Introduction: Pen & Paper Catan - for Emergencies

Do you love Settlers of Catan? You do!? Great, me too!  Do you carry it with you wherever you go? No? That's what I thought.

Few of us carry a hex-board, road pieces, dice, resource cards, and all the other trappings a of good game of Catan with us on a daily basis. (If you do, then my hat is off to you good sir/ma'am.)  That is why I spent some time finding a way to play a reasonable facsimile with just things you almost always have on hand: pens, paper, and pocket change.  This is for all the times you were camping and forgot to bring the board, or were stuck at the airport for an unexpected 4 hour layover.

The final product at the end of this 'ible will look like Picture 2.  (OK. OK.  Maybe in real life, it'll look more like Picture 3, but this is an instructable and I wanted it to look extra nice for demonstration purposes.)

*Disclaimer*  Settlers of Catan is a great strategy / nation building board game that is WAY more fun than it sounds. The game was created by Klaus Teuber and first published in Germany, before becoming a world-wide hit.  This instructible is not meant as a replacement for owning the real game, just for use in emergency situations.  If you like Catan, you should go buy it (but who are we kidding, if you like Catan you probably already do.)


Step 1: The Board and Robber

The most iconic part of Settlers of Catan is the hex board.  It took several tries before I learned how to draw it quickly and nicely, and I'll mention some tips in a later section.  For now, let's go over the basics.
  • Your board will need 19 hexagons, arranged in a regular pattern in columns of 3-4-5-4-3, like the picture above.
     
  • Each hex gets one resource (draw a picture or just write the word).  3 Stone, 3 Bricks, 4 Wood, 4 Sheep, 4 Wheat, 1 Desert. Take turns placing resources, or play rock-paper-scissors, or flip a coin, until all hexes are filled.
  • Each hex also gets a number, 2 - 12.  These are usually arranged in a counter-clockwise spiral in the following sequence, starting from any corner hexagon and skipping the desert: 5-2-6-3-8-10-9-12-11-4-8-10-9-4-5-6-3-11.  I've arranged them differently in the picture to show that there should be two of every number except 2 and 12, which each get only one.  (Do as I say, not as I do.)
  • You need 9 ports arranged regularly around the board.  I draw dotted lines to help see where they should go.  5 of the ports are 2:1, each with its own resource.  The other 4 are 3:1 with any resource.
  • You need a coin, or a pebble, or a crumpled gum wrapper to act as your Robber.  Place it on the Desert to start.
  • Roads, Settlements, and Cities are simply drawn on the board.  Once placed they never move again, so pen or marker is OK.  Each player is allowed 5 Settlements, 4 Cities, and 15 Road segments.
I realize this looks like a lot to remember and draw.  But it's really not that hard, and with a bit of practice you could whip one of these boards out in under 10 minutes, which when you think about it is almost how long it takes to set up the real game.

Step 2: The "Dice"

I don't have dice in my pocket.  I do have coins.  I spent some time (and a few Microsoft excel spreadsheets) devising a system of coin flips that approximates, pretty closely, the probabilities of rolling a pair of Catan dice.  I believe this is as close as coin flips can reasonably get, but if anyone with a better background in probability or statistics would like to tackle the problem please go ahead.
  • Draw 5 circles, divide each in half. The "H" above the left half of each circle is for "heads", the "T" above the right is for "tails".
     
  • Put the numbers as you see them in the picture above into the circles: 0/1,  0/1,  0/3,  1/3,  1/4.  I labeled the circles "penny, penny, nickel, dime, quarter" but you could also just flip one coin 5 times, and get the same effect.
  • You now flip your 5 coins, or your one coin five times, and add up the values of the faces or tails.  This number corresponds with the numbers on your Catan board, just as if you had rolled dice.  For example, flipping Heads-Heads-Heads-Heads-Heads gives a sum of 0+0+0+1+1 = 2, while flipping Tails-Tails-Tails-Tails-Tails gives the sum 1+1+3+3+4 =  12.
I won't bother to go too much into the probability of 'rolling' each number using coins instead of dice.  For those who are curious, here are the probabilities of rolling any given number using regular dice versus using my coin method:
  • ROLL                   DICE                 COINS
  • 2 or 12 ======== 3% ========= 3%
  • 3 or 11 ======== 6% ========= 6%
  • 4 or 10 ======== 8% ========= 6%
  • 5 or 9 ========= 11% ======== 13%
  • 6 or 8 ========= 14% ======== 16% 
  • 7 ============ 17% ======== 13%

Step 3: Resource Cards

Instead of having individual resource cards, simply draw a Resource Bank like the one pictured above.  Each resource starts with 19 in the bank, and as people draw cards from the bank simply subtract them from the number left in the bank and write the new total.

