Carcassonne Central

Carc Central Community => Quizzes, Puzzles and Challenges => Topic started by: Paul on January 07, 2016, 03:35:11 AM

Title: Facts and Feats with Carcassonne
Post by: Paul on January 07, 2016, 03:35:11 AM
Another thread launched early this year that will build over time!

This thread is for your own self finding facts and accomplished feats.

If you find any facts or feats made by others, feel free to post here as well with source links and a little description.

Let me go first see if anyone can top this!

Fact: I have enough tiles that if I were to lay them in one single line of row it would measure more than 500 meters (547 Yards)!
Title: Re: Facts and Feats with Carcassonne
Post by: Decar on January 07, 2016, 05:54:32 AM

Fact: I have enough tiles that if I were to lay them in one single line of row it would measure more than 500 meters (547 Yards)!

Id like to see a photo of that!
Title: Re: Facts and Feats with Carcassonne
Post by: Decar on January 07, 2016, 07:41:06 AM
The latest Carcassonne boxes state that 10 million copies of Carcassonne (& expansions) have been sold.

If all the tiles from, 10 million copies of the base game (72 tiles) were placed, they would cover a surface area of 1.458km^2.  Enough to cover Vatican City 3 times, and still have 2.1 million boxes left over.  :(y)
Title: Re: Facts and Feats with Carcassonne
Post by: Paul on January 07, 2016, 08:37:47 AM
The latest Carcassonne boxes state that 10 million copies of Carcassonne (& expansions) have been sold.

If all the tiles from, 10 million copies of the base game (72 tiles) were placed, they would cover a surface area of 1.458km^2.  Enough to cover Vatican City 3 times, and still have 2.1 million boxes left over.  :(y)

10 million of base game content of tiles in one row lines up to almost 1/10th of the distance between the earth and the moon!
Title: Re: Facts and Feats with Carcassonne
Post by: Decar on January 07, 2016, 08:41:21 AM
and HiG needs to sell another 2.3 million before the tiles could run the Earth's circumference.
Title: Re: Facts and Feats with Carcassonne
Post by: Paul on January 07, 2016, 09:08:22 AM
and HiG needs to sell another 2.3 million before the tiles could run the Earth's circumference.

 :(y) I was just about to post this. Lol!
Title: Re: Facts and Feats with Carcassonne
Post by: jungleboy on January 08, 2016, 11:37:52 AM
I'm not sure if this is kind of thing that should be posted in this thread, but as I noted here (http://www.carcassonnecentral.com/community/index.php?topic=2326.msg32734#new), I played a game of Carcassonne: the Castle today where the winning score was 57, which is much lower than usual in our games (around 80-90). Can anyone remember having a lower winning score? 
Title: Re: Facts and Feats with Carcassonne
Post by: Paul on January 08, 2016, 11:44:38 AM
I'm not sure if this is kind of thing that should be posted in this thread, but as I noted here (http://www.carcassonnecentral.com/community/index.php?topic=2326.msg32734#new), I played a game of Carcassonne: the Castle today where the winning score was 57, which is much lower than usual in our games (around 80-90). Can anyone remember having a lower winning score?

I suppose that's a feat in it's own. Winning with a very low score. One would say that this is a whole new low and a sweet victory all wrapped up in one.  ;D
Title: Re: Facts and Feats with Carcassonne
Post by: whaleyland on January 08, 2016, 11:58:44 AM
Just played 2-player Carc last night with my partner. 80 tiles (we included Decar's new Astronomy expansion) and I ran away with 194 points! Partner had 128. That may honestly be the highest score I've ever achieved with mostly just the base game. 70-point scoreboard indeed.
Title: Re: Facts and Feats with Carcassonne
Post by: Decar on January 08, 2016, 12:22:13 PM
Those extra 8 tiles make all the difference!
Title: Re: Facts and Feats with Carcassonne
Post by: Carcking on January 08, 2016, 12:27:24 PM
...(we included Decar's new Astronomy expansion)...
What is that? Something new?
Title: Re: Facts and Feats with Carcassonne
Post by: whaleyland on January 08, 2016, 12:41:18 PM
...(we included Decar's new Astronomy expansion)...
What is that? Something new?
Good question. Decar, do you have a thread for that expansion yet? We did actually have a few questions about it.
Title: Re: Facts and Feats with Carcassonne
Post by: Decar on January 08, 2016, 12:58:39 PM
The version we prototyped at the UK Meetup is in the download section.  The latest version isnt up there yet, but Ive created a new topic in the Workshop:

