Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby somitomi » Wed Oct 24, 2018 6:39 pm UTC

That was damn cool. Congrats everyone and thanks for replacing, Madge. You were way better than I ever could've.
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Mark_Cangila » Wed Oct 24, 2018 6:41 pm UTC

This game was a lot of fun tbh.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Mark_Cangila » Wed Oct 24, 2018 6:43 pm UTC

Can I post scum qt?

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby LaserGuy » Wed Oct 24, 2018 6:59 pm UTC

@Mark: Maybe wait till bessie can check in. She had mentioned she might want to edit a few posts.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Mark_Cangila » Wed Oct 24, 2018 7:05 pm UTC

Ok

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby moody7277 » Wed Oct 24, 2018 7:13 pm UTC

Lesson 22: If it looks too good to be true, it usually is
Lesson 23: Even Sabrar is fallible (that reads list though)

Madge: very nice on the vig shot for the win.
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Tigerlion wrote:Well, I imagine as the game progresses, various people will be getting moody.


BoomFrog wrote:I still have no idea what town moody really looks like.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby SuperJedi224 » Wed Oct 24, 2018 7:15 pm UTC

Wow

GG guys
My youtube channel.

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Re: Texas Hold'em Mafia (Day 1)

Postby Zenii » Wed Oct 24, 2018 8:07 pm UTC

BoomFrog wrote:
Zenii wrote:
BoomFrog wrote:Wow. That will teach me not to rescind doom.
<3 I was planning for it to be me you and plytho in the end for the ultimate zen-boom showdown.
8-)
That's some serious Hard Mode there, though. You would have NKed Vic and mpolo over plytho? Now Zenii, BoomFrog, Vic would have been a delightful endgame.
Nah, I was hoping they'd be lynched or vigged. I was thinking something like this,

N2
No kill
Jedi vigged

D3
discussion about single kill
madge distrust, moody, distrust, wam distrust
moody lynched

N3
kill wam
mpolo vigged*

D4
this would have been the fun day that everyone turns on each other
vic and plytho would have have likely would have gone after you, i would white knight. not sure what madge would've done.
ideal end of day would be vic lynch

N4
kill Madge
mpolo vigged*

*i'd need to convince madge/town not to vig on one of the days in order to keep the pool open.

zen-boom-vic would have been fun, but I'd have preferred zen-boom-plytho. I have no doubt that you would have eventually come to the conclusion that I was scum. I also couldn't kill you, because if I remained alive while you were dead, town would probably come to the conclusion that I was scum. If I was going to make it, it had to be me vs you in the end. Vic is too swingy. I can never tell if he's going to go with his intuition or not. Even though Vic had suspicions of you, I think you would have had a higher chance of out towning there. I think plytho better reads my mind (and my simulated mind) and I would have been able to form a solid case against you that would have appealed to him in the same way it would appeal to me.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Wed Oct 24, 2018 8:33 pm UTC

Oh wow, amazing. Sabrar nails the scum team with his reads list but then gets caught up linking me with two of them :D :D :D

Yeah, I don't know what I would have thought if I'd been getting to endgame, once moody and SuperJedi went down, I'd have to start getting a hell of a lot more paranoid.

Amazing call by Madge there, saved us so much trouble.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby BoomFrog » Wed Oct 24, 2018 8:38 pm UTC

I nice plan, but D4 would have been the showdown there. My "scum is being too tricky" alarm would have been blaring. Although given the lack of listening to dead town that happens you might have won anyway if you got me lynched D4.
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Wed Oct 24, 2018 9:08 pm UTC

@LaserGuy: sorry for thinking you changed your answer or something, it's just Sabrar sounded so damn certain when he went and reworded my question before it got answered, but I guess that's just Sabrar :D

Setup did seem as if it ended up pretty balanced in how it got drawn, town just happened to immediately start crushing scum apparently.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Wed Oct 24, 2018 9:15 pm UTC

@Sabrar: ha, take that, 99.9% certainty! But really, great job this game, damn. Just wish you'd tunneled on your initial reads list instead of me after I'd roped myself in a bit.

