Author Topic: Opening tile strategy?  (Read 987 times)

Offline Bugo Hoss

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Opening tile strategy?
« on: January 30, 2024, 04:51:45 AM »
Hello,

As the opening tile possiblities are limited, is there commonly agreed Game Theory for tile #1?

How about #2? I understand that the game branches exponentially as the tiles are drawn, but how far is it possible to "know" the best move? Is there exist opening theory in general, like in chess?

Additionally has anybody done any AI simulations on the game (AlphaZero/Chess style) to figure out best game styles for repeating situations?

Linkback: https://www.carcassonnecentral.com/community/index.php?topic=6581.0

Online kothmann

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Re: Opening tile strategy?
« Reply #1 on: January 30, 2024, 06:21:32 AM »
Welcome to the forum, @Bugo Hoss!

I love this question!  There must be something more recent, but the only CarcBot I know of is from Maastricht in 2009, discussed in this thread:
https://www.carcassonnecentral.com/community/index.php?topic=542.msg5804#msg5804

I also mention this work in the context of wondering what the value of an extra meeple might be--see here:
https://www.carcassonnecentral.com/community/index.php?topic=5228.msg77118#msg77118

Here's what I think I do with my first tile:
Any city tile: connect to the city on the start tile and place a knight.
Cloister: connect to field on start tile and place a monk.  On FFFR cloister, point the road downward to encourage surrounding the cloister?  Hmm...
FRFR: connect to the road and place a thief
FFRR: connect to the road and point the road up to make it less likely that the opponent tries to join the road?
FRRR: connect to the road with the field segment down and place a thief on the 2-tile road
RRRR: only one play allowed, and place a thief on the 2-tile road.

There are 24 tile edge topologies (only 17 in the base game), so even by the time you reach tile 2, it is a pretty big matrix of options.  It also seems like the outcome is not very strongly affected by the early play.  Having said that, if the city is still open I try to claim it.

I'm super interested in Alpha-Zero type AI applications to Carcassonne.  Hopefully someone else might know more...

Thanks for an interesting post.

Offline Decar

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Re: Opening tile strategy?
« Reply #2 on: January 31, 2024, 01:48:44 AM »
Open strategies are often a bit tricky to determine if they make a significant difference to the final result.  Unlike Chess where the opening move sets players in particular decision spaces, I think Carcassonne has a lot more variability.  Like at the star of the game investing a meeple on a cloister might seem like a good idea because you have more opportunity to complete it; however there's more opportunity for your opponent to block it.  So would it be better to keep a meeple in hand.  I think it's usually too early to say at the very start of the game; and I'm not sure that the positions of tiles at the very start of the game greatly impact the end-resulting map.  There's obviously some significant tiles like the cloisters, or CCCC or RRRR which if they come out early mean that they won't appear later.  I think @wallaceprime did some research into Carc-AI. So probably has a much better grasp of what you're considering.

Offline Bugo Hoss

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Re: Opening tile strategy?
« Reply #3 on: January 31, 2024, 05:02:26 AM »
Seems like this is a bit un-documented area then. What could be a better place to start :). So lets go! I will do these as separate edits, and update occasionally when I have time. Hopefully this will be completed soon enough.. I will also write my initial thoughts, but will update based on feedback.

Move #1 in Base game 1v1:

Option 1: Any tile with city only on one side, that can close the city - Probability: 18/71=25,35%

x5x4x3x3x3

  • These are easy, complete the city and get 4 points.

Option 2: Any tile that can close the city, but opens another city as well - Probability: 5/71=7,04%

x3x2

Tile rotation is trivial here, so options should only focus on meeple placement. There are five choices, in order of (my) preference:

1. Claim the city and get 4 points.
  • Most obvious choice. Instant points in the bank.
2. Close the city and claim the new city.
  • CFCF: Prevent opponent from claiming that city instantly (probability is 18/70=25,71%) by placing meeple on the new city that is secured, i.e. cannot be directly attacked from any direction.
  • CCFF: Prevent opponent from claiming that city instantly (probability is 18/70=25,71%) by placing the meeple in the new city is more risky as opponent can directly influence it on the next turn. 

3. Close the city and place meeple on the field:
  • Start claiming a lucrative field. However, opponent gets a free pass in a new city.

4. Close the city and don't place a meeple: no benefits
5. Place the tile above the opening tile (not closing a city), place a meeple on the field or on the city: does not make sense in my view, but would make an interesting start. Not placing a meeple does not make sense either.

Option 3: CFCF tiles - Probability: 3/71=4,22%

x2x1

Rotation is trivial, two placement options:

1. Continue city and:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Don't place a meeple: not recommended
2. Place the tile above the opening tile and:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Don't place a meeple: not recommended

Option 4: CCFF tiles that are not in category 2 - Probability: 5/71=7,04%

x2x3

Rotation is trivial, two tile placement options:

1. Continue city and:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Don't place a meeple: not recommended
2. Place the tile above the opening tile and:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Don't place a meeple: not recommended

Option 5: CCRR tiles - Probability: 5/71=7,04%

x2x3

Two tile placement options:

1. Continue city (rotation is trivial) and:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Place the meeple on the road: not recommended
  • Don't place a meeple: not recommended
2. Place the tile connecting the road, city on the same field:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Place the meeple on the road: not recommended
  • Don't place a meeple: not recommended
3. Place the tile connecting the road, city on the other field:
  • Place the meeple on the city: Optimal
  • Place the meeple on the field: not recommended
  • Place the meeple on the road: not recommended
  • Don't place a meeple: not recommended


Option 5: CCRR tiles - Probability: 1/71=1,41%

x1

One tile placement option, two meeple placement options:

1. Continue city (rotation is trivial) and:
  • Place the meeple on the city: Optimal
  • Don't place a meeple: not recommended
« Last Edit: February 08, 2024, 05:49:06 AM by Bugo Hoss, Reason: update on the post »

Offline Bumsakalaka

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Re: Opening tile strategy?
« Reply #4 on: January 31, 2024, 07:47:00 AM »
Best opening strategy is to be prepared and you have to say to yourself - I will win. Then you will win (probably) :)
Check JCloisterZone Add-ons with fan expansions and also some Slovak sci/fi projects in English https://www.scifi.sk/en/

Online kothmann

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Re: Opening tile strategy?
« Reply #5 on: January 31, 2024, 11:32:50 AM »
@Bugo Hoss you might be interested in my brief “tactical tuesday” series:
https://www.carcassonnecentral.com/community/index.php?topic=5461.msg79378#msg79378

Sadly the embedded image links to google drive seem to be broken.  Here’s a link to the top level folder in which you can find each week’s files:
https://drive.google.com/drive/folders/1cAJGnCsf0ubrGSJ4lmXBSIbT0UjM3nnj

+1 merit from me for posting in the usually quiet “Strategy Guide” forum!  Keep it coming!


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