I also draw a Building Costs chart just for reference purposes, it's easy to forget how much each item costs to build.

Step 4: Your Hand

Each play should take a scrap of paper as his or her "hand"  This paper is where they will write down how many Resource cards they have, and how many Development cards they have.  It's up to the honor system to make sure no one cheats and writes down more cards than they really have.

Step 5: Development Cards and Special Cards

Drawing Development cards is also done via coin flip, since there are no physical cards to draw.  I wont go into the probability of 'drawing' a card via coin flip versus drawing an actual card from the deck, but they are very similar. 

Each time a person buys a Dev. Card they must flip coins to see which one they 'draw'.  Then they subtract one card from the bank.  When not in use, the Dev. Card bank should be folded under the rest of the board, so other players don't see which card you've just 'drawn'.  Obviously, you also will have to shield your roll from them so they don't see that either. 

Again, use the honor system. No cheaters!

Picture 2 shows the two Special cards "Longest Road" and "Largest Army".  Simply write the name of the player who controls these cards on the lines to the right.  Longest Road goes to whichever player has the longest road of at least five or more road sections.  Largest army goes to the player with the most knight cards revealed, more than three.

Step 6: Other Alternatives

Here are some hints, tips, and short-cuts for playing Pen and Paper Catan.
  • When drawing the Hex-board, don't draw hexagons, draw the vertical zig-zag lines I've outlined on the left-hand side of Picture 1 above.  Then connect the zig-zags with horizontal lines to form the hexagons.  This is much faster and makes a nicer board than trying to freehand 19 hexagons.
  • Or, don't draw hexagons at all.  It is a well kept secret that you can create the same exact board using only offset rectangles.  Simply draw the rectangles as you see on the right-hand side of Picture 1, and remember to add the 6 dots (3 on each side) necessary for completing the board.
  • If you have a deck of cards handy, use it.  Not for the resource cards; a single deck doesn't have 5 x 19 cards.  Use them for your Development cards, which only requires 25 cards.  This eliminates the hassle of flipping the coins and creating a Dev. Card bank.
  • Make a pair of dice.  You can make paper dice from an origami paper cube (a 'kami-fusen' or 'Paper-Balloon' in Japanese).  They won't be as perfect as real dice (not balanced, and 2 of the 6 sides will never be quite flat) but they are a bit easier to play with than the coin flipping.  Obviously you can't know the probabilities of different rolls when using these dice, because every die is different, but it probably doesn't vary too much.  To learn how to make kami-fusen you can go to this nice instructable (which is not mine) or this video also shows how they are made.
Remember, this is only for emergencies!  I swear you'll have even more fun kicking back with the real game, friends, and a few beers!  Happy Settling!

Comments

author
kelseymh made it!(author)2011-06-30
Okay, I did find a second solution for the dice, which gives "lucky sevens" :-) It was fun to set up the spreadsheet and then just fiddle with the "tails" values. Using 1/2/2/3/4 (instead of your 1/1/3/3/4), I get the following percentages:


Roll Dice Coins Difference
2/12 2.8% 3.1% +0.3%
3/11 5.6% 3.1% -2.4%
4/10 8.3% 9.4% +1.0%
5/9 11.1% 12.5% +1.4%
6/8 13.9% 12.5% -1.4%
7 16.7% 18.8% 2.1%


So with these coins, sevens are a couple of percent more likely to come up than with real dice, but they are also now the highest probability.

I've uploaded my spreadsheet to I'bles and attach it here, if you or anyone else wants to play around with it. In principle, given the constraint that the five heads have to add up to 2, the five tails have to add up to 12, and you want the percentages to approximate real dice, it ought to be possible to set up an Excel optimization (Solver) to find the best solution. I'll leave that as an exercise for the reader.
CoinsForDice.xls
author
ATTILAtheHUNgry made it!(author)2011-06-30

I'm glad to see other people are Excel dorks like me :)

While I was fiddling for this 'ible I did consider using 1/2/2/3/4, but eventually settled on 1/1/3/3/4 because it created more variation in the rolls, rather than having 2/12 = 3/11 and 5/9 = 6/8. But both ways work and I think both would be fun to play. I guess it comes down to how much you want the robber to come into play. :)

I wasn't expecting people to be interested in the probabilities, but since you are I'll include my spreadsheet. It also shows the probabilities of 'drawing' Development cards using coin flips rather than a deck of 25 cards.

