New on Desk #94 — Zero-Sum Multiplayer

Well past the autumn doldrums now, with productivity increasing every week. Hopefully that lasts.

Playing Dicewars

I discussed my drug-habit of playing the Risk-alike Conquest a few weeks back. That got Heikki to suggest another similar game to me, Dicewars, so I’ve been ticking away at that one since then instead. I imagine that fidget spinners play a similar role for some people; I seem to work best when I have some simple, quick game like this on hand. It’s important that the game is shallow and quick, as that keeps the break length small and gets me back to work faster.

Thematic interrupt: Fidget Spinner games

In case it’s not obvious to less office-oriented readers: the purpose of a “fidget spinner game” is to act as a quick relaxation and redirection device during focused cerebral work. I imagine that others in similar lines of work are aware of the concept. Turning attention to something routine and orderly at regular intervals allows the brain some rest and processing space, which then enables coming back to the actual work with a fresh perspective. A mental palate cleanser.

So, what other fidget spinner games are there? The following at least have made the rounds at my office at one time or another:
Slay
Minesweeper
There are probably others, but let’s not slow down to think here.

On the other hand, I can say that Slay the Spire (no relation to Slay) that I played last year is too heavy to be a proper fidget spinner; a run-through takes well over an hour, which is simply too much. Peggle, which I also played a fair bit last year, fails due to UI issues: a game that involves full-screen launch and menus and a general sense of being a “real game” is simply too cumbersome, even if the actual game is fairly brainless. I could imagine a Peggle version that was quick and streamlined enough, but the published game is not it.

Also, I tried Tetris in this particular niche in the summer, and it suprisingly doesn’t work either. I think it’s because twitch reflex games are at their best when played in ~1 hour training slots; throwing a quick single run in between other work is just frustrating. A good fidget spinner is probably not a real-time game that increases heart rate.

Back to Dice Wars with you!

Dicewars is also Risk-like, but it’s not an exact clone, belonging rather in the ideal nimbus of variants defined by the core qualities of the game: multiplayer, zero-sum, Cartesian plane territorial game board, units placed in regions, players go round in a circle, etc. The main differences are a different attack dicing function, different reinforcement distribution, a limit of 8 armies to a territory, and no continent bonuses. Risk-like, but not literally Risk.

The particular Dicewars force distribution rules are pretty wacky, and do the most to define the game’s nature: you gain one army per controlled territory at the end of your turn (instead of start, note!), and these armies get randomly placed between all of your controlled territories. The outcome of this rule is that border territories and interior territories participate in the round-by-round dynamics of the war very differently. Mostly it runs along the usual lines of managing border lengths that most of these games work with, but it’s also pretty interesting how interior spaces can act as production multipliers (once the territory has maximum armies, its production share basically gets randomized into some other territory) as well as “doom stacks” that get to march to war if ever an enemy penetrates deep enough to get in contact with the interior territory that’s been collecting armies without ability to send them to war.

There’s also a “keep your territories connected” theme, as your round production is actually equal to the number of territories in your largest cluster (rather than totaling them all), but the way the combat math works, this is generally a minor matter.

Arguably being novel is the only thing you can do in this design space, so mission accomplished in that regard here. Also, elegant simplicity. Dicewars gets my blessing as a fidget spinner and a study in zero-sum multiplayer by being elegantly simple.

The big emergent flaw in Dicewars is that its specific combat dicing logic has a fairly high chance of getting deadlocked. And this isn’t even the usual multiplayer deadlock where players A, B and C can’t act against each other without throwing the win to the third party; no, in Dicewars it’s fairly usual for the game to end in a two-way draw, or an extended-length roll-off, simply because the geography is so inflexible and a defensive bottleneck a very real possibility. It can be so bad that you can force a draw in a 1:3 force proportion situation, given a suitable geographical bottleneck.

