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PaperclipPerfector  3mo ago (text post)   2298 thread views

Friday Fun Thread for September 6, 2024

Be advised: this thread is not for serious in-depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.

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I just watched a few minutes of Space Marine 2 cutscenes. Every time the camera cuts to a character, all the fabric on his body does the default T-pose-hang-and-fall like when you load new clothes in DAZ studio.
Literally every single shot starts with their armor skirts/tabard dropping down around their legs while they talk about purging heretics.
The dangling incense skulls keep clipping through their robes. Everyone looks like they got their faces done by the grimmest, darkest one-star yelp review post-op buffalo bill plastic surgeon in the galaxy.

This is a $70 game with a massive budget that requires a 3070 GPU to play. It looks worse than the one from 2011.
Is the the devs, or is the unreal 5 physics engine just awful? "Chaos engine" is hilariously on point for a Warhammer game

It doesn't run in UE5, it uses the proprietary engine they cooked up for WWZ.

Of my many complaints about the game, the visuals are in a distant last place. The gameplay is somehow, in its attempt to be deeper than the flat puddle of the first game, worse. Counter and parry timing is inconsistent between enemies and difficulty. There is no real meaningful way to sustain in the heat of combat due to a lack of the first game's health regen, and the game is ridiculously punishing of small mistakes. Certain points of the campaign seem like they were designed by people who don't understand what game design is, and whole chunks of the PVE operations mode seem like they were designed by people who think stat increases are meaningful improvements.

Woefully, the sound design makes bolter fire feel pathetic, even if it was doing more than pathetic damage to elites. I winced when the first game turned the melta, a literal fusion gun, into merely an overpowered shotgun, and a lascannon into a sniper rifle, but rubric marines in this game can soak several shots from a multi-melta without going down on the harder difficulties.

TBF don't rubric marines have feel no pain rolls that let them laugh at multi-meltas on a coin flip? Or am I mixing up editions again

Come to think of it, how do I know any of this I've never even played Warhammer.

On the weekend, I hand fed an actual quokka and gave it a bunch of pats. They're actually pretty cute and friendly in real life (although a bit lazy), and they actually grab your hands with theirs when you feed them to make sure you don't take away the food. That had me thinking about the motte, and then I saw an advertisement on the way back home telling me that the mainstream news was going to be presented by a Mr. Overton. Nothing particularly relevant, but it was enough of a synchronicity I felt like posting it here.

Non-glowing brain: Ten thousand dollars ($10k)
Slightly-glowing brain: Ten kilodollars (10 k$)
Galaxy brain: Two hex byte dollars (or two four kibidollars, |¦¦¦ ki$)

Inspired by @ThisIsSin's recent comment, but I have been using "kilodollar", "megadollar", et cetera for a while.

The hex dollar has been offered in Knuth rewards for decades!

Kilobucks and megabucks is, like, ancient slang. Evergreen, though.

I saw the new Beetlejuice film today on a whim (an air-conditioned movie theater sounded more appealing than the 96-degree weather we’re suffering through in San Diego this week) and I thought it was solid! I haven’t seen the original film since I was a teenager, so I likely missed most of the nostalgia triggers, but as a standalone film it’s still enjoyable. Macabre and wryly funny, with the right level of restrained camp. For a woman in her fifties, Winona Ryder has aged fairly gracefully (although maybe I’m just biased because I believe that in her prime she’s arguably the most beautiful woman to have ever lived), and even Jenna Ortega, whose appeal has always more or less eluded me, is used well. I share the general opinion here that the era of recycled IP we’ve lived in for the last decade - endless sequels, prequels, reboots, and spinoffs - has made TV and film pretty unenjoyable, but as sequels go I think this one is a fun time, even for someone with little or no investment in the original film.

I believe that in her prime she’s arguably the most beautiful woman to have ever lived

Apparently a demon in the sack as well.

I haven't seen the original film in years. I watched quite a bit of the cartoon show as a kid. I'll have to check it out.

Oh man, I was so shocked when I first saw the movie and Beetlejuice was the bad guy. Not at all what the cartoon led kid me to expect.

Caught up to the present episode on the History of the Germans podcast. I like to think I know a lot about Carolingian/Medieval history, and this is easily the best podcast I've found on that period. He's good with the sources, presents historiographical debates where they're important, and, as a banker-turned-lawyer, brings real expertise to describing economic and legal matters in particular. A must-listen if you like history podcasts and are interested in finding one on the Middle Ages (Germany is also the best place to cover most of Europe, because their central location and the Imperial crown means that they get involved basically everywhere except Iberia and Russia).

Fun idea - Miller (the Capitan played by Laurence Fishbourne in Event Horizon) is actually Doom Guy from Doom 2016. Event horizon always vibed more Doom than Warhammer to me. He gets thrown into hell at the end of EH. And is actually pretty good fit as someone who would become unkillable demon slaying machine driven by pure willpower and hatred.

I always liked the fan theory that Event Horizon is set in the Warhammer 40k universe as the discover warp travel without Geller fields.

Vidya thread

Im back to playing Starship Troopers. Still thoroughly enjoy the game. Only downside is low player counts. One of the recent additions that has made a dramatic atmospheric improvance is that corpses do not automatically despawn. And corpses can be climbed over. So you end up with situations like in the movies when stacks of bugs outside of the walls form a smooth ramp up to your poor troopers. Flamethrowers are more important for cleanup now.

