This infomation applies to the IBM PC version of the Bard's Tale, Tales of the Unknown. (Bard's Tale I)
Brave, Brave Sir Robin, he bravely ran away!
At the beginning of each encounter, and between rounds, you will be informed how many and what kind of enemies you face, and then you will be given a choice whether you want to F) Fight, or R) Run. If the enemy is bigger and meaner and uglier than your party, perhaps you should try applying the wise adage, "He who fights and runs away... lives to fight another day."
There is a chance the enemy is also faster than you, in which case you can't elude them and you fight anyway. Whether your retreat is successful is a dice roll between your front line character and the front most enemy. However, you are each given bonuses. The enemy bonus is pretty much how deep is the dungeon he came from. Your party bonus depends on how high level your front guy is, what class he is, how lucky he is, and whether or not he's using a luckshield. Probably the Speedboots were supposed to help, but they seem to be broken.
You also get an extra chance to run if you are still in the city, and it is still daytime.
This is very important for starting parties. How many of us have had a total party wipeout because we ran into 8 Barbarians at the wrong time, and couldn't elude them?
Luck makes a HUGE difference whether you can run or not. A level 2 Hobbit Conjurer with 18 luck can run from anything in town over 90% of the time if it is still light outside. A level 1 Dwarf Warrior with only 10 luck will get caught by Barbarians more than two thirds the time.
For more specifics on the exact formula, read about Saving Throws.