Author Topic: An Introduction to Tile-Counting  (Read 3358 times)

Offline danisthirty

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An Introduction to Tile-Counting
« on: January 16, 2015, 06:31:30 AM »
Hi guys.

This is very much a work in progress at the moment but I wanted to share what I've already written to see if it's the sort of thing that will be of benefit.

I haven't really brought it to any kind of conclusion which I still intend to do, and I will add headings and various examples with pictures too, but haven't got round to this yet. I'm just starting to lose momentum with it a bit so thought I'd post it in it's incomplete form to get some guidance/ feedback from everyone here...



In the middle-ages, those who could accurately predict what tiles were left to be placed towards the end of a game of Carcassonne were cruelly drowned or burnt at the stake. Sadly, attitudes haven’t changed a lot since then and many Carcassonne players I’ve encountered in real life remain dubious over such witchcraft. Some will mix multiple copies of the base game and then draw a set number of tiles at random, thus ensuring that nobody can know for sure what tiles will be available before the game has begun. Then there’s Sheep & Hills which includes an anti-tile-counting mechanic at its core by way of the hills which allow players to “hide” a tile under another tile without showing it to any of the other players.

My view of tile-counting is that it’s an important skill that’s required if you want to be able to hold your own against top Carcassonne players. It’s not easy and comes with experience, but you don’t need to have played a lot of Carcassonne to have realised that there is only one 4-sided city tile and similarly just one 4-sided road tile. If you’re aware of this and happen to notice when either of these tiles goes down during a game then you immediately know that there aren’t any tiles like this left and can use this to your advantage. By doing so you are tile-counting... whether you like it or not!

Fear not though, as tile-counting is not about employing some evil power to psychically tell you what the next tile to be drawn is going to be. It’s simply about recognising what tiles exist and adjusting your game depending on whether they’re still available, and if so how many. I’ve played against people who have told me that they don’t like tile-counting and refuse to do it, but I would contend that if you’re familiar with the game and are trying to win it’s almost impossible to avoid it (albeit at a basic level).

By extension of the above, it’s easy to tell when all the cloisters with roads leading up to them have gone as there are only two of these to start with. Assuming you notice when the second of these is placed (or can spot them on the table in front of you as they’re pretty obvious), you know you’re no longer going to be able to sneak a farmer around a road and onto an adjacent farm unless you create a loop in the road. This may have a significant effect on your game plan and you may also become aware of opportunities to steer your opponent’s roads towards fields and block them such that a fffr tile (which no longer exists) is required to complete the road. Of course, blocking your opponent in this way isn’t necessarily a bad idea even when both fffr tiles are yet to be placed, but it’s certainly risky as there’s every chance your opponent will draw one of them and use it to complete their road as well as scoring good points from the cloister at the same time.

Similarly, there are also just two ccff tiles where the two city segments are not part of the same city (these are the ones you rely on for preventing someone else from getting into your city). So if you’re trying to get in to your opponent’s city and you know that both of these tiles have already been placed elsewhere then it becomes a matter of drawing the tile you need before the end of the game rather than before your opponent draws one of these tiles. It’s always nice to know something like this that your opponent doesn’t, even if it doesn’t feel like this knowledge is winning you much of an advantage.

Other easy tiles to spot/ count are the normal cloisters (i.e. the ones without roads leading up to them) but once you go beyond these, things start to get a little bit more complicated as the tiles themselves can be difficult to recognise, let alone count. Two things that are worth remembering though are that there are 10 two-sided city tiles (excluding the two “city splitter” tiles: 5 x ccrr and 5 x ccff) and 7 three-sided city tiles (3 x cccr and 4 x cccf). Because these stand out from the rest of the landscape if you’re looking for them, it isn’t difficult to calculate how many are left in the bag/ tower and as such you can use this knowledge, combined with a little bit of probability, to help swing things in your favour:

(Example 1: A quick scan of the landscape reveals to Blue that 4 x ccrr and 2 x ccff tiles have already been placed. This means there are 4 two-sided city tiles left and only one of them has road on the remaining sides. If Blue wants to reduce Red’s chances of joining his city it is in his interest to point the road towards the joining tile rather than the field)

EDIT: Also, please bear in mind that this is very much an introduction and shouldn't be considered an authoritive guide to tile-counting. These are literally just thoughts on where I am with tile-counting at the moment and how I'm starting to discover how it can help to change your game plan

Linkback: http://www.carcassonnecentral.com/community/index.php?topic=1458.0
« Last Edit: January 16, 2015, 06:35:42 AM by danisthirty »
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Offline jungleboy

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Re: An Introduction to Tile-Counting
« Reply #1 on: January 16, 2015, 06:58:14 AM »
An integral aspect of tile-counting is knowing what tiles aren't available in the first place (i.e. the ones for which the tile count is 0 from the beginning of the game). Off the top of my head, the tile combinations that do not exist in the base game are:

CFRF
CFFR
CRFF
CRCR
CRCF
CCRF
CCFR

All of these tiles are available in various expansions.

Offline danisthirty

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Re: An Introduction to Tile-Counting
« Reply #2 on: January 16, 2015, 07:07:39 AM »
That's interesting. I've always viewed tile-counting as the ability to know what's left in the bag and play accordingly, so hadn't really seen the relevance of the "missing tiles" unless for creating holes in the landscape and trapping opposing meeples in the process. But if you're counting tiles down until all tiles of a certain type have been played then you're basically adding them to the list of missing tiles as you play, a list which contains the tiles you describe from the start of the game.

