Roll for Representation is a write and roll game for between two and seven players, using yahtzee style rolls on an election map.

Welcome to Representation Island! We’re about to have an election!

The island is divided into five constituencies, each with different priorities. In the north-west the residents are interested in dice rolls of pairs or triples, while in the east it’s all about throwing a straight. In order to help the political parties (that’s you, the players) win over the voters in each area, you can use up to five different campaigning techniques, which are explained under stage 3.

Get the printable map here
Download a copy of the scoresheet here

What do you need?

You’ll need one printed copy of the map, five standard six-sided dice, and a different colour pen per player. (It’s not absolutely vital to have different coloured pens, but really does help to see who has scored what.)

If you would like to score yourself, you’ll probably need a calculator. (On your phone is fine.) Otherwise use the downloadable scoresheet here.

Getting started

Each player should write their initials in their coloured pen in one column of the box in the top right-hand corner. These are the campaigning upgrades.

Decide who goes first by rolling dice.

How to play

Each player, in turn, rolls all five dice. They may choose to re-roll as many of the dice as they wish once. They may also chose to use any of the five campaigning upgrades in the top right of the page. The aim is to get as high as possible a score to write in one of the five constituencies on the map. The player can choose in which constituency they enter each score, but by the end of the game each player must have entered a score in each constituency.

The constituencies are not all looking for the same type of result from the dice roll. Two constituencies ask for straights (three or more consecutive numbers), two constituencies ask for pairs or triples (or both if you have them), and the last constituency asks for dice which are the same.

Example: one player ends up with 3, 4, 4, 5, 5. As a straight, count 3, 4, 5 to get a score of 12, and discard the extra 4 and the extra 5. As pairs/triples, count 4, 4, 5, 5 to score 18, and discard the 3. As all dice the same, count 5, 5 to score 10, and discard 3, 4, 4.

Write the player name or initial under “P” (although players should have different coloured pens, an initial also helps). Write the total of the scored dice under the die symbol. Write the total of the discarded dice in the third column labelled “D”. The discarded dice number acts as a tie breaker if players get the same score.

Each player rolls and scores in turn until all players have entered scores in all five constituencies.

Campaigning upgrades

There are five campaigning upgrades, and they are shown in the grid in the top right-hand corner of the page. Each player may use each upgrade once, and there are no benefits to not using the upgrades. Each player should cross off the upgrade in their column once used. The upgrades are:

• Another roll. Roll as many dice as wished again.
• Turn to 6. Change one die to a 6.
• Flip. Turn one die to the opposite side (2 becomes 5, etc).
• Mirror. Change one die to match another die shown.
• Plus/minus 1. Change the value of one die up or down by 1 (including between 6 and 1).

How to score

There are two ways to do this…using the scoresheet, or by doing the calculations yourself.

If you like spreadsheets, or you want to quickly see how your election results would work out under several different systems, download the scoresheet from googlesheets. This gives you absolutely accurate results for two different counting methods: D’Hondt, and Hare. Both are Proportional Representation electoral systems, and both use a party list method, which means that the party publishes a ranked list of candidates who will get the seats won by that party. (To see exactly how the two counting methods differ, you’re best off doing the calculations yourself.)

The scoresheet will also give you interpretations of two other systems: First Past The Post as used in a multi-member ward, and Single Transferable Vote. The reason that FPTP and STV are not 100% accurate is because the election would actually need to be run in a different way — for example, you’d need to roll five times in each constituency for FPTP to represent five different candidates. And for STV you’d need to know how votes might shift between players, which isn’t possible. Because of that, those models are interpretations rather than accurate calculations.

The other way is to do the calculations yourself. The reason you might want to do that (besides for the joy of maths) is to see how the two different methods work. Both are Proportional Representation, but they sometimes produce different results.

For both these methods, we’re saying that each constituency contains five seats.

D’Hondt method

The D’Hondt calculation is the number of votes divided by the number of seats allocated plus one. Let’s represent this as Score / (Seats +1). It’s done constituency by constituency, and within each constituency seat by seat.

Take any constituency. Look at the scores. Divide each score by (the number of seats +1). Since no one has been allocated any seats yet, that’s 0+1, so every score is divided by 1. Give a seat to the person with the largest score.

Now look at the scores again, and run the calculation again. Now one person has one seat…so, if you calculate Score / (Seats +1) then the person who got a seat last time has their original score divided by two. In the example below Jess gets the first seat with a score of 20, while Oliver gets the second seat with a score of 16. Oliver’s score will become 8, so Matilda will get the third seat.

If we run that calculation on until the last (fifth) seat, you’ll see it becomes:

It’s possible that players will have the same score. In this case, the player with the highest discard value should be considered to be slightly ahead. If two players have exactly the same score AND discard value, then the player who rolled first (and so wrote their score higher on the paper) is considered to be slightly ahead.

Hare method

The Hare method is different. It works on a quota. That quota is going to be different for each constituency, because it’s the total of the players’ scores (in that constituency) divided by the seats available (5). If we use same example scores, we have a total of 48 divided by five seats, and so get a quota of 9.6.

The next step is to see how many times that quota goes into each score, and to give the players that number of seats. So, 9.6 goes into 20 twice, 16 once, and 12 once. This means that Jess gets two seats, Oliver one seat, and Matilda one seat. As there are five seats, there is one seat left. If we take 9.6 away from Jess’ score twice (because she has two seats) and Oliver and Matilda’s scores once (because they each have one seat) then we see that the person with teh highest remaining score is Oliver. The last seat should therefore go to Oliver.

Just as with the D’Hondt method, it’s possible that players will have the same score. In this case, the player with the highest discard value should be considered to be slightly ahead. If two players have exactly the same score AND discard value, then the player who rolled first (and so wrote their score higher on the paper) is considered to be slightly ahead.

Another method: FPTP

On the scoresheet you’ll see that there’s also a First Past the Post option. It’s not exactly correct, because in a FPTP election where there are multiple seats (local council wards in England and Wales, for example) then not all voters vote for all candidates of the same party — voters can and sometimes do split their votes between parties. However, in order to make it fit the game I have assumed that vote splitting doesn’t happen.

Scoring FPTP is very simple. Give three seats to the player with the highest score and two seats to the person with the second highest score.

What does this show?

On the scoring sheet you can compare the percentage of the vote overall to what each player gets under each system.

FPTP is notoriously unfair, and the more parties (players in this case) there are the more unfair it becomes. The D’Hondt and Hare systems of counting votes are both sensible forms of proportional representation, but occasionally they’ll throw up different answers.