I'm happy that people were predicting me getting dogpiled immediately D2 and that I was able to prove them wrong :P

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby LaserGuy » Wed Oct 24, 2018 9:18 pm UTC

Vicarin wrote:@LaserGuy: sorry for thinking you changed your answer or something, it's just Sabrar sounded so damn certain when he went and reworded my question before it got answered, but I guess that's just Sabrar :D

Setup did seem as if it ended up pretty balanced in how it got drawn, town just happened to immediately start crushing scum apparently.


Yeah, Town was so strong in the day phase this game I don't think that the PR balance likely would have had a big effect unless scum's power was overwhelming. I feel like maybe this setup is a bit swingy if anything... if scum gets off to a bad start they're likely to continue on losing; if Town gets off to a bad start they're likely to continue losing. I may have underpowered scum's PRs a bit by making them Even/Odd/2-shot, but I didn't want to end up with something like Vig + Gunsmith + IC vs. Full roleblock + rolestop, which would be very scumsided IMHO.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby plytho » Wed Oct 24, 2018 9:24 pm UTC

LaserGuy wrote: I feel like maybe this setup is a bit swingy if anything... if scum gets off to a bad start they're likely to continue on losing; if Town gets off to a bad start they're likely to continue losing.
Isn't that somewhat true for most setups?
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Wed Oct 24, 2018 9:30 pm UTC

I think most setups will have somewhat snowballing effects anyway just because of a loss losing a PR randomly is. Stuff like a tracker definitely steps up a LOT in power once there's only 1 scum left (though gunsmiths seem way more useful in general). Unless you take specific countermeasures (like, I think last year's Halloween game?), setups will always be swingy. And if you do put in countermeasures, it can feel bad because you can feel like you're getting punished for doing well.

Ninja'd yup :)

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Wed Oct 24, 2018 9:33 pm UTC

plytho wrote:Also, I almost counterclaimed BoomFrog. Good thing I checked my role pm again.


I'm wondering what would have been going through your head as you counterclaimed a vanilla role, while knowing scum has safe claims :P

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Madge » Thu Oct 25, 2018 8:28 am UTC

All credit to sabrar. I copied my vig list from his reads post. Wasn't able to properly read the thread. Figured sabrar was killed for a reason and he's confirmed town! Absolutely thrilled I was able to bring town to a win by playing my way :lol:

Take that everyone who says I need to play better! You are already gazing upon perfection :lol:
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Thu Oct 25, 2018 10:05 pm UTC

I do find it funny that you copied the list from his initial reads, and not his later reads or even his explicit instructions for PRs. Oh well, worked out well :D

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Madge » Thu Oct 25, 2018 10:13 pm UTC

Honestly it's because I was in a hurry so I grabbed the first one I found. :oops:

I am now off work but also away from computers until Monday.
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Zenii » Fri Oct 26, 2018 1:38 am UTC

I had a feeling that might happen.

Scum qt

Vic and Sabrar, do you think you could walk us/me through how you came by the probabilities on the first page?

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Fri Oct 26, 2018 1:58 am UTC

Oh, the first page?

Well, it's not pretty to do it analytically because of the condition that there needs to be more town PRs than scum PRs. Sooooooo I just made up a MATLAB script that drew 9 numbers from 1-39 (for town) and 3 from 1-13 (for scum), without replacement. Any town number from 1-12 was a PR and a scum number from 1-4 was a PR. Then, if there were more town PRs than scum PRs, I chucked that simulation out. Then, ran it 10^5 times, and just looked out how often each thing happened.

Basically just brute forced the problem :P

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Fri Oct 26, 2018 2:00 am UTC

That should be kept the run, not chucked out. Chucked it out if no of scum PRs was greater or equal to town PRs.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Fri Oct 26, 2018 2:28 am UTC

@Zenii: ha, I thought after you posted that very silly response to me arguing probabilities with Sabrar that you weren't keeping up with the discussion, but you DO know your conditional probabilities after all :lol:

@bessie: as I said in thread, I thought Sabrar's reason for reading you as scum was pretty bogus as well, but that just made him read us as scum buddies harder so I don't know :?