Offline CarcinFool

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Re: An Introduction to Tile-Counting
« Reply #3 on: January 16, 2015, 11:30:31 AM »
Another good topic and article!

I like how you kept it simple and focused on the tile configurations that are limited and how you can use that to your advantage. Anyone can easily incorporate these tips into their play. Remembering or figuring out something like "how many FCxx tiles are left" is much more difficult. Jungleboy's addition is relevant as well.

Offline t2k

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Re: An Introduction to Tile-Counting
« Reply #4 on: January 08, 2020, 03:21:07 PM »
Tile-Counting is really not easy.  I started playing Carcassonne with the Windows software version, for which I paid one dollar and got the River II expansion free.  This software includes the option to display left over tiles and displays places where it is impossible to place a tile.  You can never tell when a tile will play or be used and if counting is really possible.  With the I&C expansion, you have 99 tiles to consider as left over in the beginning.  Being a Pinochle player, you learn to count trump cards as part of strategy, but that is limited to less than 14 excluding what you hold in your hand.  With 99 tiles to consider, counting them is a bit daunting.

My strategy is to look at what was played and what openings there are, and then playing the odds of completing that City, Road or Cloister you have already claimed and where you can block an opponent.  Just remember that this varies greatly with the number of players.

Two is a nice player count for me, or maybe three.  When you get to four players or more, the odds change so much you may need to consider the quick score of small cities, and the tactic of just limiting other players scores becomes imperative.

Like it or not, that's my take on counting.  Good only to that person who has a real "photographic memory"?

Offline cicerunner

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Re: An Introduction to Tile-Counting
« Reply #5 on: January 25, 2020, 04:02:08 AM »
Good to see that others think along similar lines to me ...

I came here because I just started creating a spreadsheet to enable checking of what tile join patterns are available within any given game. But I just wanted to check I wasn't re-inventing the wheel first ... Has anyone else already done this I wonder?

As a relatively new player (less than 12 games) I've already done some basic, intuitive tile counting as described by danisthirty eg, in the base game, 1 x CCCC, 4 x FFFF monastery, 2 x FFFR monastery etc. Inevitably as I become more experienced I'm going to learn other numbers - I just learned 1 x RRRR (base game) just from reading this thread for example!

I envisage using the sheet, not to slavishly learn the numbers myself, but as an aid when teaching/playing with new players (to reduce the advantage of knowing certain tiles just don't exist or that all the monasteries are gone for example).

Plus it'll be fun, obviously!

So, am I reinventing the wheel?
If not, would it be useful if I shared the Google sheet publicly for others to see?
« Last Edit: January 25, 2020, 04:05:33 AM by cicerunner »

Offline Meepledrone

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Re: An Introduction to Tile-Counting
« Reply #6 on: January 25, 2020, 04:46:01 AM »
This week I started to teach how to play Carcassonne to some colleagues of mine. I used the following Wikipedia image to illustrate some concepts:
* Know your tiles: no all the tile types are available in the base game so you may use this into your advantage to block features from other players.
* Tile counting: if you keep track of tiles already in the game, you can compute the odds you may have to get a tile you may need to close a gap.

So I kept this image projected during a training game as a visual aid to discuss tile options for the different open gaps coming up. It exactly covered what we were using: the base game and River I.



It is more visual a tool than a plain spreadsheet. Do you find it useful for your training purposes or do you still prefer a spreadsheet?
« Last Edit: January 25, 2020, 04:51:35 AM by Meepledrone »

Offline cicerunner

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Re: An Introduction to Tile-Counting
« Reply #7 on: January 25, 2020, 06:00:32 AM »
It is more visual a tool than a plain spreadsheet. Do you find it useful for your training purposes or do you still prefer a spreadsheet?
I feel like spreadsheets is my native language - my friends often tease me on this - I have created spreadsheets for everything from my running to cooking and serving a roast dinner.

The visual element really adds clarity, particularly for beginners although (and this is intended as an observation, not a negative criticism) it does emphasise city and road connects over field connections which I find really new players often overlook when considering where their tile might fit.

I'm intending to add a column for each expansion so that - a little like wikicarpedia does with the rules - you can select all the expansions you are using and get an overall summary of all the tile connections available.

So yes, true to my inner nerd, I'm going to stick with a spreadsheet :)

Offline Meepledrone

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Re: An Introduction to Tile-Counting
« Reply #8 on: January 25, 2020, 09:30:07 AM »
This is a preliminary test by wolnic of what is to come regarding the Tile Reference:

http://wikicarpedia.com/index.php/User_talk:Wolnic#Tile_Reference_Display_with_Expansion_Selector

Just in case you want to play with it.  ;)

We were discussing the approach here a few days ago:

http://www.carcassonnecentral.com/community/index.php?topic=4115.msg65830#msg65830


Offline wolnic

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Re: An Introduction to Tile-Counting
« Reply #9 on: January 25, 2020, 01:05:45 PM »
I updated it earlier today with the Tollkeepers and Spiel19 tile.
Complete: AutumnForest (C2), Catch Of The Day (C1/2/WD), Cliffs&W'falls (C1/2), Coast (C1/2), FishHuts (C2), Fluvium (C2), NewForest (C2), Harvest (C1/2), Stone Circles (C1/2), Wells (C2), Jordan River 2 (AotC)
Development: Sakura (C2), WinterEdge (C1), WinterCoast (WD/WE) and others

Offline Meepledrone

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Re: An Introduction to Tile-Counting
« Reply #10 on: January 25, 2020, 02:11:30 PM »
Thank you, wolnic!!!  ;D


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