Musings about optimal play

I’ve brought up the concept of optimal play, recently. Which brings up two points: Is it desirable and is it possible?

What is optimal play? I’m going with the act of consistently making decisions that have the greatest likelihood of resulting in the destined outcome. Which is probably winning the game, since we are talking about gaming, but not necessarily.

Frankly, I think that’s a more nuanced definition than ‘Making the best moves to win’

When I think of optimal play as a concept, I often think of a scene from the manga/anime Hikaru no Go, which proves that the game of Go is more thrilling than a light sabre duel over a pit filled with shogoth. When Touya is forced to play three games simultaneously with his back turned, his joseki is strong enough that he can pull it off.

Joseki, as I understand it, is the equivalent of Chess opening moves but involve a lot more moves and deal with smaller percentages of the board. Because a Go board is a HUGE piece of board game real estate. The Hikaru no Go example isn’t realistic but it does give an example of how understanding a game leads to optimal play.

Go may be the perfect example of a game for optimal play. Perfect information and no random elements. Go is all about the skill and Go has been researched for centuries with no final conclusion in sight.

With most other games, I think there are three elements that make me question optimal play as a viable concept. Random elements. Multiple paths to victory. Variable desired results. (Which is not the same as multiple paths to victories but can be related)

Random factors are the least important element. I mean, seeing as how most games have random factors, they are just something you have to factor in. Optimal play doesn’t mean a game is solved. Unless a game is solved. Then it’s not a game anymore. It’s a puzzle.

And while winning is kind of the core concept for most games, the nature of winning can be more complicated. There may be more than one way to win. And interactions with everyone else at the table can get affect how and what you do.

Ultimately, I think optimal play is a loaded term. I’m not saying that folks shouldn’t do their best to play their best. However, as much as games are about winning and losing, the process and experience just isn’t that binary. 

A five-year-old’s experience with Go

I recently took a crack at introducing our five-year to the basics of Go. 

And while I have heard Go described as having five rules with one of those rules being that you play it on a board, quite a bit of it didn’t sink in. Go is theoretically simple in theory but it is ridiculously complex to understand in practice.

But it was his idea so I ran with it.

The one thing that he really clicked on was the concept of eyes and that having two eyes makes a group of stones safe. Which, to be fair, is a very important idea.

I wonder if he will ask for Go again and what he will learn if he does.

I fail at Abstract classification

I have this really silly tendency to divide abstracts up into putting pieces on the board and moving pieces on the board. 

Which is nonsense as a taxonomy. Not only are there abstracts where you do both, like Hive (or ZERTZ or Amazons or Six or YINSH or...), there are games where neither term really fits. The Mancala family really doesn’t fit the concept of moving pieces on a board, for instance. It’s its own thing. And an abstract like Zendo is completely off the grid.

I think the reason I tend to do this is because I have found that I like putting stones down more than moving stones. I admire Chess but I don’t really have any desire to play it. I admire Go and I do want to play it more. There’s a number of reasons but putting stones down is just more satisfying for me.

I don’t think it’s the biggest reason anymore but this tendency started for me because putting stones down also acts as a timer. You know the maximum number of moves in a game. Someone once wrote Othello was a great game for kids before bedtime since it had a predictable time frame.

However, stones on the board also lets you see the history of the game at a glance. For me at least, it’s a lot easier to read. It also makes it easier, at least for me, to feel the tempo of a game and to have a strong sense of what stage the game is at. 

And for me, it feels less likely for a stones on the board game to stall out. Stale mates in Chess just make me feel depressed. 

Atlantean, one of Knizia’s more minor games, has stayed in my collection in part because there’s a maximum of eleven moves per player. (Variable opening set-up that’s under the player’s control also helps) When I want a quiet, thoughtful abstract that will take ten, fifteen minutes, it’s one I consider. 

And, while I consider it to be one of the weaker Pyramid games, I still occasionally play Branches and Twigs and Thorns because being a stones on the board game on a very small board turns it into a knife fight in a telephone booth very quickly. Mind you, the first few moves tend to determine the game but it’s so fast that the rest of the moves don’t take very long.

But I’m not just saying I like stones on the board because I can play some quick games. Go, the ur-example, is a longer game but you get to see the board develop and it becomes so wonderfully complex. The history of the play is there for you to see, even at my pathetically limited understanding of Go. It’s a living tapestry, which is a great turn of phrase even if it is too pretentious for words.

For me, I find myself using stones on the board as a category because I find that mechanic an act of meditation and creation as well as competition.

Thoughts on abstracts you can get in while adulting

I wanted to write about abstracts that I like since being an adult doesn’t give me the time to pursue Go. (To be fair, having hobbies other than Go also didn’t give me time to pursue Go) Games that I think would click with folks who don’t normally play abstracts. But when the list hit the double digits, I realized I was never going to come to an end.

