A three-player Pictionary variant

[This blog post is a collaboration with Paige Kubenka and Alicia Torres Hoza. It was originally a standalone webpage, posted on 11/29/2018. I edited it a tiny bit for the blog.]

Background

Pictionary is a classic game in which players try to guess what other players are drawing. Quintessentially, Pictionary is played by two teams of two players (one teammate draws while the other teammate guesses.)

Hasbro's official Pictionary rules also describe a "three-player" version of the game. In Hasbro's "three-player" game, one player is designated as the artist for the entire game; the other two players compete to win by guessing. Hasbro's game has some merits, but the poor artist can hardly be considered a "player" in the game. Hasbro's game is more like a two-player guessing game.

In this blog post, we describe a Pictionary variant with no teams in which every player has a shot at winning. Our game is designed for three players, but it also works with more than three players.

How to play our game

Necessary materials:

• A source of words (e.g. the cards from the original Pictionary game)
• A drawing surface that everyone can see
• A one-minute timer

Gameplay:

• In each round, one player is the artist and all other players are guessers.
• The artist gets a word from the word source and spends up to one minute drawing it. (Standard Pictionary rules apply: no alphabet symbols, no gestures, etc.)
• If a guesser correctly identifies the word, the round is over. The successful guesser and the artist each get one point. (In the rare event that multiple guessers correctly identify the word simultaneously, each successful guesser gets one point.)
• If none of the guessers identify the word within one minute, the round is over and nobody gets any points.
• Players take turns being the artist with one exception: if it would be your turn to draw, but your score is strictly greater than each of the other players' scores, then you are "ineligible to draw" and your turn is skipped.

Winning:

• If you have at least 9 points and you have strictly more points than each other player at the beginning of a round, then you are "eligible to win" during that round.
• If you get a point in a round in which you are eligible to win and no other guessers get points in that round, then the game is over and you win!
• Example: At the beginning of a round, A has 7 points, B has 8 points, and C has 9 points. B draws and C successfully guesses the word. The game is over. The final scores are (7, 9, 10) and C wins. This example demonstrates that the win condition is not simply "game to 10, win by two."

Discussion

The reader may wonder why our rules are so complicated. For the sake of discussion, let's consider some simpler rules, focusing on the three-player case. Let's imagine a game where players take turns being the artist; the artist and guesser each get one point when the the word is successfully identified; the first player to 10 points wins the game. To handle ties, we'd better stipulate that the game continues until some player has strictly more points than each other player.

These simple rules have a serious defect: in some situations, a player knows that he or she will not win even though the game isn't over. For example, suppose the scores are (8, 9, 9). It's impossible for A to win, because if A ever gets a point, then so does either B or C.

To fix this defect, let's change the winning condition. Let's say the game continues until some player has at least 10 points and is ahead by a margin of at least two points ("game to 10, win by two"). These rules still have some serious defects:

• In some situations, one guesser doesn't want to guess. Suppose the scores are (7, 9, 8) and B is the artist. If A successfully guesses the word, the game will end and B will win, whereas if C successfully guesses the word, the game will continue. So A would rather wait until C is the artist to guess.
• Even worse, in some situations, neither guesser wants to guess! Suppose the scores are (5, 6, 9) and C is drawing. If A or B correctly guesses the word, they'll immediately lose! They'd rather wait until one of them is the artist.
• In some situations, the artist doesn't want to draw. Suppose the scores are (7, 8, 9) and A is the artist. If A draws, there's a risk that C might correctly guess the word and win the game. On the other hand, A can just wait for B's turn as artist. When B draws, even if C successfully guesses the word, the scores will be (7, 9, 10) and the game will continue.

Our rules avoid all these defects:

• With our rules, there can never be a tie. After all, in each round, at most one player is eligible to win.
• With our rules, if the game isn't over, any player might win. Indeed, no matter what's happened so far, you'll win if from now on, whenever you're a guesser, you successfully guess the word, and whenever you're the artist, the guesser with fewest points successfully guesses the word.
• With our rules, it's always reasonable for all guessers to guess. After all, if another player is eligible to win, guessing will prevent that player from winning.
• With our rules, it's always reasonable for the artist to draw. After all, if a guesser is eligible to win, that guesser will still be eligible to win next round if you refrain from drawing. You're going to have to get points eventually if you want to ever win.

Admittedly, even with our rules, there are still some contrived scenarios in which someone might choose to not guess or choose to not draw. For example, the two guessers might feel that the artist is actually much better than they are and is only eligible to draw due to bad luck, so they might refrain from guessing. For another example, suppose A is the artist and B is eligible to win. A might feel that B is particularly good at guessing A's drawings and A is particularly good at guessing C's drawings. A might therefore choose to not draw. In practice, we haven't encountered these issues.

We hope you enjoy our game!

Acknowledgments

We thank Paige Hardy for helping us playtest.