(The reason I characterize that as a flaw is that the game design doesn’t account for it. You could just say that any side that can hold majority of the board for three rounds in a row wins. The problem is strictly caused by the victory condition of eliminating everybody being unnecessarily strict.)

Structural theory of zero-sum multiplayer games

So, as I’m apparently discussing these simple zero-sum multiplayer games regularly, I should also share my basic analytical theory of how this type of boardgame functions. That’s after all my best value proposition here, revealing the secrets of the universe.

First, let’s define the terms. “Zero-sum multiplayer” games are a common type of boardgame that arguably began with Risk, but became one of the dominant forms of gamer boardgame over the latter half of the 20th century. It’s still one of the top boardgame structures today.

Zero-sum: A game is generally zero-sum if a player cannot improve their final position (however that gets understood) without decreasing another player’s position proportionately. A game is specifically zero-sum if individual moves made in the game can only bring advantage by bringing commensurate disadvantage to another specific player.

Chess is both generally and specifically zero-sum: you can’t win without your opponent having to lose, and a move you make is only beneficial to you if it is also disadvantageous to your opponent. All two-player games where the victory condition is exhausting the opponent’s position are zero-sum in both ways.

Monopoly is generally zero-sum, but not specifically: at the end of the game your ranking can only possibly be better by lasting longer than another player, who consequently gets a worse ranking. (Or, if you’re only counting winning: I can only win if you lose.) However, during the game it is possible for you to land on a non-owned space that you can purchase, thus (likely) improving your position without disadvantaging another specific player. (You of course disadvantage every other player in the general sense when you do well, but the game doesn’t assign the disadvantage specifically.)

Multiplayer: A game is multiplayer if it has more than two competing player sides. That should be pretty obvious.

When discussing zero-sum multiplayer games, we generally mean games that are specifically zero-sum, not just generally. This is because another major category of multiplayer games, that tends to play pretty differently, is also characterized by being generally zero-sum: racing games, a category that’s much larger than it sounds like, are games that while generally zero-sum do not for the most part revolve around specifically zero-sum moves. You have a winner at the end, but during the game your moves do not detract from other players’ positions.

Snakes and Ladders is multiplayer, but only generically zero-sum; it is a racing game: the players are each trying to reach the goal first, by rolling lucky dice rolls in turns. Whomever gets to the goal first wins, and that victory prevents others from winning, but the individual rolls and moves you make do not decrease the positions of the other participants. You’re racing for a finish line, not trying to kick each other off the track.

Both zero-sum and multiplayer are on their lonesome pretty important typologies of game, but when you take them together, that’s when you’re cooking with gas: a competitive game where multiple players are attempting to pull each other down has historically proved to be something of a solidified trope in Ameritrash game design in particular. From Risk and Diplomacy on, the core conceit has multiplied like crazy, particularly in the shallow parts of the wargaming pool, and in geeky gamer games, going through a multitude of variations.

(Side note, the Wikipedia article on Ameritrash boardgames is pretty hilarious. “These games are sometimes referred to as Ameritrash. This is in reference to their propensity to use themes aligned to trashy low budget horror movies.” Yeah, sure Virginia, that’s where the name comes from. True blue subject matter expertise on display right here.)

Anyway, what I wanted to do is define some analytical terminology that I feel is useful to perceiving what’s actually going on in zero-sum multiplayer games when they are being played. Here’s the deets:

Resources are position elements that players can spend in maneuvers to affect game state. It’s a fairly generic concept, but not all game state is a resource; for something to be a resource, a player has to be able to choose to spend it to achieve something else. Your board position in Monopoly is not a resource, as you can’t voluntarily worsen it to achieve something else. Your money is a resource, because you can choose to spend it or not in various decision points during the game.

Attack resources are resources that can be expended (through whatever specific whirligigs) to worsen another player’s specific position. This could well be symmetric, like in Risk: both you and I have armies, and I can attack you to burn up my armies in exchange for burning yours as well. Monopoly money, on the other hand, is not a fighting resource, as you can’t expend it to specifically target another player’s resource base.

