Risky :: Analysis

Risky :: Analysis & speculations

Terminology
Number of players
Territories
- Assumptions
- Overview
Continents
- Assumptions
- Overview
Missions

Term	Meaning
P	Player
T	Territory
D	Door or bridgehead: territory connected to foreign continent
I	Inland: territory bordering continental siblings only
N	Neighbour (connection, either touching or remote)
N_D	Neighbour which is a door
N_I	Neighbour which is inland
FN	Friendly neighbour (same troop colour)
FN_I	Friendly neighbour which is inland
C	Continent
cpt	Continent points/value (supply units for owner)
n(…)	number of …
A	Attractiveness

Number of players The game offers the options of 2+1, 3, 4, 5, and 6 players, where 2+1 indeed equals 3.
For some of the later formulas we'd appreciate a single value representing that number - any kind of average is fine.
Simplest way, of course, is arithmetic mean: (3+3+4+5+6)/5 = 4.2
Is it representative? Let's look at the two main reasons of starting a game...

Casual player: fights boredom, perhaps filling a break, being at least engaged or even entertained.
Low time investment, preference for short games with early and frequent rewards.
Probable choice: 3.
Hardcore gamer: tries winning well-earned in the end, experience the joy of success after considerable effort and time investment.
Probable choice: 5 or 6.

Given there's more casual players than hardcore gamers, the average value should be lower than 4.2; hence our statistical number of players, n(P), will generally be 4 in the calculations below.

Territories :: Assumptions The following calculations of attractiveness apply to an (eventual) owner of a territory and its continent, using isolation to secure own estate.

Assumption	Reasoning	Expression
The less connections, the better.	Can't be attacked easily	Insularity 1 / n(N)
Inland is better than door.	Can't be attacked directly from the outside	Inl.bonus 1
The more (friendly) neighbours, the better.	Less hostile environment	Homeland n(FN) / n(N)
The more (friendly) inland neighbours, the better.	Buffered by secure siblings	Security n(FN_I) / n(N)

Territories :: Overview In case of doors, n(FN) includes external neighbours whose probability of friendliness is 1/n(P) (inversely proportional to the number of players), hence 1/4 (or 0.25).

An attractiveness formula can be derived by averaging the terms from the above assumption list:
A = (Insularity + Inl.bonus + Homeland + Security) / 4

Name	Type	Connections			Insularity 1 / n(N)	Homeland n(FN) / n(N)	Security n(FN_I) / n(N)	A
		ext.	int.	=
North America
.	.	.	.	.	.	.	.	.

As it turns out, Argentina, Japan, and Eastern Australia seem easiest to defend, while Middle East, having a central position, clearly is a conflict ridden trouble spot, just like in real life.
However, if trying to invade neighbouring areas, then Middle East is worth most, followed by Southern Europe, Ukraine, and North Africa.

Continents :: Assumptions The following calculations of attractiveness apply to an (eventual) owner of a continent, using isolation to secure own estate.

Assumption	Reasoning	Expression
The more territories, the better.	More siblings can deliver more (fortifying) units, e.g. for door strengthening. More continent points (= reenforcement units in general).	Size n(T)
The less doors, the better.	Can't be attacked easily.	Isolation 1 / n(D)
The more cpt units per door, the better.	Doors can be fortified more effectively.	Supply cpt / n(D)
The more attractive its territories, the better.	(self-evident)	Quality ∑(A(T)) / n(T)

Continents :: Overview An attractiveness formula can be derived by averaging the terms from the above assumption list:
To normalize size, it's divided by 12, which (in the case of Asia) is the max number of T per C.
To normalize supply, it's divided by 2, which (in the case of Australia) is the max number of cpt per n(D).
A = (Size / 12 + Isolation + Supply / 2 + Quality) / 4

Name	cpt	Size n(T)	n(D)	Isolation 1 / n(D)	Supply cpt / n(D)	Quality ∑(A(T)) / n(T)	A
.	.	.	.	.	.	.	.

As expected, Australia is the winner in terms of defence due to its intrinsic isolated location, while Africa and especially Atlantis are hardest to defend because of their openness (external connectivity).
If, on the other hand, the owner wants to expand, that is, invade neighbouring continents, then Australia is worst, while Africa and Atlantis are perfect.

Missions Min = minimal, Std = standard, Ext = extended

Task	Selection
	Min	Std	Ext
Conquer continents
	-	-	✓