I did notice two things about the games I was choosing. They had short playing times, really under a half an hour as a rule. Second, each move tended to be dynamic and really change the board.

As a comparison, take Checkers. Someone much smarter than me once said that a game of Checkers is slowly working your way to making one big move. I think Checkers is a brilliant game and there’s a reason it has stuck around for centuries. But I don’t enjoy it. Even more so than Chess or Go which I can break down into individual pieces, Checkers is one big picture with lots of tiny pieces that I can’t hold together in my head.

Is Checkers a good game and one with a surprising amount of depth? Yes, particularly when you actually use the the rule that if you can capture, you must capture. But it is not a game I really like or have time to understand. If I had that time, I’d spend it on Go.

In contrast, I’ll use Pentago as a counter example. As a Tic Tac Toe variant, it’s one of the simpler abstracts I enjoy and it takes probably five minutes to play. Place a stone and turn one of the quadrants. Have five stones in a row at the end of your turn and you win.

In Pentago, every move has a dramatic effect on the board, particularly seeing as how you are actually moving the board itself. The board is small enough that the patterns you form aren’t overwhelming. At the same time, there are enough options that the game isn’t a simple formula like actual Tic Tac Toe. It does make your brain work.

Pentago isn’t my favorite abstract (although I’d always be willing to play) but it is one that feels like a classic abstract while still having modern innovation. It exemplifies what I’ve found I’m looking for in an abstract. And it’s one I can get other folks to play.

I know that pure abstracts aren’t for everyone. But I think that there are games out there that are accessible and fun for a large audience. And I love Go but I don’t have the time for it. But there are abstract games that I do have time for. And there are games where those two things come together.

Adulting made Go to hard for me :’(

Go was a huge milestone for me. Not only is it one of the most genuinely brilliant games ever created and incredible training for your brain, one of my major gaming groups started out as a Go group before becoming a more general gaming group. (My decision to bring Blokus Trigon so we could have a three-player game had a lot to do with that transition)

And I haven’t played Go in years and I don’t see that changing any time in the near future. And that’s because GO IS _HARD_

Seriously, a good game of Go is something that you should set aside an afternoon for and try not to go in with your head cluttered by other stuff like responsibilities and exhaustion. Adulting makes Go more difficult!

I realize that if I had played Go long enough and with enough dedication, I’d have started to have some understanding of Joseki, which might have helped some of the strainof play. Joseki are patterns that are considered optimal for both sides. In other words, Joseki can help you with the minutia and focus on what really are the critical moves.

I view Joseki as understanding the game to a subconscious level, although I know that’s not what it really means or is. But being able to use Joseki denotes a deeper understanding of Go, one that I’m in no danger of reaching.

Instead, my abstract journey has led me to more short-form abstracts. My mind still craves patterns and decisions. Just ones that can fit in adult life.

The changing maze of Quoridor

Quoridor is a game that I've come back to and found out that it is a lot better than I had remembered.

There's a very simple reason for that. I first played Quoridor during my 'so many games, so little time' phase, when I would play a game once or twice and then move on to a new one to try out. Now I'm more inclined to play fewer games but over and over again. Quoridor really benefitted from a more thorough examination.

Quoridor is one of those short, simple abstracts that has a lot more depth than its simplicity or brevity would immediately imply. Played out on a nine by nine grid, your goal is to get your pawn to the other side. Where the clever bit and the name comes in is that each player also has a supply of walls. Each wall is two spaces wide and will fit in between the grooved spaces.

On your turn, you can either move your pawn one space in an orthogonal direction or place a wall. However, you aren't allowed to wall anyone in. There must always be some sort of path for them to get to the far side.

You can play the game with two players or with four players but as far as I'm concerned, Quoridor is really a two-player game. More players feels off and makes the board to cluttered.

The meat of the game is the walls. You're are fighting to give your opponent the most time-consuming path possible while making sure they don't do the same to you. Moving the pawns is just acting out the conclusions that you've come to.

Which isn't to say you build a maze and only then start moving your pawn. No, sometimes you have to move to either force a decision on your opponent or escape the trap they're setting up.

In my earliest exposure to Quoridor, I was just using my walls to try and block my opponent. However, when a friend of mine had me sit down and play game after game with him online, I started to realize that I was missing a lot of important gameplay.

The first thing that clicked in my head and I felt like an idiot for not realizing so much sooner was that I could cut a line my opponent was building by playing a wall along the same line but with a one-space gap that they couldn't fill. 

From there, I realized that cutting was at least as important as blocking and that I would have to figure out how to react to my opponent's cuts. I realized that, like Go, Quoridor is a game of patterns. You need to see what patterns are emerging from the wall placement and how to use them for your own plans.

Of course, nine walls a piece on a nine-by-nine board is a lot simpler than the kind of patterns you're going to see develop on a Go board. On the other hand, a game of Quoridor is also probably only going to take you fifteen minutes to play, as opposed to the hours of a good Go game.

