Suppose a maze like pic related

Suppose a maze like pic related
The goal of the blue guy is to avoid the monster in green and find the exit
They both move randomly and simultaneously,but they cannot access the grey areas and the last cell they've been in,and the monster cannot exit the maze himself
What is the chance the blue guy finds the exit without being caught after only 6 moves? (The move from the last cell into the exit also counts as a move)

Attached: gorillion hours in paint.png (696x448, 10K)

chances of finding the exit randomly in 6 moves is very low
why the question?

i think youd be better off describing the experience you are attempting to create than the methods you are using to attain it

I don't know much game theory or graph theory, so if I wasn't lazy I'd simulate the puzzle it in a program, run it numerous times, and keep track of the statistics.

"What is the chance the blue guy finds the exit without being caught after only 6 moves?"

that isnt the experience

Without taking into account the monster:
He needs to reach the exit-adjacent cell by move 5, which means he needs to reach a blue cell by move 4, therefore a green cell by move 3, therefore a yellow cell by move 2
If he ever gets to a red cell, he's fucked

Attached: 2.png (696x448, 15K)

So let's see:
First move is always a freebie
Second move (first cell blocked):

If he moves to cell A:
- cell B kills him (can't get to exit in time)
- cell 2A continues

if he moves to cell B:
- cell A kills him
- cell C kills him
- cell 2A continues
- cell 2B continues

is he moves to cell C:
- cell B kills him
- cell 2B continues

Attached: 2.png (696x448, 13K)

I got a 1/648 chance of him making it to the exit randomly in 6 moves and a 1/4 chance that the monster takes a path that will actually kill him making 3/4 of those chances successful leaving us with a 3/2592 chance that he takes a path that will get him to the exit without running into the monster

what the fuck are you even talking about "experience"

He's thinking about it in terms of game design for some reason

First move is 1/3 tiles are good
Second move is 2/4 tiles are good
Third move is 1/3 tiles are good
Fourth move is 1/3 tiles
Fifth move is 1/4 tiles
Sixth move is 1/3 tiles
These multiply to 1/648 (roughly .1543%)

The monster has to guess the correct direction, left or right so 1/2 and then after that the only move he can make to run into the dude is to take tiles that use up an extra turn not really going anywhere to stop from passing by each other (since they both move instantaneously). this gives him a 1/2 chance of moving either out of the center (if that was his first move) backward left or right, or 1/2 chance moving to the center out of the direct left or right (if that was his first move) instead of straight forward. This means the monster will hit the dude 1/4 times

So multiply the 3/4 safe times by 1/648 and you get 3/2592 times where he doesn't run into the monster and makes it to the exit which is about .11574%

Screw that, I'm going after the monster.

What do you mean first move 1 in 3 tiles are good? First move literally doesn't matter
See

First move is for free
Second move 1/2 from top * 1/2 from bottom * 2/4 from the middle
Third move 1/3 from top * 1/3 from bottom
Fourth move 2/3 from top * 2/3 from bottom
Fifth move 1/2 from top * 1/2 from bottom * 1/4 from the middle
Sixth move 1/3 chance
=1/7776
Also monster has a 24% chance of catching him on the third move

So for the 2nd move, 4/8 moves continue
For the 3rd move, 4/12 moves continue
For the 4th move, 4/6 moves continue
For the 5th move, 3/8 moves continue
For the 6th move, 1/3 moves continue

[4/8]*[4/12]*[4/6]*[3/8]*[1/3] = 0.01388
(can we just multiply them all? not sure about this step)

Don't you need to count the A - 2A and B - 2A scenarios separately? That's why you're getting six different moves on move three and I'm getting twelve ()

Let's see what the maze looks like for the monster.
No exit for him.
If he ever gets to red, he's fucked (or the guy was dying anyway).
He can only occupy the same cell as the hero starting on move 3 - before that, they're each on their "half" of the dungeon.
So he needs to be on 3A/3B, 4A/4B/4C, or 5A when the hero is on those tiles, otherwise he's out of chances.

Attached: 3.png (696x448, 9K)

This is the monster you're running from.
Oregano

Attached: 1558733347565583742589.jpg (2000x2000, 502K)

Oh I didn't account for the symmetry, real answer is 1/1728

All I know is the guy needs to get there in 6 moves,doesn't matter what path he takes

I think it matters if you're trying to find out the odds of him doing it (because you need to count the number of scenarios where he succeeds or fails, and A - 2A is a different scenario than B - 2A).

Okay, so the monster actually has six different victory conditions, one for each of the cells he can capture the hero in.
For instance, if hero is on 3A by move three, the monster can get there by 4A-4B-3A, 4B-4A-3A or 4C-4B-3A. So his first move is always a freebie, and so on.
You would have to find out all the captures and subtract those from the number of scenarios where the hero otherwise escapes to find out the final odds. I'm done, if anyone wants to finish it.

taking off the false 1/3 first move (thanks )
makes 1/216 chance without monster
then do the 3/4 chance of monster and you get 3/864

idk if this is fucking right lmao