Scaling for Large Games

[Christopher]

Hello all!

I had a post months ago about scaling tiles for large games, and another about cloister ratios and such. However, subsequent to a recent post in a topic about eight players, a new thought occurs to me.

Mechanisms such as towers, bridges and castles scale down as you add more players, to prevent over-use, I suppose. But, could these features scale up for large games?

Take castles, for example. In a game with BC&B, each player will receive two or three castles depending on how many players you have. If playing with just this and the base game, this means two or three castles for 84 tiles. This works out fine. But if playing with more expansions, adding up to several hundred tiles, is two castles enough? Could a player receive more castles?

I plan to do some maths tonight, but does anyone have any thoughts on scaling up features such as bridges, castles and towers?

Linkback: https://www.carcassonnecentral.com/community/index.php?topic=2540.0

[Decar]

You might like to look at the 10080 tile game!  I am now beginning to understand why, the introduction of the Big meeple in Inns and Cathedrals and Wagon are so important.  The AI in JCZ ran out of meeple well before 100 tiles!  Towers, bridges and Castles probably need just as much tweaking.  If I were to run the game again, I'd give the AI another 600 meeple to see them through to near the end.  That's near a 2x multiplier, for every 72 tiles, if that makes sense!

[Christopher]

You might like to look at the 10080 tile game!  I am now beginning to understand why, the introduction of the Big meeple in Inns and Cathedrals and Wagon are so important.  The AI in JCZ ran out of meeple well before 100 tiles!  Towers, bridges and Castles probably need just as much tweaking.  If I were to run the game again, I'd give the AI another 600 meeple to see them through to near the end.  That's near a 2x multiplier, for every 72 tiles, if that makes sense!

I've been reading that post with interest! I thought about meeples too, and the meeple shortage has been often mentioned, but the difference of course is that meeples are a re-usable resource, as it were, unlike things like castles and bridges which are deployed just once. I can't wait to see how the numbers will work out! I need an evening free to work on it though.

[Christopher]

Howdy.

I've done some of the maths which looks at scaling features for larger games. This time, specifically, I was looking at towers, bridges and castles. The numbers aren't pretty.

I took the ratio of how many castles and bridges each player gets in an 84 tile game, this being the number of tiles in a game with the base game and with BC&B. Taking this to be the correct ratio, I worked out how many castles and bridges each player gets per tile and used that to work out how many castles and bridges a person gets in a game with any number of tiles. I did this for both two to three players and four to six players. I then did the same for tower pieces.

With 500 tiles in a three player game, each player gets, wait for it, 50 tower pieces. Now, obviously I would need to play test this, but straight off of the bat it sounds horrendous. Each player able to capture 50 followers throughout the game? Painful. In addition, you would need to buy 120 additional tower pieces on top of what comes with the expansion. Not really feasible. I suspect I need to introduce some sort of diminishing returns. All that being said, it's possible that 50 tower pieces would be about right. In a large game, I find that features become diluted. Nine tower pieces (which you would normally get in a three player game) don't last long in a 500 tile game. In order to increase the prevalence, you need a few more pieces. Of course, you're also restricted by the number of tower foundation tiles. 18 tower tiles don't come up very often in 500 tiles. The other problem is that 150 tower pieces between 18 tower foundations is also problematic, in that you'd have towers able to capture huge distances across the board, and, in a physical sense, you'd probably end up knocking over the towers. In addition, the number of tower pieces in the expansion doesn't account for other follower removing features such as dragons and plagues. Like I said, I would need to test this number, which I'm unlikely to be able to do (unless someone wants to play with the coding in J Cloister Zone to allow variable numbers of tower pieces ).

In a 200 tile game, three players would get 20 tower pieces each.

Bridges and Castles are slightly different. These scale far better as each player has fewer to begin with. On top of that, castles and bridges are less aggressive than tower pieces. Okay, castles are aggressive, but only in a point-sharing manner. It's not the same as whipping a player's follower off of the table. And bridges are not aggressive. I was particularly excited to scale these, as I always felt that you weren't given enough. Bridges especially, two or three just doesn't seem sufficient. Three castles is also not very many, but it could be contentious to scale these up. So, in a three player game with 500 tiles, each player gets 18 bridges and 18 castles. Now we're talking! I feel that with this many, you could make a significant use of them. This almost feels like too many, but again, over 500 tiles, they would be spread nicely. Perhaps this would also benefit from diminishing returns.

