Mind Mind Game Game

We consider several categories of game: games of chance, games of strategy, games of both chance and strategy -- in various proportions. Archetypically: poker, chess, and everything else. So far, so good.

There is another element which is missing, or drawn into the other two: games of mind. "Bluff" would be another term, or "second-guessing". Poker is chance, but the real game is convincing other players what chance has befallen you -- and this may have nothing to do with the cards in your hand. Even chess, with no hidden information, may hide traps and feints: the mechanics are complex enough that a player can conceal his strategy in a maze of future possibility.

Are there games of mind alone?

Last year I was introduced to Werewolf, or Mafia. See that page for a full description, later. For now, know that every player is assigned a secret role, good or evil. Evil knows its own; good knows (initially) nothing. Each team tries to eliminate the other. First, the evil players collaborate secretly to eliminate a good player; then, all the players vote publically to eliminate a player; then the cycle repeats. (There are many variants, and in the most common versions, one good player gets to secretly peek at someone's status once per turn. But set that aside for the moment.)

In the voting phase, of course, everyone pretends to be good, and exhorts each other to root out and destroy evil. But the evil players are trying to throw suspicion off themselves; they accuse the innocent. And what are suspicions based on? Only on demeanor, expression, words... and other accusations. And who has already died, and what they said. There are no cards, or dice, or positions on a board. Some players are bluffing, but they're bluffing only on whether other players are bluffing.

(As I said, in most versions there is a source of real information. But the peeking player has no way to prove he has privileged information -- and he does not want to, since the evil players will probably eliminate him if they suspect his power. So he must inject his true accusations with as much subtlety as the evil ones inject their false ones. The underlying nature of the game remains the same.)

Werewolf, by the nature of its mechanics, requires a large group: it doesn't work well with less than eight players, plus one impartial to coordinate the whole system. I have long been seeking a smaller game that has the same essence.

One well-known two-player mind game is Rock Paper Scissors. Players simultaneously choose moves, and Rock beats Scissors beats Paper beats Rock. (There, explained it in one sentence, so I haven't wasted your time -- there are no English-speaking humans beings who don't know RPS. But scholarly consistency demands.)

This is a mind game, in the sense that there is no hidden information, no chance, and strategy is based solely on what the other player has already played in past rounds. It's also completely unengaging -- at least for your humble author. There's no distinction between possible moves; the three are identical. You can impose a double-guessing analysis of "Did I change moves last turn; did I change my mind about whether to change moves; did I change my mind about that..." but it seems fairly pointless. (Note this entertaining ad-absurdum on the subject of Rock Paper Scissors strategy.)

Consider Mind Chess. Two players face each other. One says "Check." The other says "Check." The first says "Check." This continues until one of them says, instead, "Checkmate." That player wins -- superficially. In fact, the challenge is to put off checkmate for as long as possible, while still winning. This may be better stated: you truly win Mind Chess if you call "Checkmate" just before your opponent was about to.

This is even purer a game than Werewolf. Yet it works, if the players treat it with the right spirit. The currents of bluff and counterbluff, victory and defeat, are palpable to the point of agony. (I play Mind Chess rarely. I don't have the nerves for it.)

There are, nonetheless, problems. Without cool players, it doesn't work. (See the Icehouse Cool Problem.) There's no way to verify a win. And there's a tremendous asymmetry: someone must go first. This isn't an advantage, exactly, but it does tempt the first player terribly towards a sudden breakdown in his cool.

Consider a variation: Mind Chess With Cards. Each player has a small hand of cards (four is enough); one has a picture of a chess king on it, the rest are blank. Both players lay down two cards. They then simultaneously reveal one, and return it to their hand. Then they lay down another; then simultaneously reveal the previous card. This cycle continues: lay down new cards, then reveal the old cards.

If two kings are revealed simultanously, or two blanks, the game continues. But if exactly one player reveals a king, he declares "check". On the next flip-up, if the other player turns up his king, the first player has checkmate and wins.

This is simple, verifiable, has no first/second advantage, and can be played standing up if you have three hands. I haven't tried it yet, but I certainly will this weekend.

(Actually, maybe you don't need three hands to play standing up. Fan your cards, and pull one halfway up. Pull it out, pull another halfway up, and show the first. Continue.)

