On the offered skills in Heroes of Might and Magic III

In this document I will try to describe, to the best of my knowledge, the work and the results that are available online on problems related to the offered skills while leveling up a hero in HOMM-III. A new result is presented in section 4.4 as well as two unified tables with probabilities for hero classes; namely tables 3 and 4. Those that are interested in the problem might want to have a look on [9] which deals with a similar problem but is not within the scope of the document. 1 Instead of introduction I guess everyone who reads this document is familiar with the game Heroes of Might and Magic III (HOMM-III for short). If not, details are given in section A in the appendix. I will summarize, to the best of my knowledge, the work and the results that are available online about matters regarding skills, and skills offered during level-ups. For me everything started with the thread Heroes’ Stats and Skills Chances [11]. In that thread some weight tables were presented and are these weights that influence the skills that appear during level-ups. The way the weights are used for determining the offered skills is presented in section 2. Since we are dealing with a weight table, it is inevitable that we have some sort of randomness. However, practice indicates that heroes might get exactly the same skills as in a previous game. Therefore, the weight table alone is simply not enough to justify skill-advancing given that the implied state-space is huge [3]. That extra information we need is a model on how things work. More on that can be found in section 2. However, before I proceed I need a definition which is central throughout the document. Definition 1.1. Skill-advancing or (abusively) level-up is the process in which a hero gains one or more new skills. 1.1 Why is it important to know about skill-advancing? Perhaps the most significant part of the game is actually played on the way you level-up your (main) hero. The time that you accept or refute certain skills has an impact until the end of the game. And basically, all end-fights (as well as all previous fights against the map) are judged by the skills the main heroes have at that moment. Hence, the development of the heroes is the most crucial part of the game. This gives us a motive to spend our time with problems related to skill-advancing.