This inherently assumes the executioner was in cahoots with the judge beforehand through day PMs. Obviously, if the judge proposes this at the last minute, then it's not going to effective. Also, people are biased towards SK during endgame. If this were a game where executioner needed to survive until the end of the game, I could see it working. But in most cases where they don't, I believe it's a better idea to do the Monty Hall technique assuming SK and GF are familiar with it.
Breakdown under Monty Hall, assuming execution sides with SK by default:
1. SK knows GF
- SK kills Judge to win
2. SK doesn't know GF
- GF kills exec 67-100% of the time, SK kills exec 67% of the time, Judge wins anyway
So if SK doesn't know GF and you've been keeping track, Monty Hall solution is the way to go. If SK knows GF, then I'd use your solution.
This inherently assumes the executioner was in cahoots with the judge beforehand through day PMs. Obviously, if the judge proposes this at the last minute, then it's not going to effective. Also, people are biased towards SK during endgame. If this were a game where executioner needed to survive until the end of the game, I could see it working. But in most cases where they don't, I believe it's a better idea to do the Monty Hall technique assuming SK and GF are familiar with it.
Breakdown under Monty Hall, assuming execution sides with SK by default:
1. SK knows GF
- SK kills Judge to win
2. SK doesn't know GF
- GF kills exec 67-100% of the time, SK kills exec 67% of the time, Judge wins anyway
So if SK doesn't know GF and you've been keeping track, Monty Hall solution is the way to go. If SK knows GF, then I'd use your solution.
- Exec will side with SK simply because winning as SK is much more respected and harder
- You don't know who anyone is
Then you'd simply night talk that you're the judge and will side with whomever kills the exec. In fact, this is a good opportunity to tell GF and SK to choose first, reveal that you're judge, and then convince them to switch to the other and abuse Monty Hall's problem. Monty Hall's problem works like this:
1. You choose one of three doors (1 door has a car, 2 doors have goats)
2. Host chooses a door with goats and opens it and asks you if you want to switch
3. By probability complement without the information of #2, the probability of you choosing a goat door was initially 2/3 so by switching, you're more likely to hit the exec (2/3) so the chances of exec not dying are (1/3)*(1/3) = (1/9) = 11%
So assuming everyone is knows the Monty Hall problem including SK not realizing it's in his best interests not to kill Judge, then he'll aim for the exec too since both SK and GF have a 2/3 chance each of winning. And you'd automatically win by removing yourself from that equation by exploiting game theory of Monty Hall problem.
Of course, people are emotional, so what will end up happening is classical probability anyway where you only have a 44% chance of living by random choice.
Specifically, what matters is whether judge lives or dies. Assuming GF and SK don't know each other's identities, then by classical probability:
- Exec will side with SK simply because winning as SK is much more respected and harder
- You don't know who anyone is
Then you'd simply night talk that you're the judge and will side with whomever kills the exec. In fact, this is a good opportunity to tell GF and SK to choose first, reveal that you're judge, and then convince them to switch to the other and abuse Monty Hall's problem. Monty Hall's problem works like this:
1. You choose one of three doors (1 door has a car, 2 doors have goats)
2. Host chooses a door with goats and opens it and asks you if you want to switch
3. By probability complement without the information of #2, the probability of you choosing a goat door was initially 2/3 so by switching, you're more likely to hit the exec (2/3) so the chances of exec not dying are (1/3)*(1/3) = (1/9) = 11%
So assuming everyone is knows the Monty Hall problem including SK not realizing it's in his best interests not to kill Judge, then he'll aim for the exec too since both SK and GF have a 2/3 chance each of winning. And you'd automatically win by removing yourself from that equation by exploiting game theory of Monty Hall problem.
Of course, people are emotional, so what will end up happening is classical probability anyway where you only have a 44% chance of living by random choice.
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