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### AuthorTopic: Apparently this is where people talk when it's night  (Read 102026 times)

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#### Jimmmmm

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##### Re: Apparently this is where people talk when it's night
« Reply #2350 on: January 25, 2020, 10:36:47 pm »

Even if you've just flipped 10 heads in a row, the next one is still 50/50 if it's a fair coin.
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#### sudgy

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##### Re: Apparently this is where people talk when it's night
« Reply #2351 on: January 26, 2020, 03:22:58 am »

That line of thinking is a classic example of the gambler's fallacy.  The probability of getting two heads in a row is 25% before you flip the first time.  At any time, when you flip a [fair] coin, no matter the circumstances, the probability is 50%.
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#### silverspawn

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##### Re: Apparently this is where people talk when it's night
« Reply #2352 on: January 26, 2020, 05:24:02 am »

That line of thinking is a classic example of the gambler's fallacy.  The probability of getting two heads in a row is 25% before you flip the first time.  At any time, when you flip a [fair] coin, no matter the circumstances, the probability is 50%.

Yes.

The reason that flipping heads twice in a row is unlikely is not that heads is unlikely on any one flip. Rather, when you flip two coins, you have the four possibilities (heads, heads) and (heads, tails) and (tails, heads) and (tails, tails). All of those are equally likely, but because only one of them has two heads and two of them have one of each, it's twice as likely to have one of each.
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#### Awaclus

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##### Re: Apparently this is where people talk when it's night
« Reply #2353 on: January 26, 2020, 10:01:45 am »

Rather, when you flip two coins, you have the four possibilities (heads, heads) and (heads, tails) and (tails, heads) and (tails, tails). All of those are equally likely

And notably, when you flip a coin for the first time and look at the result, two of those possibilities are eliminated, which leaves you with two possibilities, both of which are still equally likely.
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2354 on: January 26, 2020, 07:42:38 pm »

Three years ago

Ash: “hey, it’s it 50/50 every coin flip no matter what?”
Everyone: “no dummy, it’s only 1/4 to go heads twice!”
Ash: “but, each time I flip a coin...seems like there are only two outcomes?”
Everyone: “nope! Probability man!”
Ash: “okay, I’m a math dope so okay.”

Three years later

Ash: “hey, since most people think it’s 50/50 every time you flip a coin, can’t we exploit that with this probability stuff?”
Everyone: “no dummy, every time you flip a coin it is 50/50.”

Argh.
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2355 on: January 26, 2020, 07:47:42 pm »

I thought that for any set of two coin flips, there are four outcomes.
If there are four distinct outcomes, there is a 1/4 chance of any of them.
If you gamble on that outcome, you have a 1/4 chance of winning.

With prior knowledge, I can increase my odds of winning.  (I.e., I know that TT and TH are impossible because the first flip was heads.  I can bet on HT or HH safely.)

In my scenario, the opponent gambler is unknowingly betting on a 2-coin set because the coin has already been physically flipped.  The dishonest part is not informing them that he is gambling on a set of flips.   The chance that he correctly calls a two-flip set is 1/25, no?

Three years ago I would have just said they still have a 50/50 chance since it is one coins. But you all convinced me that it’s 1/4 because it is part of a set of two flips.
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#### Jimmmmm

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##### Re: Apparently this is where people talk when it's night
« Reply #2356 on: January 26, 2020, 07:54:49 pm »

Do you remember where we convinced you of that?
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2357 on: January 26, 2020, 08:23:05 pm »

Do you remember where we convinced you of that?

I do.  That’s why I’m asking now and you are trying to convince me of the opposite (that it’s 50/50 again instead of 1/4).

Even if you've just flipped 10 heads in a row, the next one is still 50/50 if it's a fair coin.
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#### Jimmmmm

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##### Re: Apparently this is where people talk when it's night
« Reply #2358 on: January 26, 2020, 08:28:14 pm »

Where?
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2359 on: January 26, 2020, 08:59:10 pm »

Where?

Somewhere on the board.  I think there was Monty Hall and mafia alignments involved.
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#### shraeye

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##### Re: Apparently this is where people talk when it's night
« Reply #2360 on: January 26, 2020, 10:25:03 pm »

mafia alignments are weird.  I mean Monty Hall is too.  And probability can get pretty complicated quite by accident too.

