nature's Claim) to the one we updated from Europe (Fatestitchers, Sun Titan, fast mana).  This is basically like a Mana Drain or Workshop deck changing 15+ cards.  In Vintage, that *IS* an entirely new deck.  Something to think about.  I would say that if you look at the Gush decks people had been playing (say, for example, Rich Shay and Brad Granberry's Gush/Vault control deck without Bob or Trygon), that they're probably within 15 maindeck cards of Paul/Steve's deck.  So, should I say Paul and Steve "backed into" their success at Champs as well, since all that changed is the meta got better for Gush?

Also, your early comments about Gush and the metagame - chiefly that it wasn't all that prominent early in the year before Champs - are US exclusive.  Gush was the key deck in Europe for a big chunk of the 2011.

Regarding the Dragon decks, I think the deck is considerably better than you're giving it credit for although obviously I think it is the second-best Bazaar deck as well.  Here's why.  First, look how many Dragon decks hit top 8 in 2011:

http://morphling.de/search.php?type=3&app=10&sorting=DESC&search=worldgorger+dragon&sent=1

Four wins in 2011 plus a top 8 at Vintage Champs.  Now, that might not seem THAT significant, but... how many people actually PLAYED this deck last year?  If you look at conversion percentage in terms of making top 8, and winning once you get there, that number is pretty unreal.

[dicemanx]

obviously I think it is the second-best Bazaar deck as well.

This might now change with Grafdigger's Cage, especially if the card ends up in maindecks instead of SBs. Dragon can actually afford to play some great maindeck solutions such as EE, Deed, or even just Hurkyl's Recall (EE and Deed gain in value if the format shifts to more aggro-control strategies), and Dragon's draw engines/card filtering are mostly unaffected by Cage. If Cage is played out of the SB, that could also be to Dragon's advantage, since Dragon has much better tranformational SB options (not Oath as that is hit by Cage, but there are a few great aggro strategies that can really punish those that aggressively mulligan into graveyard hate and/or Cage).

I'm really excited about the impact Cage will have on the format, and excited by the prospect of Dredge being pushed to the margins and WGD rising to be the premier Bazaar deck again.

[Shax]

Not trying to detract anything from this topic but I agree with the previous poster, and it doesn't help Dragon's chances game 1 of stopping your Grafdigger's Cage if they run x4 Mental Misstep maindeck. Of course if Grafdigger's sticks  the Dragon player is cooked most of the time. The sideboard transformational plan into Tezzerett is hampered a little bit though. Having a Grafdigger's Cage means the Tezzerett-Dragon player won't be able to Tinker up that sweet Blightsteel Colossus in their sideboard or play Y.Win as often for critical. But, having Mental Misstep main or in the side, does give the Dragon player confidence in resolving those Duress/Thoughtseize.

[Commandant]

Not trying to detract anything from this topic but I agree with the previous poster, and it doesn't help Dragon's chances game 1 of stopping your Grafdigger's Cage if they run x4 Mental Misstep maindeck. Of course if Grafdigger's sticks  the Dragon player is cooked most of the time. The sideboard transformational plan into Tezzerett is hampered a little bit though. Having a Grafdigger's Cage means the Tezzerett-Dragon player won't be able to Tinker up that sweet Blightsteel Colossus in their sideboard or play Y.Win as often for critical. But, having Mental Misstep main or in the side, does give the Dragon player confidence in resolving those Duress/Thoughtseize.

I believe dicemanx is trying to say that Cage makes Dragon a better choice.

[CHA1N5]

Most specifically - Kevin, I think you underestimate the changes that went into morphing Dredge from the build in early 2010 (slower build, Chalice, Leyline, Petrified Field, maindeck Nature's Claim) to the one we updated from Europe (Fatestitchers, Sun Titan, fast mana).  This is basically like a Mana Drain or Workshop deck changing 15+ cards.  In Vintage, that *IS* an entirely new deck.

