A blog about anything I want. I don't need to explain myself.

Tag: game theory

Magic is Infinite

What is the hardest game ever?

Chess is hard.

Most people refer to Chess as a “smart” person’s game.

Culturally, Chess is the epitome of human intelligence, often referenced in other games when someone makes an extremely clever move. “He’s playing Chess, not checkers.” Checkers really got the short end of the stick there.

Chess is very complicated.

In fact, research has proven that the number of move variations in Chess is somewhere around 10123. That’s a 1 followed by 123 zeros. To put that in perspective, there are only 1081 atoms in the observable universe. There are more possible games of Chess than all of the atoms. That means that every game of Chess hasn’t been played before. Next time you play Chess, remember you’re making history.

That number, 10123, is called the Shannon Number. Its namesake comes from some smart guy named Claude Shannon who had way too much time on his hands.

The number appeared in his 1950 paper “Programming a Computer to Play Chess” which, you guessed it, led people to program a computer to play Chess.

But is Chess the most complicated game?

There’s another contender: the lesser known game of Go.

Go is an ancient Chinese game played on a 19×19 grid. Two players take turns playing their respective colored “stones,” both white and black, on the intersections of the grid. The goal of the game is to capture the opponent’s “stones” and control more territory on the board.

Sounds like weird checkers, but it’s not.

Once you place your stone you cannot move it. You capture stones by surrounding your opponent’s stones. You can pass the turn by handing one of your stones to the opponent. When the turn has been passed by both players, the game ends and points are calculated by captured pieces and controlled territory.

Because of the size of the board, the number of possible move variations in Go is 10360.

That’s 3 times the amount compared to Chess.

I think it’s safe to say that Go is more complex than Chess.

Go wins, right?

The most complicated game ever?

Are there any other challengers?

Any others think they can do better than 10360?

No?

I didn’t think so.

Here’s your crown, Go.

Champion of being the most difficult and complex game ever played.

You deserve it.

What now?

Do you want to get lunch or something?

Nah, I don’t really like Burger Ki-

Wait…

Who is this?

In the distance…

Approaching slowly and maniacally…

Shrouded in darkness…

I can’t see his face clearly…

Is that?

Oh my god…

He’s wearing a canonically accurate robe of Gandalf the Grey, the servant of the secret fire, the wielder of the flame of Anor with a matching wizard staff that looks like it was given to him by Galadriel herself.

And what’s that in his other hand?

Are those…

Cards?

It’s…

It’s…

Magic: The Gathering.

A recent study by independent researcher Alex Churchill has scientifically proven that Magic is the most complicated game ever.

More complicated than Go.

More complicated than Chess.

Because, while both have more variations than atoms in the known universe, Go and Chess are still solvable games.

Meaning they technically can be solved by a computer.

A computer can calculate all possible variations in both Go and Chess to make consecutive moves that will most likely return a win.

If you imagine that every board state in Chess is a puzzle, a computer can mathematically solve it.

The computer will always win.

Two computers playing each other will always draw.

“But Jason. I beat my computer at Chess all the time.”

No, you don’t.

The computer lets you win.

It wants you to think you’re better.

It wants to make you feel safe.

Meanwhile, it’s making plans for world domination.

In game theory, it was thought that every game was, to some extent, solvable.

Magic can’t be solved.

Because the possible variations in Magic are infinite.

In 2012, Alex Churchill, independent researcher at Cambridge, published a paper titled “Magic: The Gathering is Turing Complete.”

This paper was really complicated and filled with computer science jargon.

I hate science jargon, but I read it anyway.

This what I took from the reading: Turing complete means a system can compute any algorithm given which basically means it’s a computer.

Alex and his buddies found a way to make a computer within a game of Magic.

Don’t ask me how.

If you want to know, go read the paper.

In layman’s terms, they use the function of specific card rules to create a scenario where you can input an equation and receive a correct output.

Theoretically, you could input “2 + 2” and the game would give you “4.”

This specific game scenario can only be finished by what is known in computer science as the “halting problem.”

Halting Problem: the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever.

wikipedia

Alan Turing, the inventor of the Turing machine and the namesake for “Turing complete,” proved that no computer algorithm can solve the halting problem.

Considering that this problem can exist in Magic, Alex Churchill and his buddies proved that Magic is unsolvable.

From Churchill’s paper, “This is the first result showing that there exists a real-world game for which determining the winning strategy is non-computable.”

Silly computers can’t even play Magic.

I guess we should be less worried about the whole “world domination” thing.

Here’s the paper if you feel like reading, but this is more to prove that I’m not making all this up.

Perfect Stoke

Ludology is the study of games or gaming. Recently, it has been associated with video games, but this is a misnomer. Video games have thrown a proverbial wrench in the ludologist’s view of games. Before video games, ludology was about tabletop games and sports and was mainly concerned with anthropology, or human society and culture surrounding games. The introduction of video games broadened the study of gaming into fields such as sociology, psychology, and, more controversially, the humanities.

The combination of ludology and the humanities is still a heated topic today.

I’ve been reading about ludology too much.

And there’s a lot.

I’m overwhelmed.

This was deeper than I thought.

For now, I’ll explain a central point made in game studies: the classification of games.

Believe it or not, tabletop games came before sports. The oldest known sport was wrestling dating back 15,000 years ago. That seems obvious. The first sport ancient humans made up involved forcing our will on another human. That’s probably the first game I played too. I played it all the time with my brother.

But before sports, we played tabletop games, or what we now know as tabletop games because back then there probably wasn’t a table. These games took the form of throwing objects on to the ground as a form of dice rolling. I like the idea that before we decided to fight for sport, our ancestors were like, “Hey check out these cool rocks! I have more than you! I win. Ooga ooga.”

Tabletop games are the oldest form of games and they can be classified in two ways: Outcome uncertainty and state uncertainty.

Games where the outcome is random are called stochastic games. Games where the outcome is known are called deterministic games or abstract strategy games.

Games where the state of the game is random are called imperfect games. Games where the state of the game is known are called perfect games.

Perfect Deterministic games: Chess, Go, Mancala

Perfect Stochastic games: Backgammon, Monopoly, Craps, Roulette, Yahtzee, Parcheesi    

Imperfect Deterministic games: Battleship, Stratego, Mastermind

Imperfect Stochastic games: Poker, Blackjack, Gin, Scrabble, Risk, Mahjong

Chess is considered perfect because the board state is always known and deterministic because the outcome is always known. There are no secrets in chess.

Poker is considered imperfect stochastic because both the state and outcome of the game is random. There are only secrets in poker.

I like the idea of using these terms as a personality test.

I think I’m a perfect stochastic kind of guy.

I’m gonna rename it.

I’m a perfect stoke.

Which means I like knowing things but I have no idea what to do with that information.

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