Elevator Chase

OK, two qualifiers before I lay this out.

One: I just awoke from a nap and a dream in which this came to me, so it is not fully flushed out. I want to get it in writing before it leaks out of my memory.

Two: This is my original thought, as far as I know. I am not consciously borrowing, stealing, or modeling this after any other thought experiment or game, so there is no ulterior motive or hidden trick or anything like that.

With that out of the way, here is my puzzle/game.

Using game theory, what would be the best strategy in this elevator tag scenario?

Scenario: You are on the 6th floor of a 6-story building with two elevators. They are not particularly fast elevators; they move from one floor to another about as fast as someone running up or down the stairs can move from one floor to the other. There are also stairs on one side of the elevators. While getting into one of the elevators, you notice the Texas Chainsaw Massacre Dude running after you, suddenly revving it up as he runs towards you. You assume he's decided you're his next intended victim. The elevator door closes. You assume he's going to jump in the other elevator and chase you. There is no one else in the building as far as you know (it's late at night) or any building or standby security, so there is no help to call or depend on. You are unarmed.

What button(s) do you press upon entering the elevator? You cannot pull the emergency button and get the elevator stuck between floors. You have to choose a floor to get off the elevator. Which floor button(s) do you push, and which floor would you get off the elevator on, assuming your escape plan is to eventually run out of the building and to your car parked two blocks away in a parking lot or deck?

If you are the Texas Chainsaw Massacre Dude, and your goal is to kill me, what floor would you head to and how (in the other elevator, or on foot down the stairs)? How would you catch me and prevent me from escaping?

How would your strategy or plan differ, if at all, if you start on the 6th floor, but it's a 10-story building?

It's just a thought experiment and I don't have a methodical plan yet. I'm just posting it and soliciting input and ideas. Feel free to tell me it's just a fever dream.

CH

I'm going to figure that a chainsaw-wielding maniac in full attack mode isn't going to be terribly subtle. He can probably anticipate me going to the first floor and isn't going to think it through more than that. I would go to the second floor and look for escape opportunities from there.

Chainsaw Guy can go to the first floor and wait. Escaping involves finding a safe exit not mentioned in the OP.

DrMatt wrote:

Chainsaw Guy can go to the first floor and wait. Escaping involves finding a safe exit not mentioned in the OP.

Hmmm...where's that pic of Leonardo DiCaprio in Inception pondering while someone asks him, "Why can't you just have the kids sent to Paris?"

I guess the hypothetical needs tweaking, like allowing for a wait it out until morning option, which brings to mind how TCMD might be allowed to hunt you down wherever you choose to hide. Hide, run, wait, play a game of hide and seek among the various floors?

CH

gnome wrote:

I'm going to figure that a chainsaw-wielding maniac in full attack mode isn't going to be terribly subtle. He can probably anticipate me going to the first floor and isn't going to think it through more than that. I would go to the second floor and look for escape opportunities from there.

Purely on a gut level, I was thinking along the lines of push all the elevator buttons and get out on 3. I was thinking that he has the ability to see which button(s) light up when you get off, so he can hunt you down on that floor. You have to have the elevator continue to stop at all the floors so as to confound him.

Matt went right to the easiest way to defeat my strategy. I didn't intend for there to be such a quick and dirty way of beating my escape plan, but there it is, without modifying my scenario.

CH

You could suppose as a condition that the chainsaw guy is berserk and will not camp

gnome wrote:

You could suppose as a condition that the chainsaw guy is berserk and will not camp

In the context of the kind of horror movie TCM is and the kind of fear/terror it is supposed to instill in the audience, that's a reasonable condition. Of course, assuming TCMD is a rational actor and will apply Game Theory might be asking a little too much.

CH

You don't want to push all the buttons--if he gets on at a different floor, and sees that the only one not lit up is say, floor 3, he knows that's where you went.

push 6
as the elevator starts,press emergency stop. alarm will sound. doors will remain closed. requires key to open from outside...though a chain saw may do. by the time he gets through, you will have escaped up the roof hatch.

What’s the coffee situation on the elevator?

Nyarlathotep wrote:

What’s the coffee situation on the elevator?

Let's just say I'm extremely uncomfortable with invitations for beverages from the Texas Chainsaw Massacre Dude regardless of the time of day.

Rob Lister wrote:

push 6
as the elevator starts,press emergency stop. alarm will sound. doors will remain closed. requires key to open from outside...though a chain saw may do. by the time he gets through, you will have escaped up the roof hatch.

From the OP:

What button(s) do you press upon entering the elevator? You cannot pull the emergency button and get the elevator stuck between floors. You have to choose a floor to get off the elevator. Which floor button(s) do you push, and which floor would you get off the elevator on, assuming your escape plan is to eventually run out of the building and to your car parked two blocks away in a parking lot or deck?