The hidden issue in all of these questions is about perspective.  We need to resolve "when"/"from what perspective" we are asking the question (a.k.a. how much do I know about the overall context so far).  And also resolve EXACTLY what the question is ("will the next 2 coin flips be heads?" is different than "will the next coin flip also be heads?")

Like in mafia, there is a priori probability.  Before any mod rolled any dice, before any player got any PM, what are the possible distributions of roles.  This is a perspective a mod using a randomized setup might care about.  (so how likely is 2 cops AND 2 doctors?)

There is also the probability calculation that each player can do as soon as they get their PM.  ("well, I'm a JK, so let's only think about possible setups where I was assigned JK.  With that info, how likely is it that there is also a doctor?).  There's a method to do that called Conditional Probability, and there's a method that sort of cheats around the official definition of Conditional Probability.  Both get the same answer, but if one person is explaining style A and you were thinking more along the lines of style B, you could get confused by the details.

But once the game starts probability stops being a straightforward math problem.  Because we want to use actions people take to determine their alignment (voting, claiming, whatever), but the people did those actions AFTER they got an alignment.  So asking something like "raerae did YYY, so how likely is it that she's the doctor" isn't really talking about probability anymore, it's pure psychology.  But still people do vote counts and throw around words like "better odds" "more likely", not really acknowledging that we just slipped from the strict-math definition of "better odds" to a more colloquial definition of "better odds".

Maybe that doesn't clear anything up at all.
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#### faust

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##### Re: Apparently this is where people talk when it's night
« Reply #2361 on: January 27, 2020, 03:31:15 am »

There is a subtle difference in what exactly you know. If you have two coin flips, there are four outcomes: H/H, H/T, T/H, T/T.

Now, if all we know is that there is a coin among these that flipped H, that means we can eliminate the T/T option. If you now ask "knowing this, what was the result of coin flip 2?" - 2 of the 3 options have it as H, so the probability of H is 2/3. This is probably what came up originally.

There's is a subtle difference in the scenario you propose, which is that we also know which coin flipped H. It was the first one, so we can eliminate both the options T/T and T/H. Then, by the same reasoning as before, we are left with 2 options for the flip of coin 2, one H and one T. Thus the chance is 50/50 in this case.

I hope this made the distinction clearer. It's not that the extra information from you have about the previous flip does not come into play at all, it's just that it does not end up changing the probabilities.
« Last Edit: January 27, 2020, 03:33:22 am by faust »
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#### popsofctown

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##### Re: Apparently this is where people talk when it's night
« Reply #2362 on: January 27, 2020, 06:46:49 am »

Don't play Monty Hall mafia, it's lame
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2363 on: January 27, 2020, 08:20:42 am »

There is a subtle difference in what exactly you know. If you have two coin flips, there are four outcomes: H/H, H/T, T/H, T/T.

Now, if all we know is that there is a coin among these that flipped H, that means we can eliminate the T/T option. If you now ask "knowing this, what was the result of coin flip 2?" - 2 of the 3 options have it as H, so the probability of H is 2/3. This is probably what came up originally.

There's is a subtle difference in the scenario you propose, which is that we also know which coin flipped H. It was the first one, so we can eliminate both the options T/T and T/H. Then, by the same reasoning as before, we are left with 2 options for the flip of coin 2, one H and one T. Thus the chance is 50/50 in this case.

I hope this made the distinction clearer. It's not that the extra information from you have about the previous flip does not come into play at all, it's just that it does not end up changing the probabilities.

This all makes sense -- for my perspective.

The con relies on the decreased odds of the opponent -- from their perspective, they are making a 50/50 bet on a 25% chance.

If our victim is called mail-mi, for example, and they are addicted to gambling and isn't inclined to think things through.  I offer a bet on a coin flip -- 50/50 odds for you, mail-mi!  They see one coin in hand, it is a fair coin, and can only land on heads or tails.  Seems good.