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Zenii » Fri Oct 26, 2018 4:25 am UTC

Vicarin wrote:Oh, the first page?

Well, it's not pretty to do it analytically because of the condition that there needs to be more town PRs than scum PRs. Sooooooo I just made up a MATLAB script that drew 9 numbers from 1-39 (for town) and 3 from 1-13 (for scum), without replacement. Any town number from 1-12 was a PR and a scum number from 1-4 was a PR. Then, if there were more town PRs than scum PRs, I chucked that simulation out. Then, ran it 10^5 times, and just looked out how often each thing happened.

Basically just brute forced the problem :P
I tried doing something similar, but I think I messed up somewhere. Also I was doing it on a calculator and only had enough memory for about 10,000 sims. What do you think is the/how do you determine the minimum runs necessary to get an accurate picture?
Vicarin wrote:@Zenii: ha, I thought after you posted that very silly response to me arguing probabilities with Sabrar that you weren't keeping up with the discussion, but you DO know your conditional probabilities after all :lol:
I have a basic understanding, but I don't think I'm anywhere near comprehending you and Sabrar's argument. I want to learn though!

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Sabrar » Fri Oct 26, 2018 4:30 am UTC

Zenii wrote:Vic and Sabrar, do you think you could walk us/me through how you came by the probabilities on the first page?
Used the hypergeometric distribution function in Excel to get the probability of each case separately (product of 2 hypgeom.dist functions as spades are drawn independently). Discarded the scum>=town results and reweighted the remaining probabilities to total up to 100% once again.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Fri Oct 26, 2018 4:40 am UTC

@Sabrar: Guess that works too. Also reassuring my numbers matched so I probably didn't mess up massively.

@Zenii: Minimum runs necessary is just however many you can run until the numbers stop changing significantly. For example, you can do a sample of samples (run 10^5 times 10 or so times) to get a tough idea of how much the results are varying between those big runs. That can give you a good estimate for your error from such a method. I was happy with that many runs because the results seemed accurate to about 0.1% or so.

My argument about the vig situation was actually pretty similar to your example in the scum chat too. I was saying that if you're dealt a King, the chance of being in a setup where there's more than 1 King increases significantly because you're more likely to be dealt a King in a setup with multiple Kings.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby BoomFrog » Fri Oct 26, 2018 2:41 pm UTC

Zenii wrote:-boom i don't think we share the same reasoning for plytho, im curious about what it is you can "see"
Ah see, I was disappointed we didn't debate more finer points like this. I thought it was a combination of RL time limits and wakizashi style, but no, it was that you were scum and putting half your thoughts in scum chat. And probably didn't want to really engage me.

Anyway, I was thinking scum generally don't want to declare townie's definitely town as that limits their options later. Plytho is generally cautious and might stick to that generic scum behavior.
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby LaserGuy » Fri Oct 26, 2018 4:15 pm UTC

Scum chat is here.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Zenii » Sat Oct 27, 2018 1:55 am UTC

Vicarin wrote:My argument about the vig situation was actually pretty similar to your example in the scum chat too. I was saying that if you're dealt a King, the chance of being in a setup where there's more than 1 King increases significantly because you're more likely to be dealt a King in a setup with multiple Kings.
Are you sure that would apply in this situation? How would it be different from say dealing three cards out randomly three people. If person 1 received a King, that wouldn't change the probability that person 2 and 3 received a King would it?

BoomFrog wrote:
Zenii wrote:-boom i don't think we share the same reasoning for plytho, im curious about what it is you can "see"
Ah see, I was disappointed we didn't debate more finer points like this. I thought it was a combination of RL time limits and wakizashi style, but no, it was that you were scum and putting half your thoughts in scum chat. And probably didn't want to really engage me.

Anyway, I was thinking scum generally don't want to declare townie's definitely town as that limits their options later. Plytho is generally cautious and might stick to that generic scum behavior.
Ah, I see. I usually declare people town because it's the easiest way to look like you're actually thinking about people's alignment.