Victory points are a game state that determines who wins the game at the end. In many games, particularly in present-day game design, victory points are consciously treated as a resource as well! However, there are also plenty of games where the victory point is more of a specific game state than a points comparison: you win when you force the board into your own victory constellation, e.g. usurp the entire board from the other players.

Attack vector is a game structure that allows a player to expend fighting resources against another player. These come about in various games in different forms, like how in Cosmic Encounter you get the opportunity to select an attack target on your turn out of a random subsection of alternative targets, or how in Risk you are allowed to attack neighboring enemy-held territories, but only with the specific resources you have neighboring them.

Hopefully this terminology allows me to dress my specific insights on the matter into intelligible words. We’ll see!

The idealized zero-sum multiplayer game

This is the core understanding: zero-sum multiplayer games are all very similar to each other because the multiplayer privilege of targeting attack resources at discretionary targets among other players is so very, very decisive towards determining victory that everything else going on in the game ends up being so much window dressing. Perhaps pleasant window dressing, but still just that; victory is not determined by the window dressing, it’s determined by who decides to expend their attack resources against whom.

In Risk, assuming you get past the window-dressing of continent control and snipe elimination and such, and survive until there are only three players left, the player who wins the game will be the one who does not burn their armies to eliminate another player. What determines the victor is who gets attacked by whom.

In Small World, a more complicated example, the player who wins is the one whose empire the other players choose to not attack. (In practice, who gets attacked less.) The game is entirely about counting the points to figure out who is in the lead, telling this to the other players so you can reduce the leader, lying to the other players so they don’t decide to reduce you, and then being lucky enough to keep up not being attacked until the end. It feels different, but that’s mainly because the players are less aware of who’s in the lead.

In Cosmic Encounter, a game that was inspired by the former and went on to inspire the latter, you win by possessing colonies in all five solar systems. Because your attack vectors are randomized round by round, there’s a fair amount of luck in when exactly players are able to dash for victory, and when they are able to reduce each other to prevent dashing for victory. Still, the actual choices you get to make are the same: which of the other players to burn.

The common denominator of these games is that the pertinent game state consists of each individual player’s relative closeness to the point of victory (or accumulated amount of victory points, as the case may be), each player’s available attack resources, and the specific attack vectors available moment to moment. The winner in each game is the player who was not attacked by the others when they were close to victory, and then they went and won the game, who’d have guessed.

If we reduce away all the theatrics, the minimal zero-sum multiplayer game lurking behind the facade of all these games is the same:

Every player starts with 100 points.
The players sit in a circle, taking turns one after another.
Every turn you may burn as many of your points as you wish to burn the same number of points from another player. You are allowed to combine burns, targeting several players, and only finishing once you feel like it or run out of points to burn.
After you’ve lost all your points, you’re out of the game.
The last player to have any points left wins.

If this clearly absurd ur-game is really the underlying activity in all of these actually existing and popular boardgames, then what makes a zero-sum multiplayer game an actually good game? That’s the question. What enjoyment do we humans see in this activity?

Some design answers

I think that the core zero-sum multiplayer game is essentially absurd, and fairly trivial. When you’ve played enough boardgames and seen it often enough, you know all the moves:
The speaking action: “Hey Bob, don’t do that move! Can’t you see that Alice is winning right now? You should hit them instead!”
Stopping the leader: When Alice is winning, you hit Alice. When Bob is winning, you hit Bob. Maybe advance your own game in the meantime, but equally maybe don’t get too much ahead of the pack.
Kingmaking: “Well, because I’ve basically lost the game myself, I guess I might as well choose whether Alice or Bob should win this.”
Sneaking the win: Depending on the particulars of the game, try to make it so you can sneak over the finish line before the other players realize it and strike you down.