Granted that there was a significant numeric change in the lists.  I don't think your analogy holds up in comparison to Mana Drain, though:  my experience with playing against Dredge across those two eras was that *I* continued to approach the matchup in the same ways.  Yes, it changed its tool set, but it's still Dredge doing Dredge stuff.  Yes, it got faster, but people still just put 4 Leylines and 3 [Something] in their board and hoped.  Look at the Finals from Vintage Worlds:  I don't consider how that match played out to be attributable to any notable evolution in Dredge.  All those significant evolutions in Dredge that you pointed to?  Take a look at Mark's sideboard strategy for that match:

SB

+2 Ancient Grudge
+2 Firestorm
+4 Nature's Claim
+2 Darkblast
+4 Chain of Vapor

-3 Sun Titan
-3 Fatestitcher
-1 Lion's Eye Diamond
-2 Dread Return
-1 Lotus Petal
-1 Golgari Thug
-1 Mox Sapphire
-1 Black Lotus
-1 Dakmor Salvage

As I said on the show:  I don't mean to imply that Dredge did not evolve over the year.  I only mean that it did not actually force a significant change in how the metagame had to handle it. 

 I would say that if you look at the Gush decks people had been playing (say, for example, Rich Shay and Brad Granberry's Gush/Vault control deck without Bob or Trygon), that they're probably within 15 maindeck cards of Paul/Steve's deck.  So, should I say Paul and Steve "backed into" their success at Champs as well, since all that changed is the meta got better for Gush?

This is a straw man.  The success of the deck Steve and Paul played was influenced by many factors.  That deck was the first, high-profile performance by a deck with Gush and Bob.  It went against a lot of popular opinion and testing in a way that Mark's deck did not.

There is a very soft line between metagaming, building a new deck and dusting off an old deck.  Steve built a new deck for the event.  Mark did not.

http://morphling.de/top8decks.php?id=1471&highlight=Fatestitcher
http://morphling.de/top8decks.php?id=1460&highlight=Fatestitcher

Regarding the Dragon decks, I think the deck is considerably better than you're giving it credit for although obviously I think it is the second-best Bazaar deck as well.  Here's why.  First, look how many Dragon decks hit top 8 in 2011:

http://morphling.de/search.php?type=3&app=10&sorting=DESC&search=worldgorger+dragon&sent=1

Four wins in 2011 plus a top 8 at Vintage Champs.  Now, that might not seem THAT significant, but... how many people actually PLAYED this deck last year?  If you look at conversion percentage in terms of making top 8, and winning once you get there, that number is pretty unreal.

Very difficult to draw conclusions from such a small sample.  I see only two players in the US making said Top 8s.  One could conclude that they are the only people capable of piloting said deck.  One could also conclude that the deck is simply very good in the elimination rounds, but we don't have the data to demonstrate how many players brought the deck to tournaments and went 0-2.  I am willing to grant that the deck is good and underplayed.  Not enough data to support conclusions in any direction, really.

Also, ironically, what a nice segue back into the point about Dredge:  where was Nick's respect for Mark at the Champs?

[voltron00x]

Re: your first point, that's a really reductionist approach.  It's sort of like saying, Paul and Steve's decks were just Vintage Blue doing big blue deck things.  Basically, their deck is last year's Champs deck with the Gush/Bond engine instead of Jace, TMS.  In the end, they're both outdrawing the opponent with Bob and supplemental draw engine, using Trygons, and slowly taking control of the game to win with Key/Vault, Tinker, or beats.  New printings/unrestrictions aside, is the approach against 2010's finals decks that different than 2nd and 3rd place in 2011's?  That said, in Vintage, replacing Jace with Gush/Bond, adding Cliques, and swapping a few disruption spells *is* a new deck in Vintage.  I'm pretty sure we're all ok acknowledging that (and frankly that's something non-Vintage players struggle with).  I just think you're not applying your terminology equally because "Dredge is Dredge".  I don't think that's more accurate than reducing all Shop decks to "Shops are Shops", all Rituals to "Rituals are Rituals", etc.

