Theory: Defining Games in Light of the Simplest One

What’s the most minimal game you can build?

It doesn’t have to be a good game. It doesn’t need to stand up to many plays, staying interesting over time. It just needs to count as a game, with as few lines of rules as possible.

I raise the question because I think it’s an interesting way to get at the issue of what “games” are. Consciously trying to make a game as simple as possible forces one to decide what has to be included–and what can go.

My first thought was Sirlin’s rock-paper-scissors with unequal payoffs: play RPS normally, but rock is worth 10 points. The first person to 10 points wins. (Sirlin made it even more complicated, but let’s skip ahead to this simplified revision.)

So, how many rules?

1. Both players make a sign simultaneously.
2. The three signs are rock, paper, and scissors.
3. The sign for rock is a fist.
4. The sign for paper is a flat hand with fingers together.
5. The sign for scissors is the index and middle fingers extended.
6. Determine the winner as follows:
a. Rock beats scissors.
b. Scissors beats paper.
c. Paper beats rock.
d. If both players made the same sign, no one wins. Return to step 1.
7. Players score as follows:
a. If a player won with scissors or paper, he or she gets one point.
b. If a player won with rock, he or she gets 10 points.
8. If a player has 10 or more points, he or she wins.
9. If no player has 10 or more points, play again, adding the next round’s score to the current total.

(That’s more than I would have thought for RPS!)

So, nine rules with some sub-rules. That’s enough to give us everything one intuitively expects out of a game: decisions, scores, a way to win.

Of course, Sirlin’s variant has special scoring rules. Normal rock-paper-scissors doesn’t need them:

1. Both players make a sign simultaneously.
2. The three signs are rock, paper, and scissors.
3. The sign for rock is a fist.
4. The sign for paper is a flat hand with fingers together.
5. The sign for scissors is the index and middle fingers extended.
6. Determine the winner as follows:
a. Rock beats scissors.
b. Scissors beats paper.
c. Paper beats rock.
d. If both players made the same sign, no one wins. Return to step 1.
7. The player who won gets a point.
8. If a player has 10 points, he or she wins.
9. If no player has 10 points, play again, adding the next round’s score to the current total.

Yet, there are some extras here. The decision between rock, paper, and scissors isn’t much–especially when they all have the same value–but if we could get it down to two choices that would be even better. There could be, for example, only two signs: high and low. That cuts a lot of rules out:

1. Both players make a sign simultaneously.
2. The two signs are high and low.
3. The sign for high is a finger pointing upward.
4. The sign for low is a finger pointing downward.
5. Determine the winner as follows . . .

. . . uh, oh. There needs to be a way to decide who wins. Since the goal is to keep it simple, the rule could just be that high always beats low.

5. Determine the winner as follows:
a. High beats low.
d. If both players made the same sign, no one wins. Return to step 1.

Going down to two options saved us a rule and two sub-rules, while still obliging players to make a decision. Doing away with different scores for different moves also helps:

6. If a player won, he or she gets one point.
7. If a player has 10 points, he or she wins.
8. If no player has 10 points, play again, adding the next round’s score to the current total.

Those changes get us down to eight rules, with only two sub-rules. There’s still a decision to make, a score to keep, and means by which one wins.

Is this, however, still a game? Certainly there’s little of interest here. Strategy stops at “always show high.” No one would find this fun for more than a turn or two. Are the existence of various strategies and the possibility of having fun required? How many strategies? How much fun?

Although no one would (intentionally) put forward a game as simple as High vs. Low as something others should play, I think it’s interesting as a definitional problem. High vs. Low is an edge case for the definition of “game.” It challenges definitions that include it to explain why something so joyless counts as an example of an activity usually thought of as being for fun. At the same time, definitions that would exclude High vs. Low have to find a reasonably measurable element of games that it lacks.

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