I genuinely was busy and intended to more minimal (and intend to in the future) regardless of alignment. That being said, there were so many times I had to stop myself from buddying you. I didn't want you to think I was being Boom-from-crossover.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Sat Oct 27, 2018 2:54 am UTC

Zenii wrote:
Vicarin wrote:My argument about the vig situation was actually pretty similar to your example in the scum chat too. I was saying that if you're dealt a King, the chance of being in a setup where there's more than 1 King increases significantly because you're more likely to be dealt a King in a setup with multiple Kings.
Are you sure that would apply in this situation? How would it be different from say dealing three cards out randomly three people. If person 1 received a King, that wouldn't change the probability that person 2 and 3 received a King would it?


So, the interesting thing is that it does, very slightly, compared to how the probabilities are before looking at any card, if you know someone got dealt a King. Kings get removed from the deck as they get dealt to people, reducing the probability that other people will get them, but observing a King for your own card increases the likelihood that other people have Kings, because you're more likely to have a King when there's lots of Kings out there.

For a toy example, consider a deck that consists of 8 cards, where there's 2 Kings and 6 other cards, and there's 2 people. If we use K for king, and O for other, the deals are, for (you, other person):

KK: (1/4)*(1/7) = 1/28
KO: (1/4)*(6/7) = 6/28
OK: (3/4)*(2/7) = 6/28
OO: (3/4)*(5/7) = 15/28
and that all adds up to 1, so all good so far.

Now, say we want to do something similar to what Sabrar wanted to do. If we know there's at least 1 King in the game' (which was the assumption made because otherwise there's no vig to make the decision to shoot or not), then we can remove the OO situation, and conclude that there's a 1/13 chance (after normalizing it) of there being 2 Kings. However, we can do better than that, because we can look at our own card. If it's a King, then we know that the OK situation is impossible (because we've got a King), and then conclude that now that we've seen our card, that the probability of the KK situation is actually 1/7, which is significantly higher (and exactly what you'd expect from the probability of the other person being dealt a lone K out of a deck of 7 remaining cards, once you've been dealt the first King).

My original point was in response to:

Sabrar wrote:
Vicarin wrote:Actually, yeah, how did you come to that conclusion exactly Sabrar? I can't see how it matches up with the probabilities we both posted.
Why not? How would you go about and calculate this? Because I have exact probabilities based on hypergeometric distribution and those give a ~15% chance of there being at least 2 Vig-s, after which it's pretty easy to solve for 0.85*p + 0.15*(2*p2+2p*(1-p))=1


I pointed out that the probabilities needed to be updated, and then Sabrar said

Sabrar wrote:@Vicarin: if we have 0 Vig-s in the game than the actual number doesn't matter at all. Therefore I don't have to look at my card to calculate odds because I'm already assuming that we have at least 1.


Which is incorrect, otherwise the probability in the above example would be 1/13 for KK, after seeing your own card. (I'm assuming that the combination of statements meant that Sabrar renormalized the numbers and got ~85% 1 vig, 15% 2 or more vigs, after assuming that there's at least 1 vig, so I was arguing on that basis).

Of course, when there's a bunch more people, the calculations become more involved, because when you look at your own card and see a non-King, that doesn't completely rule out there being more than 1 King among other people, but it does provide evidence for it (because if there's a ton of kings in circulation, you probably would have gotten dealt one). So if you want to crunch the numbers then, it's probably best to just pull out Bayes' Theorem instead of trying to cover every single case specifically.

If you want a really extreme example, you can even say LaserGuy had different decks to draw upon. Say he said there were two setups for 9 town, that he's going to randomly select between:

1. Town gets dealt cards from a deck with 1 King and 8 non-kings
2. Town gets dealt cards from a deck with 8 Kings and 1 non-king (putting aside the issue of having 8 different kings).

You know that at least one person got a King in each possible setup, so we can then ask the questions:

How many Kings on average are there in the game before you look at your card?

You look at your card, and it's a King. How many Kings on average are there in the game now?

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Zenii » Sat Oct 27, 2018 3:33 am UTC

Wow, insane. Probability is insane.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby BoomFrog » Sat Oct 27, 2018 3:48 am UTC

Your last example is a very different situation, so let's stick to your 2 player 8 cards example and the real game example.