The hidden information is that I have already flipped that coin once, providing a result of which mail-mi is unaware.  What mail-mi thinks is a single coin flip is in fact part of a two-flip set.  I am forcing mail-mi to gamble on the 1/4 chance outcome without their knowledge.  The possible outcomes (for mail-mi) are HH, HT, TT, TH.  For the con to work, I have to force mail-mi into betting on the only possible double letter bet.  But that should be negligible for a con artist.

In your explanation, "we" know information.  In my scenario, the victim does not.  If there are four outcomes for two coin flips, the chances of predicting the right one is 1 in 4.  I don't see how that can be changed.

Even in the case of "there are two coin flips, one has been flipped but you do not NOT know the result" there are still four possible outcomes, right?  That one is closer to the con scenario, except mail-mi doesn't even know the first coin has already been flipped.

Where am I going wrong in this?
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#### MiX

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##### Re: Apparently this is where people talk when it's night
« Reply #2364 on: January 27, 2020, 08:33:28 am »

So, from your perspective, you flipped the coin once, so you know out of the 2 flips it's going to be (HH, HT) or (TH, TT), depending on whether you got Heads or Tails. But mail-mi doesn't, so it can be any of the 4 (HH, HT, TH, TT). However, he's only betting on the SECOND coin being Heads or Tails, which means if he bets that it's going to land on Heads, he's betting on HH or TH to occur, vice-versa if he bets on Tails. Regardless of what you flipped first, the odds of one of these happening is 1 out of 2 from your perspective, whereas from mail-mi's perspective is 2 out of 4, which is the same.

Does that make sense?
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2365 on: January 27, 2020, 08:43:13 am »

So, from your perspective, you flipped the coin once, so you know out of the 2 flips it's going to be (HH, HT) or (TH, TT), depending on whether you got Heads or Tails. But mail-mi doesn't, so it can be any of the 4 (HH, HT, TH, TT). However, he's only betting on the SECOND coin being Heads or Tails, which means if he bets that it's going to land on Heads, he's betting on HH or TH to occur, vice-versa if he bets on Tails. Regardless of what you flipped first, the odds of one of these happening is 1 out of 2 from your perspective, whereas from mail-mi's perspective is 2 out of 4, which is the same.

Does that make sense?

Sure.  But why?

I am secretly asking mail-mi to bet if the result of two coin flips will be HH, HT, TT, or TH.  I force him into choosing TT.
1. If no coins have been flipped at the time of betting, that's 25% every single time (1 out of 4)
2. If a coin has been flipped but no one knows the result at the time of betting, that's 25% (1 out of 4)
3. If a coin has been flipped and we know the result after betting, it's 66% (2 out of 3 -- both HH and HT are losses and would count as one outcome I think, TT, or TH)

Is #2 correct there?
If it is, why is in incorrect if I know the result but mail-mi doesn't?
Does it matter if a third-person knows but neither I nor mail-mi does?
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#### MiX

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##### Re: Apparently this is where people talk when it's night
« Reply #2366 on: January 27, 2020, 08:52:48 am »

I am secretly asking mail-mi to bet if the result of two coin flips will be HH, HT, TT, or TH.  I force him into choosing TT.
1. If no coins have been flipped at the time of betting, that's 25% every single time (1 out of 4)
2. If a coin has been flipped but no one knows the result at the time of betting, that's 25% (1 out of 4)
3. If a coin has been flipped and we know the result after betting, it's 66% (2 out of 3 -- both HH and HT are losses and would count as one outcome I think, TT, or TH)

Is #2 correct there?
If it is, why is in incorrect if I know the result but mail-mi doesn't?
Does it matter if a third-person knows but neither I nor mail-mi does?

If you force him to choose TT, knowing it first flipped H, you'll always win, right? By making him guess the second coin will be Tails, regardless of what you know of the first flip, he's betting on HT and TT at the same time, because those are the results where the second coin is Tails.
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#### ashersky

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##### Re: Apparently this is where people talk when it's night
« Reply #2367 on: January 27, 2020, 08:55:20 am »

I am secretly asking mail-mi to bet if the result of two coin flips will be HH, HT, TT, or TH.  I force him into choosing TT.
1. If no coins have been flipped at the time of betting, that's 25% every single time (1 out of 4)
2. If a coin has been flipped but no one knows the result at the time of betting, that's 25% (1 out of 4)
3. If a coin has been flipped and we know the result after betting, it's 66% (2 out of 3 -- both HH and HT are losses and would count as one outcome I think, TT, or TH)

Is #2 correct there?
If it is, why is in incorrect if I know the result but mail-mi doesn't?
Does it matter if a third-person knows but neither I nor mail-mi does?

