Tuesday, April 16, 2013

Outwitters: No Spawns! (Part Two)

Once more I am talking about...

...so if you are not deeply interested in this video game, then you might find this entry to be just a little bit boring.

Playing Outwitters without spawning any new units is a very different experience from the normal mode of play and presents its own unique challenges. In the previous entry, I discussed a particular position of units in the endgame of a match played on Long Nine. That entry focused on the idea that without spawns, the game becomes much more like Chess, and it becomes all the more important for the players to attempt to calculate who will emerge victorious in any given exchange of units prior to initiating that exchange. Veteran Chess players will be very familiar with this concept. However, there are some very important differences between Chess and Outwitters, and to me it seems worthwhile, even in the context of a fringe alternative play style, to explore some general principles that one must keep in mind. One of the most important principles that I realized as I played my way through the Micro Strategic Starting Units Tournament was this:

Adopt the most aggressive position possible without endangering your units.

This is probably much more evident from my play late in the tournament than at the beginning, and in fact, I think the application of this strategy is perhaps most clearly seen in this penultimate game played on Sweetie Plains against !_elle_!. Thus, I felt that for the second entry of the Outwitters: No Spawns commentary series, a move by move analysis of my thought process in playing this particular match would be most appropriate. I’ll also provide a few comments on moves made by my opponent, but I’m mostly going to focus on why I made the moves I made and where I might have made better moves.

P1: !_elle_!
P2: TheGreatErenan
Map: Sweetie Plains

Turn 2 (Erenan): My primary point of thinking in my first turn is to ensure that my opponent cannot capture my medic, sniper, or runner. I don't think she would actually do any of these things, as this would be far too risky of a move for not being allowed to spawn new units, but I want to be absolutely sure they are safe.

So I work out the most aggressive hexes that her runner could have moved to on turn 1. None of these hexes are within reach of my sniper, so I decide to keep it where it is this turn. I think the best thing is to boost the runner and ensure the medic can't be reached. If she had advanced her runner as much as possible on the right side of the map, then she could theoretically capture my medic, so I move my runner in the way, boost it for safety, and hide my medic behind it.

I leave my heavy where it is and move my soldier to the wit space to ensure I'd have plenty of wits later on.

Turn 4 (Erenan): My opponent has had two turns now, allowing plenty of mobility, so I need to regain visibility in the center of the map. But where exactly should I put my runner? My opponent's runner can't capture it, so I need only consider her heavy, soldier, and sniper. Her sniper obviously can't be a threat at this point. Her soldier most likely stepped on the wit space in turn 1. If it didn't, it could theoretically be anywhere in the fog on the right side of the map. I doubted it would be very far up though, as this would be overly aggressive, and in any case, I suspected that I'd win out in the ensuing exchange if my opponent were to attack at this point. The heavy couldn't really be anywhere especially threatening. So I put my runner on my central spawn space, safe from the heavy, and almost certainly safe from the soldier.

After gaining visibility, it seems my opponent has not been too aggressive. Now, I need to boost my sniper, but I want to guarantee the safety of both sniper and medic. Her runner could be anywhere at the edge of the fog of war. I realize here that if I put my medic next to my sniper, then I can block her runner's access to it with my heavy. Seems like a good move to me, so I do it.

I advance my soldier. Strictly speaking, this move is a gamble, theoretically putting it within reach of my opponent's heavy. However, I decide that her heavy had probably been on the wit space in turn 1 and wouldn't be able to reach it, so I move my soldier a hex too far south, risking its safety for an extra five hexes of visibility and reach.

Turn 6 (Erenan): I start off with a visibility grab with my runner. Technically, this is putting my runner within reach of where my opponent's soldier could have been, but I decide to go for it anyway.

I've spotted my opponent's heavy! This is useful information. I know the furthest west her sniper could be, and I decide to assume that it was her soldier that took the rightmost wit space in turn 1. This makes her leftmost spawn a safe spot for my soldier, where it could not possibly be captured. So I move my soldier there. This was likely a mistake, as it reveals to my opponent my soldier's position. I suppose I could have put my soldier a hex to the northwest of the spawn space, and it would have remained in my opponent's fog of war. However, I still didn't know where her runner was, so I didn't know the extent of her fog of war, and I figured that with this move, she'd see my soldier anyway, so why worry about the spawn space?

As a side note, it could be that the appearance of an advanced soldier from the fog of war could potentially give one's opponent the idea that your forces in general are getting dangerously advanced. The goal here, I suppose, would be to throw your opponent into a panic in the hope that she would make a mistake upon which you may capitalize.

But I'm not thinking of psychological warfare here. I am only looking for the most advanced position possible where I can safely put my units. This space appeared to be safe.

