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ZFR: And since an odd number of player gives better odds
That's a very funny pun by the way. I know my posts are usually hilarious, but sometimes I even surprise myself.
Post edited April 15, 2021 by ZFR
^Sorry dedo :(

I wrote a longish post in answer to Flocke explaining the maths in more detail, then meant to quote myself and ended up editing.

Maybe it's a sign...
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ZFR: Maybe it's a sign...
Positive or negative?
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Bookwyrm627: Vote Catte.

I'm pretty sure he's a killer.
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my name is capitayn catte: Mutiny! Throw this man in the brig at once.
And I was right that time too!
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ZFR: ^Sorry dedo :(
I'll let you off with a warning this time but please make sure it doesn't happen again.
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ZFR: ^Sorry dedo :(
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dedoporno: I'll let you off with a warning this time but please make sure it doesn't happen again.
No more self quote. Promise.

I'm sad that post is gone. You spend a long time explaining, and it just disappears :(
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Lifthrasil: nmillar, the game has started! This is your 9 o clock waking call!

vote nmillar
Sorry, was having vivid dreams about being banned from the forum.
OK, a shorter quick version of what I wrote before that was lost.


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FlockeSchnee: Because going with a no-NK wouldn't make sense for the Mafia team?
Yes, this works off the assumption that there is always exactly one NK every Night. This means that even number of players will remain even and odd will remain odd. And if we have an even number of players we should use NL to change it to odd, which gives us better odds without reducing the number of lynch-attempts that we have.

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FlockeSchnee: Generally, or just in this setup?
In any setup where there is a guaranteed odd number of NKs every Night. So nothing that can cause 0 NKs (Doctor, Blocker...) and nothing that can cause 2 NKs (Vig, Serial Killer...). In all setups where this is not guaranteed (including all closed setups), NL is very bad because we could potentially be wasting a valuable lynch-attempt:

e.g. (Good NL)
5 vs 1 - we have 2 lynch attempts before it's game over. If we first go NL and one person dies in the Night, then it's 4 vs 1 next Day and we still have 2 attempts with slightly better odds.

but

(Bad NL)
5 vs 1 - we have 2 lynch attempts. If we go NL and two[ people die in the Night, then it's 3 vs 1 next Day and we only have 1 attempt left. Our NL wasted an attempt.

OR

(Bad NL)
5 vs 1 - we have 2 attempts. We use up one (mislynch), but during the Night the Doctor saves us and no NK takes place. Next Day it's 4 vs 1 which means we still have 2 attempts (3 total).
5 vs 1 - we 2 attempts. We NL, Doctor saves at Night, and it's 5 vs 1 next Day. We still have 2 attempts; the potential extra attempt that Doctor's save could have given us got wasted.

In both those later cases NL was a terrible decision. We got less attempts than we'd have gotten otherwise.


---------------------------------

And finally

Since NK is not compulsory, then depending on a payout from a Draw, a single-NK-setup like this one with an even number of players can be game over immediately with an nevereding NL-noNK-NL-noNK... cycle. e.g. 3T vs 1M game. Town should NL to increase their chances from 25% to 33%, but then Mafia doesn't NK to keep those chances at 25%. If neither team budges, the game ends in a draw. This leads to an interesting quasi paradox, where it's better for Mafia's overall expected payout to have smaller payouts for both win and draw. See posts 51 and 58 here:
https://www.quicktopic.com/53/H/e29TzE9YP6Ra
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ZFR: OK, a shorter quick version of what I wrote before that was lost.

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FlockeSchnee: Because going with a no-NK wouldn't make sense for the Mafia team?
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ZFR: Yes, this works off the assumption that there is always exactly one NK every Night. This means that even number of players will remain even and odd will remain odd. And if we have an even number of players we should use NL to change it to odd, which gives us better odds without reducing the number of lynch-attempts that we have.
No, it doesn't. We don't have better odds if we give scum a free kill. Reducing the number of Townies by one may not change your EV calculation. But it still means one Townie less. Which means that the influence of the scum team is relatively speaking slightly larger.

It is nice that we can afford NL. But we should only do that intentionally if we have something to gain from it or if it happens naturally because we can't agree on a lynch. That is always a danger, so wasting that one NL intentionally would be stupid. I'd like to keep it as a buffer and prefer to take the chance of gettig scum over doing nothing.
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FlockeSchnee: So far, consensus on mafia-day-chat seems to be: Very useful. At least if "utilized right".
The lesson I get from that is: Win - Loose - it depends on which side plays better. Like always.
Soooo, those numbers... It's some elaborate initiation rite for mafia players that has to be applied x number of times until one can become/be considered a "full member" or something, right? You can tell me.

