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Messages - ny1050220

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16
General / Re: Do you use house rules?
« on: October 06, 2022, 07:08:17 PM »
I guess this is now a reply to kothmann's review. (Just when can I really leave academia? ;D)

Quote
It's easy to see that it's more difficult to achieve this 22-pennant feat as the number of players increases.
In a multi-player game, “conspiracy” is how you win!  This is the magic of multi-player Carcassonne!  In particular, in a 7-player game, two players would likely be happy to join two giant pennant-filled cities in order to make the game effectively a 2-player game from then on.

Completely agree. In the meanwhile, when the game effectively becomes a 2-player game in a 7-player game, you'll need those 21 tiles in your and your teammate's share of 40 tiles. Even more difficult than getting those 21 tiles in your share of 70 tiles in a real 2-player game. Therefore, my original statement still holds.

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your opponent does not help you build your monster city with a fragment containing pennants, ever. (Fair assumption, eh?)
No.  Even in a 2-player game, with I&C, you might gladly place a CCRR tile with a pennant in a way that adds to an opponent’s big city if: that city is not close to complete and contains a Cathedral; the road connects your single Inn to a long road on which you and your opponent both have one meeple (thus completing the road and scoring you all the points at 2/tile); and/or the tile connects farms in a way that is advantageous to you.  More simply, you might repeatedly add CCCF and CCCR tiles with pennants to a city with a Cathedral if the opponent gets close to completing it.
If your opponent helps you with up to 5 tiles out of the 21 you need, there are this many ways:
combination(119,50)*combination(21,20) + combination(119,51)*combination(21,19) + combination(119,52)*combination(21,18) + combination(119,53)*combination(21,17) + combination(119,54)*combination(21,16)
= 7.7e38
(I'm using WolframAlpha's terminology, as that's what I used for the calculation.)
Divided it by 9.4e40, and you get < 0.01. That's still a very small probability.

I recognize that there are more than 5 CCCX tiles with pennants that your opponent will gladly add to your monster city if they think that'll make it difficult for you to complete it, especially if there is already a cathedral in the city. Here are the catches:
1. All these tiles need to appear relatively late in your opponent's 70-tile sequence.
2. You need at least another specific tile (cathedral) to be in your 70-tile sequence.
So some of combination(119,55)*combination(21,15) = 1.9e39 need to be discounted. I'm not sure how many, and this is when wave my hands and say that needs some computer simulations.

Who cares if it is a minor deviation!?
We feel it is a minor deviation AND it makes the game more fun for us by lessening the work needed to count, so we happily adopted this one all the time. The other house rule we sometimes use, expanding the tower's range, is a large deviation, so I do like it that much. It was the "minor deviation" I wanted to defend when the nerd mode turned on.

17
General / Re: Do you use house rules?
« on: October 05, 2022, 05:24:59 PM »
I believe we always award +1 point for each city tile and PENNANT if the mage is present. It's just easier on the counting. We feel this is a very minor deviation from the official rules.
When you have a city with 20 Coat of Arms, this would no longer be a minor deviation :)

Caution!!! Nerd mode on! Scientist at work!  >:D ;)

There are somewhere around (just in case I missed anything) 28 pennants:
Base = 10
River = 1
Inns = 3
Princess = 3
Tower = 1
Abbey = 6
Catapult = 1
Halflings = 2
Plague = 1

If you pick just the base game and 3 large expansions with 3, 3, and 6 pennants, you'll have 22 pennants on 21 tiles in a game with 132 tiles. (Actually, if you pick Tower instead of Inns, you'll have exactly 20 pennants and 132 tiles in total. I claim that the numbers in the following argument won't change much to affect the conclusion without providing proof. The reader can check the math as an exercise  >:D. Oh how I love and hate math books at the same time.)

And you have to throw the extra 8 tiles from Witch. Now there are 140 tiles.
We assume a 2-player game. It's easy to see that it's more difficult to achieve this 22-pennant feat as the number of players increases. And it's worth noting that if the number of players is 7 or larger, it is impossible to have a city that has at least 21 tiles without conspiracy.
So, assume not conspiracy: your component does not help you build your monster city with a fragment containing pennants, ever. (Fair assumption, eh?)
That means you need all those 21 tiles in your share of 70 tiles in the game.
There is 1 way to select 21 tiles from 21 and 7.7e33 ways to select 49 tiles from 119. That means there are 1 * 7.7e33 = 7.7e33 ways you can have those 21 tiles with the pennants and 49 other random tiles.
There are 9.4e40 ways to select 70 tiles from 140. This is how many ways you can have 70 random tiles.
7.7e33 / 9.4e40 = 8e-8 < 1e-7. That is, the probability of your getting those 21 tiles in a random game is less than 1 in 10 million.