Catan Probabilities.xlsx
author
kelseymh made it!(author)2011-06-30

Wow! You really did that by brute force :-D You might be interested in a few of the functions I used to simplify the calculations (I did not do things as efficiently as a real Excel expert would have done it).

author
wolferrin made it!(author)2016-11-06

I don't really understand why you try to force a similar probability instead of creating an event with exactly the same probability. A roll of two dices is a sum of two numbers 1-6. Using 3 coins with values 1/2/4 you obtain numbers from 0 to 7. Ignoring the 0 and 7 (just repeat in those cases), you have exactly the same probability of a 1d6. Now do the same a second time for simulating the second dice and sum up the results.
Said that, instead of using coins I think it makes more sense to have a dice roll app at your phone or, in the worst case, use a timer and the value of the last decimal as result for each dice (ignoring 0,7-9)

author
ATTILAtheHUNgry made it!(author)2011-06-30

oh, and here's the .xls file.

Catan Probabilities.xls
author
kelseymh made it!(author)2011-06-30

:-) Thank you for this! I'm still using Office X on my Mac. The only way I can read these new-fangled ".xlsx" and ".pptx" and ".docx" files is by letting Google have its way with them :-/

author
yorkrambler made it!(author)2012-10-28

This is a great idea thank you :o)

I have made up a write on/wipe off copy for printing/laminating to save me remembering exactly how to write it up lol if anyone would like to use it
https://www.instructables.com/id/How-to-play-Catan-with-pen-and-paper-and-loose-cha/

Many thanks x

author
ATTILAtheHUNgry made it!(author)2012-11-23

thanks!

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artworker made it!(author)2012-03-01

Very creative. This technique can be used to design a new board game! 5*

author
Kaptain+Kool made it!(author)2011-06-30

Awesome! Wonderful idea and very practical!

author
orvis made it!(author)2011-07-03

Seconded. Great implementation!

author
ATTILAtheHUNgry made it!(author)2011-07-03

Thanks you guys.

author
Geli12 made it!(author)2011-07-02

király ötlet én is szwretem a tarsasokat meg az instructablest is :-)
tan te vagy az első magyar akut itt látok

author
kelseymh made it!(author)2011-06-30

This is an excellent Instructable, and a great concept! On an interesting side note, in the U.S. edition of the game, the "Knights" are called "Soldiers". That probably also helps to avoid confusion with the Cities and Knights expansion set.

If you're really doing this for a road trip (or road trips), one would probably want to make one of the nice looking boards, with resources left out, and photocopy it a bunch of times. Similarly with each player's accounting page.

I am especially impressed with how well you were able to approximate 2d6 rolls using weighted 5d2 coin flips. I think the discrepancy between 6/8 vs. 7 could be the most problematic. I might spend a little time futzing around to see whether I can get you a better algorithm, but I suspect you've done the right thing.

author
ATTILAtheHUNgry made it!(author)2011-06-30

Thanks for the compliment. And you are right, the 6/8s are slightly more likely to appear and the 7s are a bit less likely to appear, which tends to lead to a bit of a richer game (not richer as in better, richer as in "everybody has a few more resources than usual").

author
kelseymh made it!(author)2011-06-30

Ah! Actually, that's a very interesting point. It's not something you can do with real dice (except maybe by doing a rules change where the robber is tagged on "6" or on "8", instead of on 7). But the ability to tune the probabilities with weighted coin flips introduces a very nice generalization.

author
wilgubeast made it!(author)2011-06-30

This is awesome. Thanks for sharing!

author
AndyGadget made it!(author)2011-06-30

 
Settlers of Catan is a great game.  We won a set in a raffle several years ago and it's been a regular choice at our weekly family game nights ever since. (We take turns to choose the game we play that week.)  We've also introduced several friends to it.  The basic game is entertaining but we also have the 'Seafarers' expansion pack which makes it even more varied and enjoyable.

A playable travel version is a great idea.

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