Backpack Theft Problem

Suppose that you are a thief at a beach. You see a backpack on a towel unguarded.



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Assume:

1) The backpack with its contents is worth W dollars to you.

2) It takes you 1 minute to steal the backpack.

3) If the owner returns while you are stealing, you will lose J dollars. (Bribe for police, jailer, ...)

4) If the owner does not return during the 1 minute stealing process, you are not caught.

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Question: Should you

a) Steal the backpack immediately or

b) Watch for a few minutes to see if the owner returns, and then, if he does not return, steal the backpack.

Ugh, I get to be the first one to put their head in the noose on this one..


I'm going to assume that anyone losing a backpack notices within one hour and returns.

I'm also going to assume that 80% of the time the owner is using a restroom, buying an ice-cream or some other event that takes 5 minutes.


During the 20% of the time that the owner has forgotten about the backpack waiting 5 minutes will give you a 55 minute gap to aim at, although on average 30 mins will have elapsed when you arrive and so you will be caught once in 25.

stealing it straight away, you will be caught once in 30.


The other 80% of the time you will be never caught if you wait, but will get caught twice in five if you dont (assuming you notice the pack on average 2.5 mins into the owners departure)


on these assumptions you should wait...but depends on what you think may be in the backpack since the safe method means you rarely end up with the pack [img]/images/oh.gif[/img]


results:


waiting: caught with pack 1/150


pack for free 24/150


no pack 125/150


not waiting: caught with pack (long absence) 1/30


(short 12/30


escape with pack 17/30


Putting in values for pack, local fines etc will give your figure, FOR THESE ASSUMPTIONS