↑ Yosarian2 wrote:
The first thing is that the "breaking stratagy" you're talking about ("lynch non-kings at random without giving scum any information") isn't actually possible. If you're lynching non-kings, then the scum will get information in the process. And you're likely to do worse then random, since the scum can also start wagons.
It is possible. And yes, it gives information -- the information it gives is that the person who was lynched is not the King. 'Cause they're dead. This is not useful information to the Assassin.
The Assassin can start a wagon, and this acts like a second shot for the Assassin -- if he starts a wagon on the King, the town loses, since they won't go through with the lynch (loss), but then the Assassin knows who the King is and can shoot him (loss). This has less of an effect that you might think -- an assassin-started D1 wagon in a 9 player game is only 1/8 to be successful, whereas an assassin-started D5 wagon is 1/4 to be successful -- but there's a 5/7 chance (or thereabouts) that the assassin will be dead before D5. The math balances out surprisingly well.
(This is, however, the reason that any given person is only allowed to start one wagon. Anyone trying to start a second before everyone alive has started one gets lynched.)
Yosarian2 wrote:Second problem is that the more days the game goes before the assassin gets lynched, the worse the odds for the town get. Lynching at random is just a bad idea when you can do better, and you can do better.
The hypothesis isn't that the town can't do better than random lynching (hopefully, the town can; otherwise, we're all deluding ourselves here). The hypothesis is that the town has better than even odds simply *by* random lynching.
I'm not the math whiz that Llamarble is, so I fell back onto my strength: Monte Carlo simulations. You can download the code (executable is in the bin\debug directory)
here. Source is included; it's C#.
It runs through however many games you want, with the following rules:
1) A random person who has not yet lynched is selected to be the lyncher. If everyone has lynched, that flag is reset and everyone can lynch again.
2) A random person is selected to be the lynchee. If the lyncher is not the Assassin, then the lynchee will not be the King.
3) If the King is lynched, Assassin wins.
4) If the Assassin is lynched, they take a shot at a random person that is not themselves. If it's the King, Assassin wins, if it's a Guard, town wins.
5) Otherwise, a Guard was lynched, and the game continues.
There is one other permutation, which I found interesting, which was the Assassin Lynch Day. This is the earliest Day that the Assassin will lynch, if possible (they may be forced to lynch earlier if, eg, everyone else has already lynched). If this is the blank, the Assassin will lynch whenever randomly selected (this is also equivalent to putting in 1). Otherwise, if it's before the Assassin Lynch Day, if they are randomly selected and are not the only viable candidate, someone else will be selected.
Running 1,000 permutations with 9 players gives these win % for the town:
|
| (None) | 60% |
| 1 | 60% |
| 2 | 60% |
| 3 | 61% |
| 4 | 60% |
| 5 | 60% |
| 6 | 63% |
| 7 | 64% |
I'm not infallible, so feel free to examine the provided code, but barring glaring errors being pointed out to me, town wins ~60% just by random lynching. That's a broken game.
