User:Ajdedo
The number of attacking armies does not include the minimum one army that must be left behind in the territory (e.g. if the attacking territory has 10 armies total, it has maximum 9 attacking armies).
A common situation is that the attacker wants to take over a whole region of countries during the same round, by a series of battles. After each successful battle, the attacker leaves one army in that country, and continues with the remaining attacking armies into next country. The following table shows the average number of countries that the attacker can take over, as well as the 90 percentile, starting with a certain number of attacking armies in the first battle. A fixed number of armies is assumed to defend each country.
| Number of attacking armies in the first battle: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| One defending army in each country |
Average number of countries that can be defeated: | 0.42 | 1.0 | 1.7 | 2.3 | 3.0 | 3.6 | 4.3 | 5.0 | 5.6 | 6.3 | 6.9 | 7.6 | 8.3 | 8.9 | 9.6 | 10.2 | 10.9 | 11.5 | 12.2 | 12.9 |
| Number of countries that can be defeated with 90% confidence: | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 6 | 7 | 7 | 8 | 8 | 9 | 10 | 10 | |
| Two defending armies in each country |
Average number of countries that can be defeated: | 0.11 | 0.39 | 0.82 | 1.2 | 1.6 | 2.0 | 2.4 | 2.8 | 3.2 | 3.6 | 3.9 | 4.3 | 4.7 | 5.1 | 5.5 | 5.9 | 6.3 | 6.7 | 7.1 | 7.5 |
| Number of countries that can be defeated with 90% confidence: | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 | 5 | 5 |