Re: your second point... your teammate had just written an article about how Dredge would never win Champs that had plenty of popular support, so I think Mark did make something of a bold choice.  Regardless, saying Steve/Paul's deck was "new" is a Straw Man of your own, as I never said that Mark's deck was new, nor did I suggest that your teammate's innovation wasn't an accomplishment.  It is.  So was the invention of that Sun Titan deck in Europe.  I never claimed credit for it, I was just the first to play/top 8 with it in the US to my knowledge, and the first to write about it, and say that it had a shot at winning Champs.  In fact, if you go back to my article about the deck before Champs, you'd see you have no need to try to direct me to the deck's origination. 

While I understand what you're saying, and don't want to belabor the point (because this was a good podcast), some of what you wrote still reads to me as, "My teammate did something really important (changed a draw engine in blue vintage control!!), and Mark just dusted off someone else's deck".  It could be a perception thing.  I can say that I've been playing Vintage Dredge builds consistently since early 2009 and appreciate how they've changed despite being fundamentally the same, and can say the same thing for various blue Vintage control decks (regardless of whether or not they've had Jace, Tezz, Key/Vault, Drains, TS, Spell Pierce, Drains, Trygons, Ancient Grudge, etc. they're still fundamentally the same).

[CHA1N5]

Re: your first point, that's a really reductionist approach.  It's sort of like saying, Paul and Steve's decks were just Vintage Blue doing big blue deck things. 

It is reductionist, of course.  I believe you're narrowly addressing my choice of words rather than my point.   I thought my reference to the Finals match demonstrated my point well: the Finals match played out without any features of Mark's deck behaving differently than a list of 12 months prior.  Let's not get too far afield debating the originality of decks.  I simply believe that Mark did not win the tournament because of evolutionary developments of the Dredge deck he piloted.

"My teammate did something really important (changed a draw engine in blue vintage control!!), and Mark just dusted off someone else's deck".  It could be a perception thing. 

I only brought up topics related to those because you drew a parallel between the two.  I consider them dramatically different situations.  I don't intend to overstate Steve's deck, but it WAS a first.  As you've addressed:  Mark's list was not.

[MaximumCDawg]

Finally finished the whole podcast - took me too long - and I had two more comments and a minor concern.

(1) You are still just asking an epistemological question.

Your basic point appears to be that even with complete information, you may still not be able to decide on a single, optimal play.  But, you define "complete information" as knowing your opponent's hand and deck.  There is an additional element of unknown information, namely, what your opponent is thinking and will plan to do.  In other words, you've just included the opponent's brain in the stack of unknowns.

One could legitimately ask whether it makes any sense to think of your opponent's thought process, or worse, his FUTURE thought process, as unknown but knowable.  It makes sense to think of cards in a hand or deck as "knowable" even if we don't know them at the time, since we think of them as single, concrete, unchanging physical objects.  Is a human brain like that?

Yes, in two important respects.  First, and maybe this is degenerate, but the human mind is still made up of interactions between physical particles acting in a more-or-less deterministic way.  We're probably millenia away from that actually mattering, though.

Second, when you're making decisions, it doesn't matter why you don't know something, only that you do not.  In round 1 of a tournament against an unknown opponent, for example, his deck and hand are just as dark to you as his thought process.  

Thinking about your opponent's thought process as additional information is relevant, and you guys specifically do it all the time in discussing scenarios and recounting past tournaments.   You spend alot of time thinking about what the opponent will do in response to your plays.  You discuss predicting what sort of play an opponent is likely to make if you are in the happy position of knowing that particular person well.  In this most recent podcast, Stephen used exactly this sort of reasoning to decide that his Oath opponent was at least likely to no double-down on Oath if he yanked the first one with a Duress.  Knowing what your opponent is likely to do matters, possibly as much as knowing what they could do.

My conclusion, then, is you are not really posing an ontological question; you've just pushed the epidemiological question up a notch by pointing out the existence of additional unknown (unknowable?) information.

(2) The fact that there may not be a knowable optimal play does not mean there are no optimal plays.