It's a game theory exercise, not a scene from Speed or T2. Hmmm...it was inspired by a horror flick. Anyway, the elevator's just a MacGuffin.

CH

gnome wrote:

You don't want to push all the buttons--if he gets on at a different floor, and sees that the only one not lit up is say, floor 3, he knows that's where you went.

If you start at the top floor and push all the buttons going down, there's no way he could know that from outside the elevator. Even inside the elevator, he will see all the remaining buttons lit until the elevator reaches each successive floor. In other words, if it stops on each floor, there is no greater chance I got off on one floor versus any other. The most he could deduce from getting into the elevator after I'm already off it is that I was once on the elevator but I am no longer on it.

CH

Cool Hand wrote:

Nyarlathotep wrote:

What’s the coffee situation on the elevator?

Let's just say I'm extremely uncomfortable with invitations for beverages from the Texas Chainsaw Massacre Dude regardless of the time of day.

Yeah... don't do that, chainsaw guys.

Cool Hand wrote:

gnome wrote:

You don't want to push all the buttons--if he gets on at a different floor, and sees that the only one not lit up is say, floor 3, he knows that's where you went.

If you start at the top floor and push all the buttons going down, there's no way he could know that from outside the elevator. Even inside the elevator, he will see all the remaining buttons lit until the elevator reaches each successive floor. In other words, if it stops on each floor, there is no greater chance I got off on one floor versus any other. The most he could deduce from getting into the elevator after I'm already off it is that I was once on the elevator but I am no longer on it.

CH

Ahh good point. You should also specify whether the one stairwell is closer to the exit than the elevator, or vice versa.

In this senario, are we, or are we not also chainsaw wielding maniacs? The best choice hinges on this. If we are, it's a fight to the death. If not, then more thinking is to be needed.

I think that in a three floor scenario, the best move for the murderer is to go to the first floor. The best move for the runner is to go up a floor, wait for the time it takes for the murderer to go up a floor, then go down two floors. I don't know how that translates to 6 floors.

If we go by all of the horror movies I have seen and you are a good looking girl being chased by a crazed chainsaw dude, then the obvious answer is you go take a shower.

Go down to the second floor and jump out a window.

Your best bet isn't to guess what he's doing, but to act and make him respond to you. When you're off the elevator, send it to the fourth floor..he'll reach bottom at about the time it took you to set up the elevator. If he stays on floor one, you've got the jump on him. If he goes up to investigate, you've got the jump on him. Even if you injure yourself, you're more likely to get away with the head start. Either way, he is reacting to you, and therefore a tick behind.

If there are no windows, send the elevator to the first floor and climb to ten, then climb down the side of the building. If you fall, you're no worse off than if you ran into chainsaw guy.

Essentially it's zero-sum. You win or die. Taking risks is advised.

clarsct wrote:

Go down to the second floor and jump out a window.

Your best bet isn't to guess what he's doing, but to act and make him respond to you. When you're off the elevator, send it to the fourth floor..he'll reach bottom at about the time it took you to set up the elevator. If he stays on floor one, you've got the jump on him. If he goes up to investigate, you've got the jump on him. Even if you injure yourself, you're more likely to get away with the head start. Either way, he is reacting to you, and therefore a tick behind.

If there are no windows, send the elevator to the first floor and climb to ten, then climb down the side of the building. If you fall, you're no worse off than if you ran into chainsaw guy.

Essentially it's zero-sum. You win or die. Taking risks is advised.

Thanks. That's the kind of analysis I was looking for.

CH

Penny ante here, folding if the bid goes above half a buck.

Cool Hand wrote:

clarsct wrote:

Go down to the second floor and jump out a window.

Your best bet isn't to guess what he's doing, but to act and make him respond to you. When you're off the elevator, send it to the fourth floor..he'll reach bottom at about the time it took you to set up the elevator. If he stays on floor one, you've got the jump on him. If he goes up to investigate, you've got the jump on him. Even if you injure yourself, you're more likely to get away with the head start. Either way, he is reacting to you, and therefore a tick behind.

If there are no windows, send the elevator to the first floor and climb to ten, then climb down the side of the building. If you fall, you're no worse off than if you ran into chainsaw guy.

Essentially it's zero-sum. You win or die. Taking risks is advised.

Thanks. That's the kind of analysis I was looking for.

CH

You're welcome. I run across this type of thing in pen and paper rpgs. One of my best characters was an assassin, and the DM set up an ambush with several assailants of unknown power. I was an assassin, I did not fight people, I killed people. Distinct difference. My abilities were all centered in stealth and agility. So we spent quite bit of time with him trying to make this ambush work, and me finding ways to trick, outwit, and generally stay away from my assailants. Later on, I sent their heads to the person to sent them...after research and regaining the element of surprise. Sometimes the trick is not to buy into the scenario as presented.