http://www.carcassonnecentral.com/community/index.php?topic=2330.new#new

Feel free to fire questions there.  :)
Title: Re: Facts and Feats with Carcassonne
Post by: Decar on February 08, 2016, 05:48:32 AM
So I've been wondering recently, How many unique games of Carcassonne are there?  Turns out quite a lot, here's my quick calculations:

Basic Deck has 72 tiles, but the start tile is always the same.  This leaves 71 tiles to be ordered in quite a few different ways.

First you have to choose one of the 71 tiles, then 70, then 69.....

So to start of with there's 71x70x69 different orderings of tiles.  Which is 71! which is huge.

But we should remove the instances of tiles which are duplicates, like the 9 and 8 roads.

Let's just remind ourselves of all the tiles:
(http://tehill.net/carcassonne/general/BA_Tile_Dist_2.png)

I'm going to assume the tiles with Pennants are different.

I won't bore you with all the detail but take a look at "Theorem 3 - Permutations of Different Kinds of Objects" from this page:
 http://www.intmath.com/counting-probability/3-permutations.php

If you're interested, it's pretty obvious.

So the total number of games is:

....

Drum Roll

....

Total Number of Tile Sequences for Carcassonne = 71! / (8! * 9! * 4! * 1! * 2! * 4! * 3! * 3! * 3! * 3! * 5! * 3! * 2! * (1! * 2!) *(2! * 3!) *(2! * 3!) * (2! * 1!) *(3! * 1!) * 1!)

Let's simply this. 1! = 1 and 2! = 2 and 3! = 6

Total Number of Tile Sequences for Carcassonne = 71! / (8! * 9! * 24 * 2 * 24 * 6 * 6 * 6 *6 *5! *6 *2 *2 *12 * 12 *2 *6)
...
Total Number of Tile Sequences for Carcassonne = 71! / (8! * 9! * 5! * 24^2 * 2^4 * 6^6 *12^2)
... Google Tells me:
Total Number of Tile Sequences for Carcassonne = 7.8232304x10^78

Let's give this some context - It's approximately this big:

7800000000000000000000000000000000000000000000000000000000000000000000000000000

I'll try and give this some order of magnitude:

Population of Earth: 7x10^9
Age of the Universe in seconds:  4.32 × 10^17
Number of observable Stars in the Universe~: 7X10^22
Number of Atoms in a Human Body: 7x10^27

(http://www.physicsoftheuniverse.com/numbers.html)


So, if you multiple those numbers together, it's a bit like counting all the games of Carcassonne there could be.  If for every second the Universe has existed, you could count every atom, of every person on a planet the same size as Earth, around every Star you'd have counted:

1.47X10^78

So you'd need to do it ~five times.

And that's just the number of different ways the tiles come out of the bag!

I've not considered tile or meeple placement.
Title: Re: Facts and Feats with Carcassonne
Post by: Paul on February 08, 2016, 06:16:07 AM
I bet with Decar's last post about combinations in the game had Dan go: "No doubt Paul's first thought was processing this if it's possible to do."

And he would be right!  :D

This also reminds me of a challenge I was doing in the game Diablo II (with expansion). It was collecting as many El Runes as possible (an item in the game) and upgrade these to a Zod rune.

El Rune was the lowest form of runes and Zod was the highest form.

Upgrading the first 10 runes would require three of the same. 3x El became an Eld Rune. 3x Eld run became a Tir rune and so forth.
 This would quickly escalate in crazy numbers and I know that it's not possible to physically do this due to the time it would take. (200-2000 years probably, never bothered calculating).

But I did manage to collect a little over 8000 or 12000, can't remember any longer which. :)
Title: Re: Facts and Feats with Carcassonne
Post by: danisthirty on February 08, 2016, 10:26:04 AM
Those are some huge numbers! Amazing to think that there could be that many tile orders simply from the base game alone. Then there's tile placement options and meeple placement options which will undoubtedly make the numbers even more difficult to comprehend!