Having a king tells you only that other people don't have that king. There is not a higher chance that others are a king, there is actually a lower chance because you have one of the Kings.

The order of the deal doesn't matter. Everyone getting a card first then you get delt last, and you getting delt first both have the same chance that you get a King.

Having a king does increase the chance that you are in a game with multiple Kings. Of course it does. You being a king went from 4/52 to 1/1 so that raises the chances of a multi king game. But you having a king Decreases the chances that others are a king, because before it was 4/52 and now it's 3/51. (you need to use hypergeometric distribution to calculate the chance of multiple other players).

So I think Vic is understanding the probability, but (as usual) is misunderstanding/Misscommunicating with others.

@Zen: Having few dimond safe claims does increase the chance that town has more dimonds, but only by the amount that that you would calculate if you took all the cards you didn't have as safe claims and delt them to the town. However, every card you didn't have on the safe claim list was equally likely, so claiming a dimond is not more dangerous then any other unknown card.

The important thing to remember is that the order of a deal doesn't matter. If I get delt first, but I get the second card in the deck and then you get the first card, did what I get affect your deal?
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Sat Oct 27, 2018 4:11 am UTC

Yeah, I know that there's those two different effects. I'm arguing that Sabrar, in his statement, took into account the decreasing chances due to Kings getting removed from the deck as they get dealt to other people (because that's the whole point of using the hypergeometric distribution), but failed to take into account the information that people dealt kings have (that is, they have a King in front of them). Hence, Sabrar was underestimating the probability of being in a multi-king game for people who'd seen that their own card was a King.

In the first example I gave, if you take into account the first effect but not the second, you end up with the 1/13 chance, but if you take into account both, you get the 1/7 chance.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Sat Oct 27, 2018 4:19 am UTC

Half the issue is because very similar sounding questions have very different answers and different implications on the game state.

If you ask "How likely is it that there's at least two Kings in this game, given that there's at least one King?", it's got a different answer to "How likely is it that there's at least two Kings in this game, given that I am a King?". I'm saying Sabrar said he answered the second (because it's what you want the vigs to know when deciding whether to fire or not), but gave the reasoning for answering the first.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Sat Oct 27, 2018 5:25 am UTC

Bleh, went back to my model and checked with for the explicit answers for the setup:

There's a ~60% chance of there being at least 1 King drawn in a setup that isn't rejected.

There's an average of ~0.78 Kings in all non-rejected setups, and an average of ~1.27 in those non-rejected trials that have at least 1 King. As required, 0.78/1.27 is approximately 60%.

Out of the trials where there's at least 1 King, ~75% have 1 King, ~23% have 2 Kings, and ~2% have 3 Kings (I have no idea where Sabrar's 15% number came from now...)

If you look at your card and have a King, then you're in a 1 King setup ~60% of the time, a 2 King setup ~36% of the time, and a 3 King setup ~4% of the time, with a mean of ~1.44 kings. If you want to have an average of 1 person fire on N1, then you use these numbers, not the ones in the previous paragraph.

Hopefully Sabrar can agree with these :P

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Sabrar » Sat Oct 27, 2018 6:27 am UTC

I don't have my spreadsheet anymore but the whole discussion is pointless because town should never post numbers based on their own card as that explicitly tells scum whether they are PR. I'm surprised this didn't occur to you during the game.

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby Vicarin » Sat Oct 27, 2018 6:32 am UTC

That's why I posted probabilities during the game from both PoVs, for exactly that reason. In my first post. So yes, it did occur to me.

Hell, you were the one giving the PRs the instructions to begin with, I don't know why making sure the instructions are correct is such an issue :P Also, giving the instructions doesn't say anything about whether they're a PR or not (we were both vanilla and all).

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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby LaserGuy » Sat Oct 27, 2018 7:08 am UTC

You guys have put way more thought into the probabilities than I ever did :P

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bessie
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Re: Texas Hold'em Mafia (Day 3 - An Unexpected Twist)

Postby bessie » Sat Oct 27, 2018 7:30 am UTC

I am rather enjoying this argument discussion.

I’m working on my shout outs/feedback. I will try to have have something tomorrow!


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