Mind Chess With Cards is much like Rock Paper Scissors, but without the fearful symmetry. Instead of three indistinguishable elements, you have a primal choice: attack or defend. Defense is always safe. Attack is the only way to win or lose. I really have to try this. Report follows later.

There are of course many possible variations of Mind Chess With Cards. Mind Chess With Cards is a demonstration of principle, not an attempt at a real game. Some variations may well be worth playing. The following are probably not them.

The game easily accomodates multiple players. Everyone plays at once, and it's possible to knock out, or be knocked out by, more than one person at a time.

In variations, it's important to maintain the fact that there's exactly one checkmate card in your hand. So you cannot play two checkmates in a row. Otherwise it becomes rational (though not superrational) to play checkmate every move.

You can extend the chain to three or more cards. This doesn't seem to add much, but you can also add more kinds of cards, and more complicated interactions. With five cards and a two-dimensional state machine, you've invented Roborally.

In Icetraders, John Cooper advances a rule which deserves to be separated out and discussed on its own. Icetraders is a multi-player conquer-the-galaxy game, in which players are eliminated one at a time until a winner emerges. However, in addition, each player secretly chooses to be good or evil. If all evil players are eliminated, the good players immediately win as a group. If an evil player eliminates anyone, the evil player immediately wins on his own. If a good player eliminates another good player, he turns evil and the game continues. All alignments are revealed after the first player is eliminated (assuming the game wasn't ended.) Last player standing wins no matter what.

This structure was inspired by Werewolf, and I've proposed calling it "the lycanthropic variation" in that honor. It can obviously be applied to any game where players eliminate each other one at a time. One could play Lycanthropic Risk, for example; or Lycanthropic Roborally; or so on.

To test the concept on its own, one should really create an entirely trivial game, and play its lycanthropic form --

On the spur of this essay, I come up with this: Mexican Stand-Down. Start with N players. A player is chosen at random, and he then points at another player and says "You're dead." Repeat as necessary. Now, is Lycanthropic Mexican Stand-Down an interesting game? Again, I haven't tried it yet.

(It may be necessary to prevent a player from taking two turns until everyone has had one, and so on.)

A quick meditation suggests that the lycanthropic rule may have to be modified. An evil player automatically wins on his turn. (This is reasonable in Icetraders, where eliminating a player takes great effort and depletes your resources, but we're abstracting all that away in Mexican Stand-Down.) It would be better to say that an evil player who eliminates a good player wins, but if evil eliminates evil, the game continues (unless there's only one player left.) In fact, this is how I remembered the Icetraders rule, until I looked it up; it seems more intuitive to me.

See also John's discussion of why you might want to be good.

Also, all alignments are revealed after the first shot, and then it gets very dull. We could drop this revealing rule. If a good player is eliminated, the killer reveals his alignment (and wins or turn evil); but if an evil player is eliminated, the killer remains concealed. (This requires a moderator, however, to declare when evil has been entirely destroyed by good.)

Note that if all players choose evil, the game becomes standard Mexican Stand-Down, although this won't be public knowledge until the game ends. (This is a common feature of all lycanthropic games.) If all players choose good, the moderator may declare an instant win; or you can play it out. The first good player kills another and turns evil. The second may kill the first, thus ending the game, or go out searching for more evil and thus give evil a greater hold... paranoia will destroy you.

Is it always good strategy to destroy the devil you know, or might good sometimes want to attack an unknown? I'd guess the former, but psychological factors may say otherwise in a particular game. (No doubt the most convincing arguments for not killing an exposed evil player will come from other, concealed evil players...)

Lycanthropic Multi-Player Mind Chess With Cards? The mind begins to boggle in the high ultraviolet spectrum.

Well, I did test Mind Chess With Cards over the weekend. It does work (although the standing-up version is fairly awkward.) Guess when your opponent is going to strike, and anticipate. Don't mess up. Of course, the game is too simple to spend an evening playing, but the principle is demonstrated.

What do we conclude from all this?

Not much. Some games can be reduced to elemental patterns, and these are a couple of them. Some patterns can be added to existing games. The Lycanthropic Principle is one, as is (for another example) the Misère Principle (playing to lose, applicable to many (but not all) two-player strategic games.)

If I took the time to catalog patterns of many games, the result might be interesting.

Of course, a good game is much more than a sum of elemental patterns. We knew that.

Updated November 17, 1998.

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