In a game with 200 tiles, three players would get seven bridges and seven castles each.

The problem with both of these calculations is that they only take into account the number of tiles. It does not account at all for what those tiles are. The ratios from which these are calculated use only the base game and the tiles with which these features came. That means you get, for example, nine tower pieces amongst 90 fairly vanilla tiles, save for the tower foundations. Same goes for bridges and castles. Three of each amount amongst 84 vanilla tiles, save for bazaars. With 500 tiles, you need more tower pieces, bridges and castles to increase their prevalence, but not as many as indicated by the original ratios as this then gives too much going on, given that many of those other tiles will have their own functions. I think to improve on these numbers, I need to either:

• Introduce diminishing returns, in which more tiles gives fewer additional features the more you add
• Calculate the numbers of features based only on the vanilla tiles added by each expansion

I'm not sure how I would factor in the diminishing returns, but I'll play around with both of these ideas. Hopefully I'll have some more workable numbers later!


Incidentally, in Decar's 10080 tile game, each of the two players would get 1120 tower pieces, and 360 bridges and castle tokens!

[Decar]

I dont want to see the AI mess that up too!

[Christopher]

I'm still playing with my numbers! I'm looking at calculating the number of towers and bridges to have based on the number of vanilla tiles in a game.

What would everyone define as a vanilla tile? At first I thought it would be a tile which only has city, road, field or a cloister on it. Any special feature would discount it. But if you count up all of the 'vanilla' tiles across all of the expansions, there aren't very many. In addition, there are numerous tiles which have a special feature on them, but don't have a great deal of 'special actions' attributed to them. Shrines, for example. I wouldn't have originally included these as vanilla, but they're actually just cloisters with a slight addition. What about a tile with an inn, or a vineyard? That doesn't exactly trigger an event or a flurry of activity like a bazaar tile would. And a ferry, or a tunnel? Those are just roads, right? Or Rivers! Rivers are just normal tiles with more placement restrictions, that add a non-playable feature! Are they vanilla?

So, my question is this. For the purpose of calculating how many bridges, castles and tower pieces to have in a game of Mega-Carcassonne, what constitutes a vanilla tile? Does it include what are essentially fancy roads, such as ferries; or volcanoes, which do nothing but move the dragon? And what doesn't? Are not-vanilla tiles those which trigger an event, such as spinning the WoF, a dragon attack, or an auction? Or is it anything which isn't a city, road or cloister, such as rivers and Darmstadt churches?

What do people think?

[Decar]

It's probably easiest to consider 'vanilla-tiles' as: Tiles from the base game - possibly the Winter Edition 12 too.

Otherwise the door is open to just consider the number of tiles you have - what are you trying to exclude?

[Christopher]

When I calculated the numbers of towers etc from the number of tiles included, you get a huge amount of each. The problem is that the ratio of, for example, tower pieces to the number of tiles used in a game with the base game and the Tower is based on 72 vanilla tiles and 18 tiles with tower foundations. If you scale up that ratio, it doesn't taken into account that you're adding tiles which have functions of their own. Which means you then have way too many tower pieces considered everything else that is going on. Why would you get another tower piece for every 12 tiles when those tiles have functions of their own?

Better to calculate the number of tower pieces only from tiles which don't have special functions. But, when you add up all vanilla tiles from expansions (only those which have features from the base game), it's very few. 100, in fact, not including the base game. Which means you end up adding very few tower pieces.

So, I thought to calculate the number of towers from the number of tiles which do not have special functions. At the moment, I'm thinking of including things like inns and vineyards and excluding things which trigger a specific event, such as dragon attacks and auctions.