If you force him to choose TT, knowing it first flipped H, you'll always win, right? By making him guess the second coin will be Tails, regardless of what you know of the first flip, he's betting on HT and TT at the same time, because those are the results where the second coin is Tails.

Again, I agree that what you are explaining is sensible in the context of real life.

My point is why does the probability thing not work out?  Nothing has changed in regards to the four possible outcomes from mail-mi's perspective. . Or to put it another way, isn't that win where the second coin hit Tails something that happens 25% of the time?
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#### MiX

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##### Re: Apparently this is where people talk when it's night
« Reply #2368 on: January 27, 2020, 08:58:40 am »

I am secretly asking mail-mi to bet if the result of two coin flips will be HH, HT, TT, or TH.  I force him into choosing TT.
1. If no coins have been flipped at the time of betting, that's 25% every single time (1 out of 4)
2. If a coin has been flipped but no one knows the result at the time of betting, that's 25% (1 out of 4)
3. If a coin has been flipped and we know the result after betting, it's 66% (2 out of 3 -- both HH and HT are losses and would count as one outcome I think, TT, or TH)

Is #2 correct there?
If it is, why is in incorrect if I know the result but mail-mi doesn't?
Does it matter if a third-person knows but neither I nor mail-mi does?

If you force him to choose TT, knowing it first flipped H, you'll always win, right? By making him guess the second coin will be Tails, regardless of what you know of the first flip, he's betting on HT and TT at the same time, because those are the results where the second coin is Tails.

Again, I agree that what you are explaining is sensible in the context of real life.

My point is why does the probability thing not work out?  Nothing has changed in regards to the four possible outcomes from mail-mi's perspective. . Or to put it another way, isn't that win where the second coin hit Tails something that happens 25% of the time?

The odds of the second coin flipping Tails is 50% regardless of the first coin flip. You can't force mail-mi to also bet that the first coin is T because he doesn't know it exists.

Let's say the first coin flipped Tails. Now you're offering a choice to mail-mi: will this coin flip Heads or Tails? From mail-mi's perspective, he sees two possiblities: H or T. From your perspective, you also see two possiblities: TH or TT, because HH and HT were ruled out. Thus the odds for both of you for the coin to flip, say, Tails now is the same: 50%.
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#### Awaclus

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##### Re: Apparently this is where people talk when it's night
« Reply #2369 on: January 27, 2020, 09:04:38 am »

The information that you have is obviously not capable of affecting the result of the coin flip or any other aspect of the physical reality, unless you have psychic powers. What the information does allow you to do is to eliminate possibilities that contradict the information that you have, when you are guessing what the reality is, so that you can make a better guess.
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#### Awaclus

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##### Re: Apparently this is where people talk when it's night
« Reply #2370 on: January 27, 2020, 09:10:31 am »

The information that you have is obviously not capable of affecting the result of the coin flip or any other aspect of the physical reality, unless you have psychic powers. What the information does allow you to do is to eliminate possibilities that contradict the information that you have, when you are guessing what the reality is, so that you can make a better guess.

i.e. it is possible to orchestrate a con in which you are able to make better guesses than mail-mi because you have more information than he does (by e.g. suggesting that you both flip a coin in secret without looking at the result, and then place bets on the four possibilities, but you cheat and check out your own result). You can't orchestrate a con in which you can manipulate the result of a coin flip by knowing the results of previous coin flips.
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#### Awaclus

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##### Re: Apparently this is where people talk when it's night
« Reply #2371 on: January 27, 2020, 09:12:37 am »

Oh and if you manage to fool two people into a game where you flip two coins and person A wins if they're both tails, person B wins if they're both heads, and you win if one is tails and the other is heads, you will make money.
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#### faust

