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**General / Some Carcassonne Dice Game Observations**

« **on:**December 19, 2022, 02:56:36 PM »

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

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

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?

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...

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 thatthe 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...