In that sense, it seems clear that I have room to advance my heavy and sniper, so I do so. The medic comes along to ensure the heavy remains healthy.

Turn 7 (elle): Here it appears that the appearance of my soldier and heavy have prompted my opponent to move her forces in that direction in order to defend. Not a bad idea.

Turn 8 (Erenan): Now I know where my opponent's soldier is! However, I want some additional visibility on the right side, so I move my runner over to fill in some of that ground.

I don't spot any new units, so I'm still not sure where my opponent's runner, sniper, and medic are located. But I do know they're not on the right edge of the map.

On that note, my opponent has had four turns. This means her sniper could be near enough to take out my soldier if I don't move it. Advancing seems like a bad idea, so I retreat instead. My soldier forms a wall with my heavy, and I move my medic to buff the soldier. I'm careful to ensure it cannot be reached by my opponent's heavy or soldier.

I advance my sniper, as it seems perfectly safe to do so, and I gain nothing by leaving it where it is.

Turn 9 (elle): This turn appears to be done in the interest of gaining visibility on the right side, probably just watching out for my runner in the interest of protecting her medic, as she can already see my heavy and soldier, and she knows where my medic is (she saw it buff my soldier).

Turn 10 (Erenan): I advance my soldier to a point where it cannot be attacked by both heavy and soldier. This move was a mistake on my part. Clearly my opponent's sniper might have been capable of moving within range (in fact, it was). Nevertheless, I move my heavy forward to help if needed.

I advance my runner a bit more to gain that extra little inch of visibility, careful to ensure it cannot be within range of my opponent's sniper, which could theoretically still be hiding in the fog where it started. However, I spot the runner there instead. Now, I'll know exactly where her runner is on the next turn, even if it moves back into the fog of war.

Knowing where my opponent's runner is, I can easily calculate where I can safely put my medic and sniper.

Turn 11 (elle): My opponent moves her runner up and gains visibility of all five of my units. This is her chance. After gaining perfect information, and seeing that she could capture my soldier, she should attempt to work out who would come out ahead in a direct exchange of units. To me it looks as though she would win.

Very briefly, what would probably happen, as best as I can work it out:

She takes my soldier with her heavy and sniper
I take her heavy with my heavy and sniper
She takes my heavy with her soldier and sniper
I take her sniper with my sniper
She takes my sniper with her soldier
I cannot recapture with only a runner
She is left with a soldier and I'm left with a runner: elle wins!

But this doesn't happen. Instead, she leaves her units where they are.

Turn 12 (Erenan): I inch my runner forward, hoping to spot my opponent's sniper in the fog, but there's no sniper there.

I know where her runner, heavy, and soldier are, so I can work out safe spots for my soldier. I find an advanced position along the side where I know it cannot be captured, even if my opponent's sniper is right next to it. Her heavy, soldier, and runner cannot reach it, and the sniper alone doesn't have enough firepower. I find a spot where my medic could hop down to heal it if necessary (or the soldier could hop back up to be healed) where it cannot be reached by opponent's runner (it's blocked by my heavy).

I advance my sniper, which is still perfectly safe from harm.

Turn 13 (elle): My opponent moves her sniper toward where my soldier has just moved, probably a good idea.

She moves her soldier down on the right side. I'm not sure, but I figure she's watching out for my runner, which she knows is already over there somewhere. She doesn't spot it with the soldier, so she moves her runner over to where it was last seen. She finds it and attacks it, bringing it down to one health.

Turn 14 (Erenan): I return the attack upon my opponent's runner (might as well), and retreat it. I cannot ensure my runner's survival here. However, I make sure to put the runner somewhere as close to my sniper as possible. It seems here that if I move my sniper northeast one hex, then if my opponent were to follow my runner to finish it off, I would be able to move my sniper within range to recapture. So I follow this plan.

I now know where all of my opponent's units are except for her sniper, which could only be in one of a handful of still fog-covered hexes at this point. I work out where her heavy, soldier, and runner can reach, and I position my heavy and soldier in as advanced positions as possible where they yet cannot be captured.

I move my medic to a safe spot where it can reach either my heavy or my soldier if necessary.

Turn 15 (elle): My opponent wisely does not capture my runner. Doing so would have meant the loss of her runner as well. In this "no-spawns" game, losing your runner is a very bad thing. Visibility is extremely important.

Unfortunately, her runner's new position does not gain her enough information. She advances her sniper to the left without knowing for sure whether it will be safe there. She uncovers my soldier but cannot capture it. She already moved her heavy, soldier, and runner, so she cannot attempt to move them into position to recapture if I should capture her sniper. She might have benefited from moving the sniper first here, since then she could have moved her soldier and heavy to help take my soldier if necessary.