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##### Re: Apparently this is where people talk when it's night
« Reply #2372 on: January 27, 2020, 11:48:02 am »

I am secretly asking mail-mi to bet if the result of two coin flips will be HH, HT, TT, or TH.  I force him into choosing TT.
1. If no coins have been flipped at the time of betting, that's 25% every single time (1 out of 4)
2. If a coin has been flipped but no one knows the result at the time of betting, that's 25% (1 out of 4)
3. If a coin has been flipped and we know the result after betting, it's 66% (2 out of 3 -- both HH and HT are losses and would count as one outcome I think, TT, or TH)

Is #2 correct there?
If it is, why is in incorrect if I know the result but mail-mi doesn't?
Does it matter if a third-person knows but neither I nor mail-mi does?

If you force him to choose TT, knowing it first flipped H, you'll always win, right? By making him guess the second coin will be Tails, regardless of what you know of the first flip, he's betting on HT and TT at the same time, because those are the results where the second coin is Tails.

Again, I agree that what you are explaining is sensible in the context of real life.

My point is why does the probability thing not work out?  Nothing has changed in regards to the four possible outcomes from mail-mi's perspective. . Or to put it another way, isn't that win where the second coin hit Tails something that happens 25% of the time?
Let me try another way of explanation: Yes, TT has a 25% chance. If you know that the first coin is T, then they are betting on the 25% chance. But... only in 50% of the cases will you even get to this point, as it requires that the first coin flipped T.

Your scheme is basically this:
Flip coin.
if T, make them bet on TT
if H, make them bet on HH

So overall, you will make them bet on TT and HH, and together these have a 50% chance.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

#### Galzria

• Jester
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• Posts: 953
• Since 2012
##### Re: Apparently this is where people talk when it's night
« Reply #2373 on: January 27, 2020, 12:57:08 pm »

I believe you could set it up thusly:

“I’m going to flip two coins. One Coin will be flipped first, and the result will not be public. The second coin will then be flipped, and again, the result will not be public. Place your bet: Choose between Heads & Tails for one of the coins “

“I’m now going to reveal one Coin & give you the option of staying with your choice for the second coin, or changing your mind”.

Given the possible outcomes: HH, TH, TT, HT, if you show him a coin that is Tails, he’ll want to stay with Heads. If you show him a coin that is Heads, he’ll want to switch to Tails. Even though the coins were both flipped beforehand, and one coin flip does not DIRECTLY impact the other, by knowing which subset of {HH, TT} can be eliminated, Mail-Mi can increase his odds from 1/2 to 2/3.
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Quote from: Voltgloss
Derphammering is when quickhammers go derp.

Faust has also been incredibly stubborn this game. In other news, it's hot in the summer, and water falls from the sky when it rains.

Mafia Record:
TOWN Wins: M3, M5, M6, M11, M17, M28, M32, M105, M108, M114, M118, M120, M122, DM1, DoM1, OZ2, RM45, RM47, RM48, RM49, RM55
TOWN Losses: M4, M7, M8, M9, M13, M14, M18, M31, M110, M111, M113, M117, M125, RM3, RM4, RM54
SCUM Wins: M2, M19, M23, M100, DM3, RM1, RM2, RM48, RM50
SCUM Losses: M15 (SK), M102 (Tr), OZ1, RM55

Total Wins: 30
Total Losses: 20

#### mail-mi

• Saboteur
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• Shuffle iT Username: mail-mi
• Come play some Forum Mafia with us!
##### Re: Apparently this is where people talk when it's night
« Reply #2374 on: January 27, 2020, 12:57:45 pm »

I just wanna know why ashersky is trying to dupe me in the first place.
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I currently imagine mail-mi wearing a dark trenchcoat and a bowler hat, hunched over a bit, toothpick in his mouth, holding a gun in his pocket.  One bead of sweat trickling down his nose.

'And what is it that ye shall hope for? Behold I say unto you that ye shall have hope through the atonement of Christ and the power of his resurrection, to be raised unto life eternal, and this because of your faith in him according to the promise." - Moroni 7:41, the Book of Mormon
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