This Nash equilibrium... it's your favourite isn't it? Because I'm fairly certain I did nothing to encourage anyone to throw mathematical calculations at me.
Those math numbers are ZFR being ZFR, not anything to do with being a better mafia player--or so I tell myself, and I've been playing in most of the last 12 games.
I think ZFR is a statician or a math prof or something. So is either Catte or Flubbucket, but I don't recall whom. (Sorry fellas!)
Sometimes they get in a little corner here in chat and just toss numbers back and forth and I feel like I'm the center in the children's game "monkey in the middle/keep away" https://en.wikipedia.org/wiki/Keep_away I've gotten used to it.

The only reason I try sometimes to follow their mathiness in in case they are trying to slip one over on the rest of us by stating some complicated thing knowing that we'll go "more math....yeah, it's prob correct, so I'll take it at face value and skip the post..."

:D
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Lifthrasil: No, it doesn't. We don't have better odds if we give scum a free kill.
Yes it does. "Odds" in this case meaning mathematical odds of firing blindly increase from 2/10 to 2/9.

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Lifthrasil: That is always a danger, so wasting that one NL intentionally would be stupid. I'd like to keep it as a buffer an.
We are not "wasting" one NL in this setup. The number of kills we have remains same. But I'm not going into that discussion again. I said I won't push for NL and I'm leaving it at this.
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Lifthrasil: No, it doesn't. We don't have better odds if we give scum a free kill.
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ZFR: Yes it does. "Odds" in this case meaning mathematical odds of firing blindly increase from 2/10 to 2/9.

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Lifthrasil: That is always a danger, so wasting that one NL intentionally would be stupid. I'd like to keep it as a buffer an.
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ZFR: We are not "wasting" one NL in this setup. The number of kills we have remains same. But I'm not going into that discussion again. I said I won't push for NL and I'm leaving it at this.
OK yes. The 'dumb luck' chance for firing blindly increases with less Townies. Still not a good way to play the game.

And you misunderstood what I meant with wasting the NL: we have leeway for ONE no-lynch, without decreasing the number of Days we have. Not more. No-lynches happen sometimes and it is nice that in this game we won't lose a Day if that happens. However, if we no-lynch intentionally, we don't have that leeway anymore and if then, for any reason, another no-lynch happens, we lose a Day (and go back to an even number of players).

So, let's keep the safety net of 'a no-lynch won't hurt us'. Throwing that safety away would hurt Town.
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Lifthrasil: And you misunderstood what I meant with wasting the NL: we have leeway for ONE no-lynch, without decreasing the number of Days we have. Not more. No-lynches happen sometimes and it is nice that in this game we won't lose a Day if that happens. However, if we no-lynch intentionally, we don't have that leeway anymore and if then, for any reason, another no-lynch happens, we lose a Day (and go back to an even number of players).

So, let's keep the safety net of 'a no-lynch won't hurt us'. Throwing that safety away would hurt Town.
OK, fair enough.
I think when Town are moronic enough to end the Day on a No-Lynch when they shouldn't, then they deserve all the bad consequences. But it does happen here often enough on GOG, so let's keep that free NL as a safety net.
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Microfish_1: I love this comment. I feel the same way about any of the higher maths.
I imagine that Day chat could be very useful.
and
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GymHenson: But nah, yer cool for now.
Enter eye twitching somewhat frantically here. Are you Mafia?

@Micro: My use of "higher maths" is probably just plain wrong. Maybe something like "slightly more advanced then just the basics maths" would be right, but it sounds awful.


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Microfish_1: @mod Where is the controls for this engine? Where was part 1?
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dedoporno: Yes, they are. I hope this covers your questions.
And I almost trusted you. Almost.



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Pookina: >random.org
>min 1 max 10
>1
>participants list says ZFR

vote zfr

ironic
What irony?

" >random.org"
Are you the new old ZFR? My memory insists on having read, that he used to get his votes from there in the past. ... Oh, is that the irony?


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FlockeSchnee: What's waffles code for? Secret math problems: The next level?
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Bookwyrm627: Waffling back and forth. Leaning one way, then the other, etc.
Interesting turn of phrase. One never stops learning. And it's ok, you don't have to admit to your future crimes. - Your partner cracked under the pressure.


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Bookwyrm627: Vote Catte.
I'm pretty sure he's a killer.
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my name is capitayn catte: Mutiny! Throw this man in the brig at once.
I knew it! Well, that was a fast game. On the bright side, if a new one starts right away I can probably squeeze it in. - Bright side for me, I mean.
No sense in holding back now though. You ate the real captain, didn't you?
There's only one name that I don't recongnise in the participants list, so I think that's a good enough RVS as any.

Vote FlockeSchnee