[Decar]

Having 50 high towers is pretty crazy too, imagine if someone sneezed.  I'm not sure you need to add more tower pieces unless you are adding more tower tiles to your game.  Perhaps towers have a limited range in the same way you don't make inns more valuable in larger games because there are more road tiles being added to the game, so getting one makes it easier to finish.  They have a limited output.

eg:  18 tower tiles :30 tower pieces
36 tower tiles : 60 tower pieces.

Just because the game is getting bigger doesn't mean that tower's function has to scale across larger areas.

I think if you want to make the Tower more significant the trick is to add more tower-tiles.

[Fritz_Spinne]

In my opinion vanilla tiles are all tiles which don't trigger or enable an extra action or hinder a usual action.

Usual actions are place a drawn tile (and follower on that tile) and score.

Extra actions are features like take a follower (princess), dragon movement, place a tower piece, place a not drawn tile (abbey, german castles, halflings), move an extra figure (fairy, robber, mage & witch ...), make a basar, score the wheel of fortune, place a follower on another tile (magic gate, flyer) ...

In my opinion the river tiles alternative start tiles. Like the usual start tile they are no vanilla tiles, but they are not extraordinary.
Cathedral tiles, inns at a lake tiles and trade good city tiles are vanilla in my opinion - they only change the scoring, but they don't enable extra actions.

[Christopher]

Having 50 high towers is pretty crazy too, imagine if someone sneezed.  I'm not sure you need to add more tower pieces unless you are adding more tower tiles to your game.  Perhaps towers have a limited range in the same way you don't make inns more valuable in larger games because there are more road tiles being added to the game, so getting one makes it easier to finish.  They have a limited output.

eg:  18 tower tiles :30 tower pieces
36 tower tiles : 60 tower pieces.

Just because the game is getting bigger doesn't mean that tower's function has to scale across larger areas.

I think if you want to make the Tower more significant the trick is to add more tower-tiles.

I considered this too. The problem is that adding more tiles contributes to the problem. The idea of scaling was to make each of the features more prevalent in a large game. Adding more tiles, even if they are tower tiles, dilutes the tower pieces. Plus, all the other tiles we've added from other expansions reduce the impact of towers. Adding more tiles also continues to dwarf other features. I've considered playing with additional sets of Inns and Cathedrals to reduce their lack of impact in a large game. The good thing about towers is that you could scale it up without adding more tiles.

The other problem is that I'm hoping to apply this to bridges and castles, too. The tiles that accompany these features have nothing to do with them. So adding more of these tiles to add more of these wouldn't work. Because bridges and castles can be played on any tiles, not just the ones from that expansion, I think it makes more sense to scale these with other tiles.

In my opinion vanilla tiles are all tiles which don't trigger or enable an extra action or hinder a usual action.

Usual actions are place a drawn tile (and follower on that tile) and score.

Extra actions are features like take a follower (princess), dragon movement, place a tower piece, place a not drawn tile (abbey, german castles, halflings), move an extra figure (fairy, robber, mage & witch ...), make a basar, score the wheel of fortune, place a follower on another tile (magic gate, flyer) ...

In my opinion the river tiles alternative start tiles. Like the usual start tile they are no vanilla tiles, but they are not extraordinary.
Cathedral tiles, inns at a lake tiles and trade good city tiles are vanilla in my opinion - they only change the scoring, but they don't enable extra actions.

That's the distinction I was thinking of making. What about something like siege tiles?

[Decar]

I guess the other things you have to contend with, is that for larger games, the chances of being on a Tower's Line of Sight is greatly reduced.  Perhaps you need to consider a different distancing algorithm?

[Christopher]

I guess the other things you have to contend with, is that for larger games, the chances of being on a Tower's Line of Sight is greatly reduced.  Perhaps you need to consider a different distancing algorithm?

Yes, I've been a bit simplistic so far. There are definitely other factors to consider!

[Paul]

Regarding the Tower how about each wooden tower piece is a square from the center?

With three tower pieces I count up to three tiles using the Dragon movement style, no diagonal movements.

[Christopher]

Regarding the Tower how about each wooden tower piece is a square from the center?

With three tower pieces I count up to three tiles using the Dragon movement style, no diagonal movements.

I'll have to look at adjusting the rules slightly for large games later. I'll stick with scaling for now!