If there is one serious knock I would have to say about Quoridor is that, even by abstract standards, it feels particularly unforgiving. Particularly with players of different skill levels, the game can be decided by the halfway point and the weaker player is stuck being a rat running through the other player's maze. Which isn't that much fun.

However, if I have to be that rat and end up trapped in someone else's maze, at least I am getting to see the surprising depth in this pattern of walls.

https://boardgamegeek.com/boardgame/624/quoridor

A knife fight in a phone booth that keeps shrinking

I really like Branches and Twigs and Thorns more than I should. It's one of the slightly obscure Looney Pyramid games. By slightly obscure, I mean it isn't one of the big ones like Volcano or Treehouse or Zendo but it's generally agreed that it doesn't stink.

Admittedly, one of the things that is a blow against Branches and Twigs and Thorns is that it was originally billed as the pyramid version of Go and that is a comparison that it just can't live up to. Go is a colossal game in so many ways. Branches and Twigs and Thorns is a quick little abstract that has only sixteen spaces on the board per player.

So let's not compare it to Go. Let's call Branches and Twigs and Thorns a quick little abstract that has a bit of a knife fight in a phone booth going on. And when you look at it from that angle, it looks a whole lot better.

Branches and Twigs and Thorns is a two or four player game that uses either a checkerboard or half a checkerboard, depending on the number of players. Depending on the number of players, the game begins with placing one or two roots and one or two nulls. After that, players take turns placing one of their fifteen pyramids in open spaces.

Branches and Twigs and Thorns takes advantage of the fact that the pyramids are pyramids by requiring you to leave them on their side so that they're always pointing. They must always be pointing to either a root or another pyramid. They can never point to a null.

If you are pointing at a root or one of your own pyramids, everything is fine. However, when you point at another player’s pyramids, they gain points equal to the size of your pyramid and you lose points equal to the size of their pyramid. And the board is so cramped and claustrophobic that someone is eventually going to have to break down and point at someone else's pyramid.

The game ends when you fill the board, which is going to use up all the pyramids as well, by the way. At that point, whoever has the most points is the winner!

Most of my games of Branches and Twigs and Thorns have been two player. Those games have felt like both players were trying to get the other player in a Go ladder.

I once described Branches and Twigs and Thorns as having one or two major decisions per game. I was wrong about that. Branches and Twigs and Thorns is a game that has one or two confrontations. All of your decisions are working up to that confrontation. It's not just a knife fight in a phone booth. It's all about being the one who is able to stab the other guy.

Branches and Twigs and Thorns isn’t a life changing, amazing abstract. However, I do like how it’s a fast, little dynamic game, every move quickly pushing you towards that inevitable confrontation.

http://boardgamegeek.com/boardgame/17298/branches-and-twigs-and-thorns

Emergent Gameplay, Divine Moves, and other surprises

A concept that is central to my fascination with games, both boardgames and role-playing games, is emergent gameplay.

The core concept behind that is when simple systems come together to create complex decisions. In other words, the rules aren't that hard but they allow for tough choices. You know, a minute to learn but a lifetime to master.

Go is the poster child for this. The rules to go are very simple. I once heard someone summarize them in about six sentences, with two of the sentences being there is a 19 x 19 board and the players use black and white stones. However, Go creates amazingly complex situations. A 19 x 19 board is actually a huge playing area and allows for elaborate patterns to form.

However, there is another side to emerging gameplay. That is when the interaction of the players with the rules creates unusual or even unexpected results. This is something that video game community has become fascinated by. Heck, I would even go so far as to say invested in.

But this aspect of the emergent gameplay is also very important to role-playing games and even board games. Honestly, the sandbox nature that is intrinsic to role-playing games actually makes this pretty much what role-playing games are about. They also play an important part in boardgames, although the tighter framework of boardgames makes this kind of a emergent play a little more restricted.

But it's still definitely exists. Back to my example of Go above. Over the many centuries that Go has been around, a lot of formula has been developed. There is a term called Joseki, which means an established pattern of play that that would work well for both players. As a sidenote, even though I did Go for a few years pretty heavily, I was never anywhere near understanding Joseki.

But there is another concept called the Divine Move. That is when a single move, one that is inspired and anything but obvious, can turn the game around. They are said to be so rare that a professional Go player may play one only once in her or his life.

But they exist. Or, a lot of Go authorities say they exist and they know a lot more than I do.

And when games allow for more flexible interactions between the players, this kind of emergent gameplay becomes more possible.

Both of these aspects of emergent gameplay fascinate me. They define the depth and the surprise of playing games.

https://boardgamegeek.com/boardgame/188/go

https://en.m.wikipedia.org/wiki/Go_(game)

https://en.m.wikipedia.org/wiki/Emergent_gameplay