Forum Competition - International Maths Day 2023

[Argo]

The Consultant has once again consulted... it would seem he doth not agree with you Dez ..
Please keep in mind here I am mere envoy lol


Dez is wrong. Jim shooting does not change whether he will survive or not. If he shoots, he will die. If he doesn't shoot, he will die (killed in the last round). Thus it is not counter to his wish to survive. His only choice is whether or not he takes someone with him. And since he wants the others to die, Jim's best choice is to shoot one of the others. Since he hates them equally much, it's equally probable that he will shoot Jack and John.

This effect is often called "kingmaker" in multiplayer games. One player may see that he has no chance of winning the game, yet he can decide which of the other players will win

Your consultant is wrong.

Actions taken that you know will result in your death is directly contrary to the want to live.

Furthermore, the Kingmaker effect is moot here as the scenario states that they want the others dead, but they want to survive. The characters wanting the others to die negates allowing someone they want dead to live, while they themselves die. You can't say that these are the rules and then ignore them in the answer.

THE CONSULTANT REPLIES:


Consider two buttons. You have to press one of them. Press button A, and you (and only you) will die. Press button B, and you plus one of the other pirates will die. Which button will you push? Not pushing any will lead to you (and only you) dying, which is equivalent to pushing button A.

In the duel, deliberately missing every shot is pressing button A. Firing at one of the other pirates is pressing button B.

Since every pirate wants to survive, but also wants the others to die, one can rate the possible outcomes like this:

A) Survive, and both the others die.
B) Survive, and one of the others die.
C) All three survive.
D) All three die.
E) You and one of the others die.
F) Only you die.

To Jim, the only possible outcomes are the two worst, E and F. E is preferable to F, so he will chose E over F. Jim has no option that will lead to another outcome than E or F.

[DezNutz]

Your consultant is wrong.

Actions taken that you know will result in your death is directly contrary to the want to live.

Furthermore, the Kingmaker effect is moot here as the scenario states that they want the others dead, but they want to survive. The characters wanting the others to die negates allowing someone they want dead to live, while they themselves die. You can't say that these are the rules and then ignore them in the answer.

THE CONSULTANT REPLIES:


Consider two buttons. You have to press one of them. Press button A, and you (and only you) will die. Press button B, and you plus one of the other pirates will die. Which button will you push? Not pushing any will lead to you (and only you) dying, which is equivalent to pushing button A.

In the duel, deliberately missing every shot is pressing button A. Firing at one of the other pirates is pressing button B.

Since every pirate wants to survive, but also wants the others to die, one can rate the possible outcomes like this:

A) Survive, and both the others die.
B) Survive, and one of the others die.
C) All three survive.
D) All three die.
E) You and one of the others die.
F) Only you die.

To Jim, the only possible outcomes are the two worst, E and F. E is preferable to F, so he will chose E over F. Jim has no option that will lead to another outcome than E or F.

Option D All 3 die is improbable. Thus not a possibility. Thus proving your consultant is an idiot.

There are only 3 Outcomes.

1. Everyone survives.
2. 2 People Survive
3. 2 People Die

Option 3 requires self-sacrifice (accepting that you will die by killing someone first). Which is contradictory to the rule that everyone wants to live.

You can't apply the rule that all players want to live and then negate it in the answer.

Using your logic. John and Jack would deduce that Jim would do E since that's his best scenario, thus one of them is going to die when Jim's turn comes around. Thus one of them dying is guaranteed. So dying is acceptable as long as they kill the other (Jim's Scenario). Thus Jack would not shoot, John would shoot Jim, and Jack would then shoot John. OR Jack would shoot Jim, and John shoots Jack. As not shooting Jim gives them a 50% of dying without killing another.

But that also flies into the problem of negating the statement that they also want to live.

[Most Lee Harmless]

If they all want to live the optimum solution for all three is not to fire their guns at all... or is that too logical an answer?

[Henry Avery]

but that doesn't solve the issue of how to divvy up the plunder!

[DezNutz]

If they all want to live the optimum solution for all three is not to fire their guns at all... or is that too logical an answer?

