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Subject: Quantifying "Layout Value" rss

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Alan Kwan
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In my strategy article, I talked about a tile having 4 "values":

1. printed values
2. layout value
3. prerequisite value
4. event value


Layout value seems the most "abstract", especially in the early game. The others are not too difficult to quantify.

In the late game, layout value is quite direct. For example, if a red-cornered tile increases my bonus by 2 Fame, its layout value for red corners is 2. If a Lounge fills in my Restaurant for 5 Fame, its layout value is 5.

But in the early game, it's not so clear how much a tile is really worth. Let me try to estimate.

Red corners:

For a certain number of small tiles, the maximum amount of red corner bonus is:


spaces Fame
1 0
2 0
3 1
4 3
5 4
6 6
7 8
8 10
9 12
10 14

To summarize, the first few spaces score very little, but then the value goes up. At higher numbers, the total averages roughly 1 Fame per space.

Another way of looking at the value is the "marginal" value: how many points this tile is going to add to my score, assuming that I'll be getting some number of other tiles anyway. Above 5 spaces, the marginal value is 2 Fame.

Sometimes one needs to Renovate once or twice to re-arrange his tiles to get the maximum bonus. This may cause a point or so to be subtracted from the total (for sacrificing the chances to get 1 Fame for Publicity).

There is an event card, but most of the time, the event either comes out too early, or not at all. The chance that one can score most of his red corner bonus on the event card is quite small.

Summarizing all these, we might estimate the red-corner layout value of a small tile (in the early game) to be roughly 1.5 Fame.

A medium tile has exactly twice as many red corners as a small tile, so that's worth roughly 3 Fame.

A large tile has twice the red corners as a medium tile, less the diamond (3 Fame) in the middle. So it's worth 3 Fame, plus a bit more.
Let's say it's 3.5 Fame . Note that a large tile is worth not a lot more than a medium tile, and we can see this from practice too.


small ~1.5 Fame
medium ~3 Fame
large ~3.5 Fame


Completion:

Filling the Hotel or the Casino takes 10 spaces, for 5 Fame. So each space averages to a value of 0.5 Fame. However, that is the best case value: you don't get any Fame (for filling a section) if you don't complete the 10 spaces, and you don't get any Fame for tiles placed into the middle white spaces. Thus, the layout value of a small tile towards the Hotel/Casino completion bonus is something less than 0.5 Fame.

Connecting the Hotel with the Casino takes at least 7 spaces, often more. However, we can assume that we're probably putting something at the entrances, so it may take something like 3 to 5 more spaces to connect. So we may count 3 Fame for 3 to 7 spaces, or roughly 0.5 Fame for the layout value of a small tile towards the connection bonus. There is an event card, if the connection is made in time.

Rather than calculating the filling-in and the connection bonuses seperately, it is perhaps easier to just count a grand total. A player may score 8 Fame (fill either side + connect) for 15 tiles (usually more), or 10 Fame (fill both sides) for 20 tiles, or 13 Fame (everything) for 23 tiles (often more, say 26). Thus, for a rough estimate, a layout value of 0.5 Fame for a small tile should be ok.


small ~0.5 Fame
medium ~1 Fame
large ~2 Fame


We can see that, the red-corner layout value is easily worth a lot more than the completion layout value. The Fancy Restaurant has a layout value of around 1.5 Fame (you need to place it in the center to get its red-corner value, and with only 1 door it cannot help connection), while the Buffet's is around 2 Fame. So the Fancy Restaurant is generally more valuable than the Buffet (in the early game), because it has printed Fame too.

Note that all the above analysis are useful only for the early game. For the late game, the practical, marginal value of each tile (which can be directly computed) is more important than these theorectical figures.
 
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