Hi Jack7, am I correct in assuming that for you, one of the prerequisites of heroism is that the hero must be willing to take action when he has no idea what his chances of survival are? This is quite distinct from not knowing whether or not he will survive, by the way - this prerequisite disqualifies a character who knows that he has a 50% chance of death but decides to act anyway from being a hero because he knows (or is able to reasonably guess) what his chances are. I will get to why I make this distinction in a moment.
Now it is true that in real life, heroes very often have no idea what their chances of success or survival actually are. When it comes to works of fiction, however, this may be true for the characters and the observers (whether the readers of a book, or the audience for a play or a movie), but this is often not the case for the author. In many cases, the author has a very good idea not only of the probability, but of the actual outcome of the character's actions.
When it comes to games, the issue is further confused because the player may assume more than one perspective with respect to his character. At the most basic level, he is supposed to be his character, or at least, to identify with him and make decisions as if he was him. However, once the player is experienced enough with the game system and familiar enough with the game rules, it is dificult to avoid a certain author-like perspective on the actual level of danger faced by his character. An experienced player with a 1st-level PC may describe how the character is horrfied by the unnatural animated skeletons advancing towards him, but still manages to summon enough courage to face them in battle even though his every instinct urges him to flee. The player, on the other hand, may know that his character has a good chance of beating the skeletons since they only have a 30% chance of getting through his armor, he has a 50% chance of hitting them on his turn with his attack bonus, he will need about two hits to bring down each skeleton, and he has enough hit points to withstand on average about four hits from his opponents.
However, the point is this: if a fictional character can be upheld as an example of heroism because he doesn't know the odds against him even though the author does, a game character can still be a hero if he is equally ignorant of the odds, even if his player knows what the odds against him actually are.
Now as to why I made the earlier distinction: if game characters can only be heroes if the players do not know the odds, then the solution is to keep the players ignorant of the rules and their characters' abilities except in the most general terms. If game characters can be heroes if they are only uncertain of their chances of success and survival, then the random elements in the game will ensure that anyway, and if you just want them to have poor chances of success and survival, then the solution is to pit them against opponents and challenges that are more dangerous than the system expects them to face. Whichever solution you adopt will depend on what you consider to be the prerequisites of heroism.