Sorry Ubby - I know its just a board game, and I was somewhat nonsensical there.
There are some games you can play, usually a bit later on in life - where you don't have the board and someone called the Dungeon Master makes up the story as you go (they usually have a script that they want the story to kind of run along to). You roll dice with varying number of sides - some have 4 sides, some have as many as 32 (the books tell you what you need to roll - otherwise its awfully complex)
Traditionally, when you roll the 1, it is seen as bad - a critical failure, and the DM will think of something bad to happen to your character, like your arrow going into your foot instead of the goblin. When you roll the highest number on the dice it is seen as good, like knocking the goblins sword out of his hand with your arrow.
I haven't played much of these but was lead to them by friends who played another kind of game, the table top wargame. You may have seen these in the shops...
Instead of having a hexagonal board, like your Heroscape, you simply have a table - you can put model hills, buildings and hedges, well anything that you can make to scale (so it looks like the size of model you are playing with is a real life person in comparison to the houses), onto the table. It then looks like a battlefield.
You have an army, with lots of different types of models in. Each model has different rules about how far it can move, what it can shoot - much like the stat cards of your Heroscape. Again, these are kept in a book for easy reference.
You usually roll lots of 6 sided dice in these kind of games (I use to have a tub of 36 Chessex Earth dice - often even that wasn't enough)
Long ago, there used to be a game called Battletech that used a hexagonal board like the one you have. This had model robots.
D