This is what I was saying a few posts up.  The fact that you may find yourself in a situation where you have several alternatives, none of which is clearly better than another - described in the Pocast as A, B, C versus X, Y, Z - implies only that there are multiple optimal plays, not that there are not any.  In your podcast, you are very careful only to say there is not "an" optimal play, which is true (with the caveat about incomplete information stated above).  However, there very well could be MULTIPLE optimal plays.  If you make any one of A, B, and C, you may well be justified in making one of the optimal plays.  How you rank them may have to do with how you value the chance of winning outright or of just not losing, which has to do with your position in the tournament, how the match is going, etc.

(3) Given all of that, here's my concern.

Your podcast suggests you're tossing up your hands and saying, "Well, sometimes the question is unanswerable, so stop looking for an answer."  That concerns me.

The fact that there may be more unknown information than people actually talk about, or that sometimes there are multiple optimal plays, does not diminish the importance of the sort of analysis you guys provide when you're doing scenarios.  First and foremost, figuring out the universe of optimal plays requires being able to look ahead at what COULD happen after each move.  Then, you need to decide how LIKELY it is that each outcome will happen, and the EFFECT of each outcome.  None of this analysis is less important if it has to do with predictions about your opponent's thought process.

If anything, your podcast suggests that future senarios might also include some tips about how to predict an opponent's next moves from what you know about him during the tournament.  For example, Steve, how did you intuit that your opponent was likely to NOT double-down on Oath?  There must have been some information you had about his inexperience or play style that led you to believe this.

[Smmenen]

An opponent's future decision is unknown and unknowable.   However, an opponent's possible future plays or range of possible plays are generally known or knowable.  The same is true in chess.

The point of this segment of the podcast was to illustrate how the idea of an optimal play may not always exist in every scenario, even if you think you know what the opponent might do.    This is the idea behind the leveled thinking article.  Making assumptions about what they are likely to do just falls into the leveled thinking trap, or opens the door to being out maneuvered.

Your 'concern' is basically an emanation of the Cartesian anxiety.  It's ok to have uncertainty and ambiguity in the modern world.  You aren't the first person to have wrestled with that. 

[MaximumCDawg]

Your 'concern' is basically an emanation of the Cartesian anxiety.  It's ok to have uncertainty and ambiguity in the modern world.  You aren't the first person to have wrestled with that. 

No, it really isn't.  I'm perfectly comfortable with making decisions in a world where you won't have perfect information.  However, more information (cards, player's intentions) will almost certainly help make a decision closer to one of the optimal decisions.

My concern is that you don't stop opining on the optimal, or perhaps "reasonable," courses of action and the analysis that goes into identifying them as a result of deciding that there may be situations where you can't really determine the answer.  It's the difference between your first Vintage senarios podcast, where you pick apart the workshop scenarios in great detail, and the current podcast, where you just say, "well, it depends on what role you want to play."  What informs the role you want to play?  You've got more experience than most of your listeners on making that judgment call, and it benefits us to learn how you do it.  Even if that sometimes involves figuring out what your opponent is going to do the future.

[Smmenen]

Your 'concern' is basically an emanation of the Cartesian anxiety.  It's ok to have uncertainty and ambiguity in the modern world.  You aren't the first person to have wrestled with that. 

No, it really isn't.  I'm perfectly comfortable with making decisions in a world where you won't have perfect information.  However, more information (cards, player's intentions) will almost certainly help make a decision closer to one of the optimal decisions.

player's intentions don't matter.  what matters is their future decision, which is neither known or knowable. 

You have perfect information of everything that is knowable.

My concern is that you don't stop opining on the optimal, or perhaps "reasonable," courses of action and the analysis that goes into identifying them as a result of deciding that there may be situations where you can't really determine the answer.  It's the difference between your first Vintage senarios podcast, where you pick apart the workshop scenarios in great detail, and the current podcast, where you just say, "well, it depends on what role you want to play."  What informs the role you want to play?  You've got more experience than most of your listeners on making that judgment call, and it benefits us to learn how you do it.  Even if that sometimes involves figuring out what your opponent is going to do the future.

You should read the article on leveled thinking. 

And stop trying to know everything.  uncertainty exists.