That would be the absolute logical answer if only living was the consideration, but the scenario states that they want to kill the other while also wanting to stay alive. So you have to consider how can they kill the others without themselves being killed. It leaves only one logical answer.

[Argo]

Your consultant is wrong.

Actions taken that you know will result in your death is directly contrary to the want to live.

Furthermore, the Kingmaker effect is moot here as the scenario states that they want the others dead, but they want to survive. The characters wanting the others to die negates allowing someone they want dead to live, while they themselves die. You can't say that these are the rules and then ignore them in the answer.

THE CONSULTANT REPLIES:


Consider two buttons. You have to press one of them. Press button A, and you (and only you) will die. Press button B, and you plus one of the other pirates will die. Which button will you push? Not pushing any will lead to you (and only you) dying, which is equivalent to pushing button A.

In the duel, deliberately missing every shot is pressing button A. Firing at one of the other pirates is pressing button B.

Since every pirate wants to survive, but also wants the others to die, one can rate the possible outcomes like this:

A) Survive, and both the others die.
B) Survive, and one of the others die.
C) All three survive.
D) All three die.
E) You and one of the others die.
F) Only you die.

To Jim, the only possible outcomes are the two worst, E and F. E is preferable to F, so he will chose E over F. Jim has no option that will lead to another outcome than E or F.

Option D All 3 die is improbable. Thus not a possibility. Thus proving your consultant is an idiot.

There are only 3 Outcomes.

1. Everyone survives.
2. 2 People Survive
3. 2 People Die

Option 3 requires self-sacrifice (accepting that you will die by killing someone first). Which is contradictory to the rule that everyone wants to live.

You can't apply the rule that all players want to live and then negate it in the answer.

Using your logic. John and Jack would deduce that Jim would do E since that's his best scenario, thus one of them is going to die when Jim's turn comes around. Thus one of them dying is guaranteed. So dying is acceptable as long as they kill the other (Jim's Scenario). Thus Jack would not shoot, John would shoot Jim, and Jack would then shoot John. OR Jack would shoot Jim, and John shoots Jack. As not shooting Jim gives them a 50% of dying without killing another.

But that also flies into the problem of negating the statement that they also want to live.

'Option D All 3 die is improbable. Thus not a possibility. Thus proving your consultant is an idiot.

Now, now.. no need for name calling. This isnt Union of Honor. Thank you.

THE CONSULTANT REPLIES

The point is that Jim does not reduce his chance of surviving by shooting one of the others. It is zero either way. Jack and John, however, would reduce their chance of surviving from 50% to 0% by shooting at one of the others (except John in the final round, when he can safely shoot Jim). And THAT would run counter to the fact that they want to survive.

If Jim somehow reduced his chance of surviving by shooting one of the others, then he would not do it. However, he does NOT reduce his chances of surviving, as his chances of surviving is 0 whatever he does

[Dmanwuzhere]

[DezNutz]

'Option D All 3 die is improbable. Thus not a possibility. Thus proving your consultant is an idiot.

Now, now.. no need for name calling. This isnt Union of Honor. Thank you.

THE CONSULTANT REPLIES

The point is that Jim does not reduce his chance of surviving by shooting one of the others. It is zero either way. Jack and John, however, would reduce their chance of surviving from 50% to 0% by shooting at one of the others (except John in the final round, when he can safely shoot Jim). And THAT would run counter to the fact that they want to survive.

If Jim somehow reduced his chance of surviving by shooting one of the others, then he would not do it. However, he does NOT reduce his chances of surviving, as his chances of surviving is 0 whatever he does

It's not name calling.

It doesn't matter that Jim is guaranteed to die. The scenario laid out was specific. You can't negate terms of the scenario so the consultants answer is correct.

"The pirates want to kill the others, but also want to live." That has a specific meaning. IE. They won't shoot another pirate if it allows the remaining pirate to shoot them.

There were no added circumstances or caveats to that statement. Thus you can't apply, well since Jim will die regardless he then will kill first since he will be killed anyway.

[PFH]