I've often thought it would be useful to know the odds of winning a combat in HOTW, and now I've finally sat down and done the calculations. The table below shows the % probability of the attacker winning a single attack under various conditions. It assumes that, if there is a tie, the attacker keeps attacking until the result is not a tie (except, of course, when one side is winning ties). The second number in each box is the average number of armies it will cost the attacker to destroy one defending army. If anyone wants to check my calculations and you find an error, please let me know.












2 dice 






2 dice win ties 






2 dice +1 






2 dice +1 win ties 






3 dice 






3 dice win ties 






3 dice +1 






3 dice +1 win ties 






Various conclusions can be drawn from these figures. What surprised me was the effectiveness of building forts. If you ignore event cards, it is always better to build a fort in a land than a second army. In open terrain the difference is small, but in difficult terrain the fort gives a significant advantage. With 2 defending armies in difficult terrain, it costs an attacker with no bonuses 2 armies, on average, to take the land. With an army and a fort, the average cost will be 2.7 armies. On the other hand, forts are vulnerable to event cards (Surprise Attack, Siegecraft and various disasters). With this in mind, I would recommend only building forts if you already have two armies in the land or in difficult terrain, and almost never in a land with a monument, as that's asking for a disaster.
Fortresses, if you're using the optional rules, are only worth building if you already have three armies in the land and you want the maximum possible defense.