Turn 16 (Erenan): I know where most of my opponent's units are now, so it's easy to work out where the safe spots are. I see that if I move my medic down on the left side to heal my soldier, my medic will still be safe. Furthermore, I see that if I move my healed soldier forward to capture the sniper, my opponent will not be able to recapture. This seems like the opportune moment, so I buff my soldier and take the sniper.

I move my sniper to make room for my runner and retreat my runner a bit further to keep it safe until I can heal it.

My heavy is advanced as far as it can be without putting it in danger, so I leave it where it is.

Turn 17 (elle): My opponent moves her runner and attacks my soldier. I suspect that she thought my medic was adjacent to this hex and that it would be within range to capture it. However, I was careful to keep it out of range, so she attacks my soldier instead. Even attacking with her soldier as well isn't enough to take my soldier out, but she nevertheless moves her heavy in to help on the next turn.

Turn 18 (Erenan): I capture the runner with my soldier. Advancing my sniper and runner, I see where my opponent's heavy is, so I retreat my soldier and heal it, careful to keep my medic out of reach of my opponent's attacking units.

At this point, I realize that I can advance my heavy by a single hex without putting it in danger, so I do so.

Turn 20 (Erenan): I see my opponent move her heavy further away from the center, and I decide that the center is where this game will end. I heal my runner and move it to capture the medic. I advance my central attacking units and move my soldier up to support the offensive. At this point, my opponent has no good moves to make. On the next turn, I'll either capture one of her remaining two units or destroy her base.

Turn 22 (Erenan): The game is over.

Until next time...

Thursday, April 4, 2013

RE: Radiohead's "Pyramid Song": Ambiguity, Rhythm, and Participation

Music notation is descriptive. There is no single absolutely correct way of transcribing any piece of music any more than there is a single absolutely correct way to express particular fractions. 1/2 is 2/4 is 4/8 is 8/16. Not a single one of these is incorrect.

However, it behooves us to transcribe music in such a manner that it is readily understandable and indicates the correct feel of the music. A person reading and playing from the score, assuming they are reasonably capable on their instrument, should be able to reproduce the music accurately. With respect to this particular goal, certain ways of transcribing a piece of music are obviously better than certain others.

There have been inordinate measures of discussion concerning Radiohead's "Pyramid Song" from their album Amnesiac. It's an excellent song, definitely worthy of analysis, and given that the rhythm is relatively unusual for a piece of music written by a rock group, the amount of discussion is perhaps understandable. In fact, for as long as I've been aware of Radiohead, my opinion has been that, in spite of all the talk of their purported innovation and weirdness, the best things they have going for them are: first and most importantly, a firm sense of effective melodic and harmonic content; and secondly and slightly less importantly, a special talent for arrangement and production that lends their work a certain uniqueness and importance within the music world. They matter in a musico-historical sense, but not because they are weird or innovative (they aren't especially weird or innovative, in fact). They matter because of compositional prowess.

Having said that, "Pyramid Song" is a special example of a piece of music that uses nonstandard rhythms in an effective way that benefits the music significantly, rather than using them for the sake of being unusual. Melodically and harmonically, it is very well written. Rhythmically, it is also very well written, and unusual rhythms are definitely my compositional specialty. So to me, it is not surprising that it has generated so much discussion so consistently. The discussion apparently goes on even today.

In the March 2013 issue of Music Theory Online, Nathan D. Hesselink offers his thorough take on the song, compiling a comprehensive list of analyses of the song's rhythm. Unfortunately, the simplest and clearest interpretation in my estimation receives relatively little coverage. Two of the comments made under the mixed meter subheading hit the mark exactly, but none of the example images highlight these, though some are close.

In my opinion, the best way to write it is as follows:

Consistent cycles of 3/4, 2/4, and 3/4 throughout the entire song. The lengths of the five chords in each cycle are two dotted quarters, a half, followed by two more dotted quarters. It is swung, so that odd numbered eighth notes are twice as long as even numbered eighths, as though we were dealing with triplets. Thus, in terms of the feel of the music, the 3/4 bars have 9 atomic note lengths, while the 2/4 bars have 6. What I mean is that if you divide the 3/4 bars into 9 equal pieces and the 2/4 bars into 6 equal pieces, this is sufficient to depict every note in exact detail. The first chord is 5 atoms long, the second is 4, the third is 6, the fourth is 5, and the fifth is 4.

Thus, you could theoretically describe the music as cycles of 9/8, 6/8, and 9/8 as some have suggested. However, this requires tying notes together just about everywhere and needlessly complicating the score. It is far simpler to use 3/4, 2/4, and 3/4 and then plainly indicate the feel of the swing at the top of the score. This requires absolutely no ties, and correctly indicates what's going on.

Compare and decide for yourself. This...

...is technically equivalent to this...

Which do you prefer?