Originally posted by geepamoogle
One of the classic games of old was one called "Hunt The Wumpus" which takes places in a series of 20 symmetrical caverns.
If you could imagine the cave was in a d20-shaped dice, where every side held one chamber, which connected to all 3 neighboring chambers via a short tunnel.
The cavern is horribly dark, however, and you cannot see into the cave ill affect the odds. Knowing should improve odds, although you still want to avoid the bat.
If it's just the Wumpus, then you move methodically, checking each room, until you find the smell. Once you've found it, you know the Wumpus is in one of two adjacent rooms because each face of a 20-sider (icosahedron I think it's called) is triangular and touches three other rooms, one of which you came from.
So, you find the smell, then you turn around and go back the way you came. Go to all the rooms that are adjacent to those two rooms while avoiding those two rooms. Locate another smell. Once you have two smells, you know where the Wumpus is. You will only need one arrow.
The pit means you need to minimize the number of rooms you move into while following the above strategy, but other than that there's nothing you can do about it. It's similar with the bat, but unless it drops you into the pit or on or adjacent to the Wumpus you can just start over from the new location with the same strategy.
If it drops you onto a smell, then you have two choices; shoot or walk. If you shoot, you have a 33% chance of killing the Wumpus and if you miss you have a 33% chance of dying. That's 2/3 chance to miss times 1/3 chance to get Wumpus-munched = 2/9 chance of dying. So, bat drops you randomly into Wumpus-Musk, you are more likely to kill the Wumpus with an arrow than to miss and have it eat you...but just barely.
Now if you get dropped into musk and walk, you have a 3/9 chance of dying. So if the bat drops you into musk and you have no other info...shoot the arrow. It's safer.