President (Impeachment Games I)

Time for another little game. It’s called President, and it is also about democracy and taxes. Good for 4-12 players.


  • Paper money (any currency will do)
  • sets of six tokens in as many different colors as there are players,
  • a tax board for each player, i.e. a sheet of paper with the numbers from 0 to 60 in a row,
  • an extra counter to mark the current tax rate, 
  • 2-4 game figures representing political parties.

Money4 2a


Each player gets $100 in small bills, picks a color and gets three tokens of that color,
sets the tax rate counter on her or his tax board to $10.
The political parties are placed in the center of the board.

The game proceeds in years. Each year consists of an election phase and and ruling phase.

Before the game begins, the players decide for how many years they want to play. 

Money4 2b


First, all players pay their taxes.
For the first year, these are $10, and each player places them into the center of the table.
If in a later round a player cannot pay the taxes, that’s ok. The poor are tax exempt. But see the variation below.

Next, each player votes for political parties by placing their tokens next to the party figures. Votes can be split, and not all votes need to be used. In the first round, a player is selected randomly to begin the voting, and then it continues clockwise.

After all votes have been cast, the winning party is determined by counting all votes. If more than one party  has the same highest number of votes, the winning party is determined randomly. You can place the tied parties in a bag and draw one, for instance.

The player who cast the most votes for the winning party is declared president. If there are more than one player with the same highest number of votes, the president is determined randomly among all players with the highest number of votes for the leading party.

All used voting tokens are returned to the players, which ends the voting phase.

Variation: If a player cannot pay taxes, he/she loses one voting counter.

Money4 2c


In the ruling phase, the elected president must make a few decisions:

  • Adjust taxes: The president can adjust how much taxes each player pays. He or she does so by moving the tax counter on each player’s tax board up or down by at most $2. The taxes cannot exceed $60 and must be at least $10. The total amount of taxes paid must remain equal to $10 times the number of players. This means that if the president lowers taxes somewhere, he/she must increase them somewhere else.
  • Adjust the number of votes: For each player, the president can increase or decrease the number of voting tokens the player has by at most one. The number of voting tokens cannot exceed 6, and must be at least 1.
  • Distribute tax income: Finally, the president distributes all of this year’s tax income to all players as he or she desires, including him or herself.

The game ends when the number of years the players agreed on has passed. Then the plaeyrs vote on one of the following three winning conditions:

  • The richest player wins
  • The player who was most often president wins
  • The player who has the most voting tokens wins

Money4 2d

That was a lot of text. I like to invent games, and I like to watch how people play games. So I programmed a little simulation to see how this game would perform while tweaking the parameters. All players in my simulation behave opportunistic. They begin with equal preferences for the political parties. When somebody’s income increases, they start favoring the ruling party in the next vote. The president uses his/her power to give more votes and more money to those who voted for his/her party.

In contrast to humans, the computer was willing to play for an extended period of time. I was expecting that the game would quickly stabilize to a single rich dictator with the rest of the population living in poverty. The pictures above show the wealth/time graph of a 4-person game with just two parties. While presidents often rule for long periods of time (50,000 years for the blue president…), the situations is all but stable. That it can take so long is only because the underlings in my simulation do not cooperate. Below are mere 5,000 years with eight players and four parties. I have run several such simulations, and it appears that change happens more often when there are more parties involved.

Money8 4a



Copycat (Election Games II)

My popular series of election games continues with a paper and pencil game for any number of player. It’s called Copycat. Let’s play the multiplayer version first. Each player grabs a sheet of paper and a pen, draws a rectangular grid of agreed size (I use 4×4 below, 6×6 to 8×8 is better for actual play), and marks an agreed number (I use 1 below, two or three is much better) of intersections with a nice, fat dot.

Move1 01

One player decides to go first and announces one of the four main compass directions. Now all players have to mark a segment beginning at any one of their dots and heading that way one unit. Above, the first player (left) decided NORTH (where else?), and all players had to follow. A player who can’t follow is out.

Move2 01

Now it’s the second player’s turn (middle), and she decides EAST. All players have to mark a segment that begins at the endpoint of any one of their paths and moves east one unit, thereby neither retracing steps, nor leaving the grid, nor ending on intersections that have already been visited by any path. The third player (right) has now only two options left (NORTH or SOUTH), and decides NORTH. This eliminates the middle player, who is out of moves.

Move3 01

Left takes revenge and moves EAST, which is impossible for the right player. This leaves left as the winner. In an (unrealistic) cooperative play, left and right could instead have continued on for eight more moves. The game becomes more interesting when the players begin with more than one dot, because then they can choose which path they extend at each turn.

To make puzzles for single players, start with a board, place a couple of dots, and draw legal paths like so:

Puzzle 01

Record the directions along each path as a sequence of letters, namely WNENESSSWWSEE and NESSWSESW in the case above.
Randomly splice the sequences into one, for instance into WNNEENESSSSWSSWWESSEWE. Then draw a new board that just includes the dots, and hand it together with the letter sequence to your best friend. She then needs to trace non-intersecting paths, following the letters as compass directions. Her only choice at each step is which path she wants to extend. This is an excellent example of an easy to make puzzle that is ridiculously hard to solve.

There are many variations: For single players, you can use an eight sided compass die or a spinner to determine the direction at each step.

Several players can also share boards, as long as they can agree on where north is. They would then use pens in different colors and could only extend their own paths, avoiding any crossings of paths.