Shaft or Share?

[stan1980]

I was having a discussion earlier about an old TV games show called "shafted", which turned into an argument. I thought the solution was quite straight forward personally, but others disagreed.

Anyway, the idea of the game show was that you built up a large cash prize between you and your opponents, with players systematically getting knocked out till you are left 2 players who have to make a decision on whether to shaft or share the prize money between them.

• If both players decide to shaft, both contestants walk away empty handed.
• If one player shafts and the other shares, the player who shafts gets all the money to him/herself
• If they both share, they share the prize money

Before they make their decision, both players make a plea to each other which normally goes along the lines of "lets share the money, as if we both shaft each other, we both go home empty handed. I've got a family and having half the money is more than enough for me bla bla bla". Once they've both made their pleas they make their decision in secret, and the results are revealed.

So what would be your decision, and would it change depending if you trusted your opponent or not?

 

[DeathMagus]

Shaft, for sure. Either way you choose, the outcome is 50-50 whether you walk away with nothing. By shafting, you guarantee that if the 50-50 comes out in your favor, you walk away with more money.

If you trust your opponent (they're a friend), then you share for sure, since that ensures that between the two of you all the money is won, and it can be split up later.

 

[InigoMontoja]

Shaft, for sure. Either way you choose, the outcome is 50-50 whether you walk away with nothing. By shafting, you guarantee that if the 50-50 comes out in your favor, you walk away with more money.

But if you both shaft you get half of zero. What is 50% of zero?

 

[keith99]

Hmm. I might just choose to mention I know where to find a few Hells Angels and they don't take well to those who break their word.

Actually these are both true statements. I never implied I know them well or at all. The fact is I just know where they drink. (And when I used to drink there I was very careful backing my car out).

 

[DeathMagus]

But if you both shaft you get half of zero. What is 50% of zero?

You misunderstand. If the other person shafts, you cannot win money, no matter what you do. We can thus disregard those instances, since our strategy will not affect them. The only other scenarios are your opponent sharing and you shafting, or your opponent sharing and you sharing. The former gets you more money.

A table:

                     [FONT=Fixedsys]Opponent:
           [U]  Share  |   Shaft  [/U]
You:  Share|  50%   |    0%   |
           |------------------|
      Shaft|  100%  |    0%   |[/FONT]

Obviously, choosing the shaft row is the wisest option.

 

[InigoMontoja]

You misunderstand. If the other person shafts, you cannot win money, no matter what you do. We can thus disregard those instances, since our strategy will not affect them. The only other scenarios are your opponent sharing and you shafting, or your opponent sharing and you sharing. The former gets you more money.

A table:

                     [FONT=Fixedsys]Opponent:
           [U]  Share  |   Shaft  [/U]
You:  Share|  50%   |    0%   |
           |------------------|
      Shaft|  100%  |    0%   |[/FONT]

Obviously, choosing the shaft row is the wisest option.

That would be wisest if it were a simple matter of probability, but it is not. It is not 50-50 odds because we are not talking about random chance. The best way to guarantee you receiving money is to enter into an agreement to share.

 

[JustMeSee]

Definitely share. I would rather someone else to win than for both of us to walk away with nothing...

 

[DeathMagus]

That would be wisest if it were a simple matter of probability. However the best way to guarantee you receiving money is to enter into an agreement to share.

Barring information the OP doesn't reveal to us (such as your opponent's trustworthiness, or if you have aspirations other than to win the most money possible at the least risk), it is a matter of simple probability.

If (as you assume) your opponent can be trusted, or if (as JustMeSee states) you'd rather your opponent win than either of you be shafted, then the situation changes.

 

[InigoMontoja]

Barring information the OP doesn't reveal to us (such as your opponent's trustworthiness, or if you have aspirations other than to win the most money possible at the least risk), it is a matter of simple probability.

If (as you assume) your opponent can be trusted, or if (as JustMeSee states) you'd rather your opponent win than either of you be shafted, then the situation changes.

Hmmm, so if they do not announce their intention then it is random, but if they do announce their intention then it is not random.

 

[The Nihilist]

clearly you've never seen the game. both people always announce they want to share, and the sneaky one shafts, and he wins.

 

[Beanieboy]

Let me see if I understand this:
YOU THEM
SHAFT SHAFT = you: 0 them 0
SHARE SHAFT = you 0% them 100%
SHAFT SHARE = you 100% them 0
SHARE SHARE = you 50% them 50%

I would say that I would probably shaft. I don't want someone getting 100% because I was a nice guy

 

[IzzyPop]

Game theory says 'shaft'.

 

[mpok1519]

this is like a syndicated gameshow called "Friend or Foe" ; i bet its from the same production studio.

Dont you also have to answer weird trivia to get to the final round though? heh....

....Ill be on jeopardy someday. i hope....

...uh....shaft...no SHAre! no wait! shaft! ah geeze. I dont know, Id just flip a coin and then choose the opposite of what i meant to choose for heads or tails....heh....yeah thats a fifty fifty shot for sure....

 

[cantata]

The problem, though, is that if everyone works it out using game theory, everyone loses.

The original:

http://en.wikipedia.org/wiki/Prisoner's_dilemma

 

[mpok1519]

yeah; if everyone says shaft all the time, the house wins; all they win is housewarming gifts.

 

[cantata]

By the way:

http://www.youtube.com/watch?v=YzZ86GYoxE0

 

[lawtonfogle]

The problem, though, is that if everyone works it out using game theory, everyone loses.

The original:

http://en.wikipedia.org/wiki/Prisoner's_dilemma

Not quite. With the PD, if you fess up, 5 or 0 years, while if you don't you'll be spending 1 or 15 years. So thinking bout it, both fessing (5 years each) is better than not and the other one does (15 years), while in this game, they are both as bad (no money).

 

[yasic]

The correct answer is to shaft... this is obvious from the table brought up earlier in the thread.

If you are playing this game, your only hope is that your opponent is bad at mathematics (or not just studied game theory) and makes the mistake of sharing.


The exception to this rule is if you know your opponent (real life friend) in which case it might be a good idea to share... though there are reasons against that as well.

 

[cantata]

Not quite. With the PD, if you fess up, 5 or 0 years, while if you don't you'll be spending 1 or 15 years. So thinking bout it, both fessing (5 years each) is better than not and the other one does (15 years), while in this game, they are both as bad (no money).

Yes, which makes the PD a far more interesting problem.

Kilroy should take note.

 

[yasic]

The problem, though, is that if everyone works it out using game theory, everyone loses.

The original:

http://en.wikipedia.org/wiki/Prisoner's_dilemma

Prisoners dilemma resembles this game only if you choose to use equilibrium points. However that is a very bad strategy to use.

In other words, there are times in Pris's when it is the right choice to 'share'

In the shaft or share game, unless you physically know your opponent, it is never the right choice to share.