# Hunt The Wumpus

geepamoogle
Posers and Puzzles 13 May '08 22:12
1. 13 May '08 22:12
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 cavern until you are inside it.

Now inside one of the cavern rooms is a large nasty beast called the Wumpus, which is known to eat hunters, and also known for its base smell, which you can smell from one cavern away, although you can't tell from which direction (as is the nature of bad odors).

Now the wumpus is asleep at this time, and you have been chosen to kill it from afar with your bow and arrows (the problem usually stipulates you have 6 arrows). However, even though the beast is asleep, it is a light sleeper, and will hear you if you enter its chamber, or if you fire in a wrong direction from a neighboring cave. If awoken, he randomly moves to the next cavern, and if he sees you at any time, you're Wumpus Chow.

So now, if it is just you and a wumpus, both assigned different rooms randomly, and if you proceed with an optimal long-term strategy, what are the best odds you can hope for for hunting the wumpus?

Suppose this cavern also includes (in random and separate places) a bottomless pit for you to fall into and a large bat which will move you to a different room at random if you come across him, what are your chances then? (You can feel a draft from the bottomless pit, and can hear the bat from afar, but also cannot determine direction. Be it noted, the bat COULD drop you into the pit or the wumpus room, with disastrous results.)

You can opt to know where you get dropped off relative to your previous position, or not to for the bat, although this probably will affect the odds. Knowing should improve odds, although you still want to avoid the bat.
2. AThousandYoung
All My Soldiers...
14 May '08 00:031 edit
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.
3. 14 May '08 00:11
Originally posted by AThousandYoung
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.
I agree with the methodology. Once you've found the smell from 2 rooms, you have the wumpus pegged.

If you don't start off beside the wumpus, then you should get a guaranteed victory every time.

If you do start beside the wumpus, then the question is whether to shoot or try moving in a direction. Which gives me the best odds of winning, though?
4. AThousandYoung
All My Soldiers...
14 May '08 04:50
Originally posted by geepamoogle
I agree with the methodology. Once you've found the smell from 2 rooms, you have the wumpus pegged.

If you don't start off beside the wumpus, then you should get a guaranteed victory every time.

If you do start beside the wumpus, then the question is whether to shoot or try moving in a direction. Which gives me the best odds of winning, though?
Shooting. I already addressed that. Either way has a 1/3 chance of you dying - unless you hit the Wumpus with the arrow.
5. coquette
Already mated
14 May '08 04:53
this reminds me so much of a frat party i went to this semester
6. 14 May '08 06:17
If the wumpus is awoken, do you hear it then?
7. 15 May '08 03:12
OK, here's how I think it works officially (there may be many variations).

You the Hunter
Every turn you can either choose to move or shoot in any of three directions at will. You have limited ammo, but plenty to accomplish the task at hand.

If you fire into the room the Wumpus is in, you kill the Wumpus and succeed. If you fire into an empty room, you lose the arrow.

You can smell the Wumpus from one room over, hear and feel the wind from the Pit room from a room over, and hear the Bat stirring from one room over. You cannot, however, discern the direction any of these. You also are incapable of hearing where the Wumpus came from or going to unless he heads in your direction (and then it's too late).

Wumpus
The Wumpus remains in place and emits an odor/musk into the three adjacent rooms. He remains asleep under normal circumstances, and starts in a random room not occupied by the player to start. One arrow kills him.

If the Wumpus is adjacent to you when you fire an errant arrow, he wakes up, and silently and randomly moves to one of three adjacent rooms. If you're in that room, he eats you. If the room is empty, he falls asleep again. The Wumpus will eat you if you enter his room (and then fall asleep again).

The Wumpus will not enter the Pit room, but he will enter the Bat's chamber without disturbing the Bat. Thw Wumpus will eat you if you enter this room.

The Bottomless Pit
Well, maybe there is a bottom, but you won't live to find out at any rate.

The Pit emits a wind which fills the chamber and the three adjacent chambers. Stepping or being dropped into this chamber means your doom.

The Pit room does not move, obviously.

The Giant Bat
If the Hunter enter's the Bat's room (assuming the Wumpus is not in there), the Giant Bat will move the Hunter at random to any of the other 19 rooms, then depart and return randomly to any room other then the chamber you are now in, the chamber the Wumpus is in, or the chamber with the Bottomless Pit.

This could mean your death if you get dropped into one of the two deadly rooms.

The Giant Bat won't bother the Wumpus. Also, in the process of taking your free ride, you lose track of where you are

Those are the rules as I understand them.
8. Nemesio
Ursulakantor
16 May '08 15:172 edits
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.
I believe I had this as a little, hand-held video game with a D&D theme.

http://dvice.com/pics/Mattel-Dungeons-and-Dragons.jpg

Except that you had one grappling hook to get out of the pit on the 'easy' level.