Some Carcassonne Dice Game Observations

[kothmann]

I recently bought the Carcassonne Dice Game on eBay.  As I said in the Postman thread:

My wife and I ... simulated playing a 4-player game, and we discovered the profound value of the "keep a meeple" option!  After two players do this, only 7 dice go to the 3rd player, who will typically throw at least one catapult, making their maximum possible score only 10 points, but it is trickier to build a 6-dice city, so then they end up keeping a meeple too.... My preliminary conclusion is that the game gets interesting and exciting with 4 or 5 players!

A few days later, I started experimenting with the dice, just to see the best way to get a high score.  My process was to roll all 9 dice, then set aside the catapults, as required by the rules, but always re-roll the meeples: I was just trying to get high-value completed cities.  I did this 30 times, and here is a histogram of the resulting number of dice in the largest city (graph from https://www.socscistatistics.com/descriptive/histograms/):



As you can see, one-third of the time, I did not complete any city!  The average score for my 30 turns was 7.35 points, but the standard deviation was 8.33 points!  (Scoring is 1 point for 3 dice, 3 points for 4 dice, 6 for 5, 10 for 6, 15 for 7, 21 for 8, and 28 for 9.)  Scoring is extremely volatile!  And it would only be more volatile if those scores are doubled because of a reserved meeple!

Since I wasn't trying to keep any meeples around, the only interesting decision I had to make was almost always of the form shown in this photo, with one roll remaining (though it could also be the first roll):

Here there is a 6-dice city that could be completed with the CFCF die, scoring 15 points for a 7-dice city.  Or, I could re-roll the CFCF die and the meeple in an attempt to get an 8-dice city worth 21 points.  I spent an hour or so doing my best to sort-out the math, and I concluded that you should essentially always accept the smaller city.  In other words, even if could have a 5-dice city worth only 6 points, don't roll 2 dice try to get a 6-dice city worth 10: the odds are not in your favor.

I suppose a game-theoretical optimum strategy is to be much more conservative than I was thinking would be best.  You probably need to try to get 3 meeples on most turns, and only go for a big city when you roll a lot of good city segments on the first roll?  But it isn't too hard to get an 8-dice city, so I don't think most people will play that way, and you will run out of turns before someone wins?  The game feels like it is too likely to be won by "shooting the moon" as opposed to at least a somewhat methodical build-up of points with calculated risks and benefits.

Now, I have not yet played a real 4-player game, so I can't say for sure.  But I'm less optimistic that the official rules will turn out to be fun than I was on that first night when I opened the box.

Fortunately, I have developed a variant that we have been playing, and it seems to be quite fun.   

Details forthcoming...

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