Inns and Cathedrals from Carcassonne
In my day job as a casino slot game designer, I think a lot about volatility. Volatility is the double-edged sword that provides the thrill of a jackpot but may also slice away a bankroll quickly. That got me thinking about volatility in board games.

Is volatility a good thing in board game design? Is it something players even want?

Maybe one of the most well-known examples of volatility in a popular game is the Inns & Cathedrals expansion for Carcassonne. In this expansion, a completed road with the Inn by the Lake tile doubles the score of that road while not completing that same road will make that road worth nothing. Also, a completed castle with the Cathedral tile is worth 1 ½ times a normal castle while the uncompleted version is worth nothing. Is that a good or bad example of volatility?

What is Volatility?

Before I answer that, I should define volatility.

Volatility is derived from standard deviation and standard deviation is the average distance from the mean (average value). So, volatility measures how spread out the numbers are in a set of data.

For you math nerds, the formula is

For those of you not mathematically savy, you can use stdev function in Microsoft Excel on a list of numbers.


For example, one could play two different games that have the same expected values . In game 1, I could pay you $1 every time you roll a 1, 2, 3, 4, 5, or 6 on a six-sided die. In game 2, I could pay you $6 every time you roll a 6. Obviously, both games will pay you the same amount overtime, but the experiences will be very different. In game 1, you would get a steady payout with every roll. In game 2, you would get paid rarely, but when the payout comes it’s big.

Place your bets: volatility example

Consider this, after six games of game 1, the best and worst you can do is winning $6. After six games of game 2, the worst you can win is $0 and the best you can win is $36! In my experience designing slot games, players greatly prefer games similar to game 2 than to game 1.

Volatility of Scoring

Ok, so with board game design, the obvious question is “the volatility of what?” Given that most games are about amassing the most points, I think the most interesting volatility to study is the volatility of scoring, specifically the scoring per turn. The average in question would be the average score per turn and volatility would tell us how much deviation a player can get from turn to turn.

What is the right amount of deviation? If the game is low volatility, a player might only be able to gain twice the normal amount of points on a turn. In that kind of game, players might feel hopeless if they fall behind more than one turn’s worth of points. If a game is high volatility, a play might be able to score most of their total game points in one turn. In that kind of game, players might feel the game is too chaotic since they can literally lose the entire game on a single turn. For my money, a balance between the two extremes seems best. I would like to think I could recover after a couple of bad turns, else the game feels too unforgiving, but I should be able to maintain a lead if I get far enough ahead.

Inns & Cathedrals

So, let’s look again at the Inns and Cathedrals example for Carcassonne. From my experience designing volatile slot games, there are certain elements that maximize the games’ appeal.

First, the player should not be forced into a more volatile experience than they want. Ideally, the player could choose their volatility. On this part, the Inns and Cathedrals tiles are very good. Players can’t choose the tiles they draw, but they are not forced to put any meeples on those tiles, or to even place those tiles on any unfinished roads or castles they already own.

A second learning about volatility, the player should clearly understand the upside of their choice. By upside, it should be clear their choice has big win potential. If the big win potential is not obvious then the choice will not be attractive. For Inns and Cathedrals, the upside seems pretty clear: get double or 1.5 times more than normal and the bigger your finished road or castle the more extra points you can score.

A third learning of volatility is that players should understand their relative odds of winning and it should feel achievable. They may not know the exact odds, but they should understand the relative likelihood, else the player may also lose interest in an unwinnable outcome. For Carcassonne, this is a bit tricky. There is no reference on how many castle tiles or road tiles there are and actually what players really care about is how many tiles will actually help finish their road or castle. I did some research looking at the composition of tiles from the base set plus the Inns and Cathedrals expansion (excluding the start tiles):

Does not end a road or castle (46)
Ends a castle (24)
Ends a road (13)
Ends both road and castle (5)

Carcassonne: number of end tiles

The Achievable Goal?

It takes three tiles to complete a castle once it’s started, while it takes two tiles to complete a road once started. Still, I think the Inn tiles and Cathedral tiles feel achievable for two reasons:

  • 1) players who have played Carcassonne have an intrinsic sense already of how hard it is to complete a road or castle and
  • 2) even if a player has never played Carcassonne before chances are they will see at least one person complete an Inn or Cathedral during the game so those outcomes will seem achievable.

Relative Odds During the Game

Which brings me to the final lesson on volatility I’ve learned, based on the potential jackpot and the relative odds, does the payout seem like a good deal? No player wants to make a bad bet on an opportunity that is hard to complete but pays out little, or on an opportunity that pays out awesomely but never happens. So, how does Inns and Cathedrals fare?

If one assumes that pieces will retain their relative odds throughout the game, then one can get a pretty interesting picture at the chances of completing an Inn or Cathedral assuming one needs two road endpoints for the Inn and three castle sides to close the Cathedral. As you can see the odds change greatly based on the number of players playing and how much of the game remains.

Odds at start of game

Carcassonne Tile Odds

Odds at halfway point

Carcassonne Tile Odds

Odds at three-quarters way point

Carcassonne Tile Odds

Carcassonne and Volatility

Of course, Carcassonne is not a solitaire game. Opposing players can build the board in such a way as to greatly restrict the types of tiles that can be used to finish a road or castle. If you are playing with one of those people, the odds may look very different from the tables above and you may want to forgo trying to build any Inns or Cathedrals.

So, how does the Inns and Cathedrals expansion fare for volatility? I think very well. It gives players choices on how much volatility they want, completing the new tiles feels achievable and they offer meaningful payoffs. One more thing I learned from slot design is that the more players play slot games, the more volatility they desire. In this way, I think it’s smart design to offer greater volatility in expansions so that expert players can enjoy chasing bigger thrills.

For further reading:

Volatility in Game Design by James Ernest
Also, James’s article Probability for Game Designers on The League of Gamemakers.
and now… Making Volatility Work for Your Game – Part 2!

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Scott Caputo

Scott Caputo loves to get creative: doubling up on board games and poems. His publishing credits include Völuspá, Kachina, and the forthcoming, Whistle Stop. By day, he manages a team of casino game designers and by night, he gets soundly beaten at board games by his wife. With her help, he’s busy raising two young boys to be total board game nerds.

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  1. neil googe on January 21, 2016

    Really nice little piece, while I don’t have much to add, it is something I have been struggling with in my design, and this does add some clarification to the problem. Especially in your D6 dice game example.

    The thrill of winning $6 on every 6 vs the $1 on every 1, even vs $0 on 1-2, $3 on 3-4 and $6 on a 5-6 which is basically what I am fighting with at the moment. Certainly food for thought.

    Good stuff.

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