It's again worth noting that some sequences of tiles may lead to situations where a tile, particularly those with a pennant, has to be discarded due to lack of legal placement. If the discarded tile, with a pennant, is removed from the game, this sequence of tiles should be discounted from the 7.7e33 ways, making the actual probability smaller than 8e-8.

In conclusion, a 22-pennant city with a witch, hence an extra 22 points, per se, is indeed not a minor deviation. But its probability is so small. Overall, the expected extra score of a 22-pennant city is about 2 millionth of a point. And that is what I call a minor deviation.

It may be of interest to calculate the expected extra points of cities with 21-pennant or fewer. However, at a certain point, e.g., a 4-pennant city or an extra 4 points, should be considered a minor deviation per se, regardless of its probability. This division is surely purely arbitrary.

Further, I maintain that in a 140-tile game, unless the total expected extra score is large enough, again, an arbitrary number, e.g., 5 points, overall, the extra score is still a minor deviation. This obviously needs to be considered in conjunction with the total score of the game. The estimated expected total score in this 140-tile game may be achieved by computer simulation and is not within the scope of this calculation. Based on experience, I reckon the sum of both players' scores may be around 400 points. That would make an extra 5 points only ~ 1% of the total score.

18
General / Re: Do you use house rules?
« on: October 04, 2022, 02:47:20 PM »
I believe we always award +1 point for each city tile and PENNANT if the mage is present. It's just easier on the counting. We feel this is a very minor deviation from the official rules.
And I think we used to switch back and forth between the official rules for capturing a follower with the tower and assigning a power range of the tower by counting a taxi distance (# of tiles moved horizontally and vertically).

Just curious, does using only tiles but not tokens from Catapult count towards house rules? ;)

19
Official Rules / Re: Can bridges lead to an open field?
« on: September 28, 2022, 03:11:18 PM »
The official rule does not seem to mention this, but my understanding is that the spirit is that bridge A is illegal. A bridge is essentially an elevated road that connects to a road or another bridge, which ultimately connects to a road. As you said, bridge A kills a road at the edge of a tile, which does not happen other than in the rare case of an Abbey.

21
General / Re: Playing a game with 2 copies of the same expansion
« on: August 14, 2022, 07:56:05 PM »
 :(y)

We decided for these house rules:
  • Two big meeples for each player instead of one
  • Every inn/cathedral on a completed road/city gives points to its owner (but if they remain open at the end of the game, the owner loses points!)
  • Who gets the most of a type of goods gets 10 points + as many points as the number of tokens for that type they got
Wish us good luck!  8)

22
I would say, just like the tournaments before, we go down the list and do them all at some point.
Does BGA allow both real-time mode and turn-based mode?

23
Voted. ^-^

24
Official Rules / Re: Stealing Cities with Phantoms
« on: March 06, 2022, 07:34:02 PM »
Without the knowledge of the timing of any rules or FAQs or clarification, I can understand and accept that one may not deploy the phantom after removing a knight with the princess tile but one may do so after removing a knight with a tower.

If there are towers, your phantom risks being captured in the next round by your opponent if they want to retaliate. Your opponent does not need to draw the tower tile to add to a tower and there may be multiple towers/bases that they can build on to capture your phantom. All they need to have is a tower piece and a tower/base that can capture your phantom.

In contrast, there is a much smaller chance that your opponent can steal back the city even if the combo in question were allowed. They have to draw a princess tile and that very tile has to have appropriate edges and orientation to connect to the city.

25
The Marketplace / Re: New GAW GiveAWay
« on: February 13, 2022, 04:46:21 PM »
Sounds wonderful. My name is Yi.

26
Quizzes, Puzzles and Challenges / Re: Circular River Town
« on: December 19, 2021, 06:56:25 AM »
Merited for the torus.  :(y)

27
The Marketplace / Re: Photo book of the city
« on: October 06, 2021, 03:31:12 PM »
exact it is this one

Now I wish I had the C2 base game to show this. Thank you so much for the postcard!

28
Reviews & Session Reports / Re: First game with CarDcassonne
« on: September 15, 2021, 05:11:33 PM »
Hahahaha. Hunters and gatherers. The first impression wasn't so great because of the colour scheme. And I vaguely remember it has something to do with the rules.

29
Reviews & Session Reports / Re: First game with CarDcassonne
« on: September 12, 2021, 08:58:45 PM »
Alright. Seeing that it's going to be a $20+ damage, let me try to lower your expectation a bit, just in case. I like all Carcassonne spin-offs but one that I've ever tried.  So me liking Cardcassonne does not mean that much.  ;)

30
Official Rules / Re: chateau Allemand
« on: September 11, 2021, 06:31:24 PM »
I thought each player selects a double-sized tile at the beginning of the game. Does that imply we should all know who gets what and you just cannot ask to view the tile once it's taken? Or is it that a faced-down tile is randomly distributed to each player?

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