[Premium Article] Lucky? Yeah, That's the Point

[Smmenen]

http://www.starcitygames.com/php/news/article/15539.html

Editor's blurb:

Stephen returns to the Monday slot, and talks about an argument that’s as old as the hills… is the role of Luck in Magic greater than the role of Skill? Does Luck devalue Skill in the overall scheme of the game? Strangely, Stephen believes that, far from inhibiting the skillful, Luck makes Magic a more skillful game… and he’s got the mathematical proof to back up his claim.

[SpaceGhost]

The editor's blurb definitely caught my attention.  I am a professor of statistics with a research emphasis on combinatorics (which is really the bread and butter of the math underlying magic).  Unfortunately, I am not a subscriber to SCG, but I would be immensely interested in hearing more about mathematical proof of luck enhancing skill.

Beyond recognizing card combinations and interactions, the central theme, in my opinion, of deck construction is probability theory.  A great deal of information can be gleaned from deck matchups by just understanding the probabilistic relationship between sets of cards that are contained in each deck and how they will interact and at what frequency.  Additionally, understanding these probabilities enables more fine tuned deck construction.  However, I would argue that skill in this vein is about minimizing luck and exploiting the fact that your opponent may know less about these probabilities.

At any rate, I am very interested in the "fleshed out" contention mentioned in the editorial blurb.

[Tareth]

Here's the equation you're interested in:

skill = a discreet, individual skill
SKILL = the sum/net effect of the collection of multiple skills
TS = Technical Playskill, meaning in-game decision-making skills

Outcomes in Chess = SKILL(Chess)= skill(TS) There are no other variables. There is no coin flip, no draws, no dice.

So, for Magic:

SKILL (without chance) = Skill (TS)

And:

SKILL (with chance) = [W * (skill(TS) + enhanced (TS)) – chance losses caused by proper TS)] + [A * skill(archetype selection)] + [B* skill(deck tuning)] + [C* skill(sideboard design] + [D*skill(mulliganing)] + [E*skill(bluffing)] + [F*skill(all other skills)]

W, A, B, C, etc are the modifiers that describe the difference in terms / importance / significance / weight that we might ascribe to each of these skills.

[Suicideking]

Its basically the same idea as a poker tournament.  Luck can get you through a game, possibly through a match, and if you're really lucky through a tournament.  But over the long run the players that make the best plays most often, regardless of previous out comes will come out ahead.  Probability will always favor the better players.  But sometimes its better to be lucky then good. 

[dicemanx]

Outcomes in Chess = SKILL(Chess)= skill(TS) There are no other variables. There is no coin flip, no draws, no dice.

Luck is definitely a variable in chess, at least as far as the way humans beings play the game. While all possibilities in chess are finite and could be theoretically exhaustively calculated, as I understand it you're making the comparison between the skill sets required to play MTG versus the skill sets required to play chess by human beings. In both instances you're working with imperfect and incomplete information (the former by virtue of the fact that information is literally concealed, the latter by virtue of the fact that it is impossible for human beings to calculate the consequences of every decision to their logical conclusion).

Success in chess is a function of proper plan selection in-game (analogous to selecting proper lines of play in MTG while operating with imperfect/incomplete information), research of openings looking for theoretical novelties or any lines of play that increase chances of victory (analogous to deck construction in MTG), proper opening selection against specific opponents (analogous to SB-decisions), proper opening/middle-game/end-game preparation against the field (analogous to deck selection in MTG), stamina and focus training to endure 6-12 hr play sessions (same issue in MTG events).

[Ishi]

As a fairly strong chess player, but horrible magic player it's always interesting to see comparisons between the two.

First of everything dicemanx says is true, there's definitely more skill to chess than just in-game decisions.

Currently, humans are apparently no longer capable of beating the best computers in Chess – and for good reason, as computers are better at Forward Thinking analysis. A player can’t accurately "weigh" one line of play against another unless they are able to forecast the outcome, which is full of contingency. This is a limitation of basic computer power, whether our brains or central processors. It takes us far longer to evaluate 30+ turn lines of play than it does for a microchip. Computers have already "solved" checkers. It is only a matter of time until Chess is "solved" as well.

I don't think you can argue that computers are better at forward thinking than humans.  Any strong human go player can easily defeat the best go computers.  It seems to depend on the rules of the game whether humans or computers are better forward thinkers.  Also it's not clear if chess will ever be solved, and it's very unlikely that go will be solved.

I don't find your SKILL() argument very convincing at all.  What does SKILL measure?  What are the units.  If you don't specify those, then how can you make any arguments about comparing the different weights.  Also, why do you say deck selection, deck tuning and sideboard design require luck?  To take luck out of magic you could do something like play with the decks face up and remove shuffle effects [edit: and make players specify their starting deck order].  Deck selection and sideboard selection would very much be part of that game.

At the end of the article you say that magic tests a wider variety of skills than chess (and by implication magic with the luck removed).  Seems to me that this statement is obviously true and more convincing then your longer argument above it.

Still, I found the article fun to read.

[LordHomerCat]

I can see chess being solved at some point in the not-too-distant future.  The decision trees are very large, yes, but not even in the same universe as in Go.  The reason Go computers are so bad is that the size of the tree expands by like 350 nodes per level at the start of the game, compared to chess where you have like 20 moves you can start the game with.  The tree in Go also only decreases by 1 node per level (not counting pruning techniqe), which means that it stays gigantic for most of the game.  The technology and algorithms just don't exist right now to be able to handle a decision tree of this size.  Chess, meanwhile, gets closer and closer every year, in that now computers can consistently beat even the best human players, and really it is just a matter of hardware advancements and AI research that is keeping the game from being solved outright.