(At my local tables, incidentally, kingmaking situations are counted as draws among the pretenders. This is a bit unusual, I understand, but how else can you even continue the game when the procedure ends up leaving the choice of the winner in the hands of a third party?)

The socio-psychological game, sometimes termed diplomatic, is always the same, and it’s not that difficult. This being the case, what qualities can these games even have to entertain people? I have a few answers to that:

The pageantry of the circus: Arguably what people actually play for in many zero-sum multiplayer games is not the victory, but rather the pleasant exercise of seeing numbers go whee, and the excitement of calculating who’s in the lead at any given time. Small World, for example, is a game that I rather enjoy playing simply because it’s pretty fun to calculate proper valuation for each faction available on a given play-through. The business of actually winning the game is the usual annoying zero-sum bullshit, essentially random for most purposes, but I enjoy the actual parts that are about playing the game well (as opposed to the parts that are about deciding which of the other players to give the boot to this turn).

Obscured positions: If players do not know who’s winning, they cannot engage in the characteristic zero-sum multiplayer coordination. A hard version of this is pretty rare in boardgames, perhaps because it reduces visceral excitement when you don’t know the current standings. Eurogames often favour an annoyingly soft version of obscured positions where all the scoring is public but the points are totaled and compared at game end. Doesn’t work for me personally, as I just end up tracking the score in my head or on a piece of paper.

Controlling the vectors of attack: The ideal zero-sum multiplayer game is trivial in large part because players always have a regular window of opportunity to attack, and they can always attack everybody equally well. Play with this freedom, and suddenly you’re adding a potentially non-trivial asymmetry to the game. like in Cosmic Encounter, the game limits your opportunities to attack other players rather harshly at times. Make it sufficiently difficult to attack, and winning the game actually becomes possible.

That last observation is, I feel, at the heart of high-quality game design in this field. Dumb zero-sum multiplayer games just go dur dur, your turn to decide whether to attack Alice or Bob. Smarter ones are all about asking the question of how much you can attack Alice, how much can you attack Bob. Is your ability to attack them fast or slow? What are you losing out on if you choose to develop your ability to influence their game?

Modern eurogames that dip their toes into this area tend towards hybrid race game designs: the game might have a fair amount of opportunity for attacking other players’ board positions, but it may also feature victory point accumulation and limited turns. The winning board position is often pretty complex and non-trivial to perceive, as it consists of VP gain through prior turns combined with end-game scoring possibilities. Makes it easier to sneak to victory when calculating who is going to end up with the most points is often difficult or impossible.

Still, though, I find that the ur-game haunts my dreams. Even a game utilizing the above conceits will, when player skill increases, rip through the veil and reduce into either a perfect draw or arbitrary victory, depending on how much chaos and forced tie-breaking the game involves.

The actual lesson here may well be that zero-sum multiplayer games are essentially a broken conceit. You are, after all, asking players to stampede (or more likely, sneak) to victory over everybody else trying to stop them. It’s like playing capture the flag with a single flag that everybody is trying to take to their own base. Let’s even say that you start the game with everybody holding the flag pole. Why would the other players let you take the flag and win? Nothing of virtue in your own play will get there, the reason must be that the other players are giving up and letting go.

Coup de Main progress

The Monday Coup missed a session again; Tuomas the GM lives such an active social life that seems like he’s going through all the influenzas this year.

Tuesday… maybe had a game? I don’t know, actually. I’ll need to interrogate the players again to find out.

I think I’ll be returning to the Tuesday game at least in a couple of weeks, when the group’s gotten more or less through the Tomb of the Iron God. Maybe the Monday game too, we’ll see how I feel about my chances with Muster.

State of the Productive Facilities

I drafted CWPs #29 and #30 this week, so pretty good. Just four more to go:
#31 — Economic Modeling
#32 — Retinues
#36 — Magic Items
#38 — Working Greyhawk

So maybe these’ll be done around the end of the month?

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