I got In Sound Mind as a free giveaway from Epic Games ages ago. I was hesitant about playing it because I was concerned it was one of these games that markets itself as a survival horror but is really just a walking simulator with periodic jump scares. The other night I started playing it around 11-11:30 and found it so absorbing that it was 1:30 before I stopped. Pleased to find it's emphatically not a walking simulator, but a real game with real mechanics. The pleasingly goofy premise is you play as a therapist who has sessions with his disturbed patients, and in order to resolve their traumas (and get to the bottom of the mysterious conspiracy at their root) you enter into surreal dreamscapes and defeat a boss. A bit like Psychonauts crossed with Silent Hill (or perhaps Alan Wake).

After spending several months trying to beat X-COM 2 on Classic difficulty, this is just the kind of game I'm in the mood for: enough of a challenge to be satisfying but forgiving enough not to be tense or stressful; spookily atmospheric but rarely actually "scary" (I've completed three dungeons and only the first one ever made me feel any degree of fright); puzzles which I don't require a walkthrough to solve 90% of the time; story which is well-written enough to be entertaining but which doesn't seem to take itself terribly seriously, like a 2000s psychological thriller (Secret Window, Identity) which is sort of aware of how silly its conceit is without fully lapsing into self-parody. The only criticisms I have of In Sound Mind so far are that the dungeons seem a bit padded with samey areas it's too easy to get lost in, and the inclusion of a stealth mechanic seems a bit half-baked and largely useless.

On XCOM 2 (well, Long War, but for both XCOM I never really played anything else), I found the opposite, if played well the stealth mechanic is extremely substantial (though I preferred the first XCOM). But I also used a whole bunch of mods, including one that made timers freeze until stealth is broken (bc that just seemed stupid except for very few exceptions).

Oh sorry for the confusion, I was referring to the stealth mechanic in In Sound Mind, not XCOM 2.

In vanilla XCOM 2, I agreed with Zero Punctuation that it's annoying that breaking concealment instantly makes every enemy on the map aware of your location until the end of the mission. It would have been nice if killing one group of enemies before another group arrives on the scene restored concealment.

including one that made timers freeze until stealth is broken

Agreed, this is one aspect of the base game that makes absolutely no sense and is blatantly a contrivance for gameplay's sake. That being said, it's hardly the only such aspect.

I'm pretty sure I had some way of restoring concealment, but it might have been from a mod as well. In general XCOM2 is imo one of those games substantially improved with mods.

I've been mostly playing old fighting games these days (with some forays back into deckbuilders like Slay the Spire and Balatro once in a while). I'm hyping myself up for the release of the MvC Collection on thursday. And building up the hype for the Fighting Collection 2 next year.

Honestly I don't know why I'm so excited about this; I could play MvC2 or CvS2 other ways at any time, for free. But there's something about having the game legally that's exciting and that I can't explain.

I finally finished Deus Ex: Mankind Divided, starting it (and its previous prequel to Deus Ex, Human Revolution) from scratch after putting them down many years ago.

Gameplay-wise, they try to stay faithful to the original Deus Ex, except for the common modern concessions (a distinct cover system, which I liked, lack of body-part-specific health, which I disliked, and health regeneration, which I despise). Playing at "Give Me Deus Ex" difficulty was too easy, apparently because the difference in damage taken vs "Give Me a Story" difficulty is only 21%, not a full 300%. One of my fondest memories of the original Deus Ex showing its colors was 10 minutes into the game, getting killed for the first time, thinking "What is wrong with this game, that I can die from a single pistol shot to the head?", then thinking "What is wrong with every game I've played before, that I don't expect to die from a pistol shot to the head?" The level of nonlinearity (lots at the tactical level, a little at the strategic level) was on-par with the original, in both good ways (many different combat/stealth/hacking alternatives, a few major story beats that can be changed, hub levels with a lot of non-combat interactions, side quests that are intriguing but not overbearing, revisiting of old locations under new conditions and with new goals) and bad (the stereotypical Die Hard Ventilation Shafts are as common in little apartment complexes as they are in big office buildings, and their routing is obviously extradiagetic everywhere). Mankind Divided also completely backed away from the biggest complaint about Human Revolution (dumb boss fights pawned off on a subcontractor or something for development); there's now only one "boss" in the entire game, the cutscene before that fight doesn't hand you an idiot ball, and the fight itself leaves you a great number of tactical alternatives (including simply finding a way out and fleeing, I'm reading).

Story-wise ... it doesn't fit as well as it should, I think because they painted themselves into a corner with the first prequel. In Deus Ex you met maybe a half dozen mechanically-augmented characters. They're in a strained position in between "superhuman abilities" and "becoming obsolete due to nano-augmentation", which is interesting, but they're mostly economic elites or their elite enforcers, and it's clear that they should have been superhuman and rare back in their day. Human Revolution did "superhuman", but to do a "baseline-vs-augs" story they gave up on "rare"; they're now common and you meet dozens of them. Mankind Divided uses the ending of Human Revolution to flip the script the rest of the way, with mechanically-augmented people still common and treated as subhuman due to the prior conflict. Even tonally in its own context this doesn't always work; the dialogue and situations mostly pattern-match the kind of bigotry you see against underperforming subpopulations, not against overperforming-but-hated ones. The ending gives some closure, albeit not as much as it should. This is clearly part of a trilogy that was never finished, but it does stand well enough on its own that I don't feel cheated.

Graphics-wise ... did we just hit "good enough" a decade ago? I'm reminded of a comparison I saw of the 2013 vs 2018 Tomb Raider video games, where the main character's hair was more flowing and realistic in the latter, and that was about it. I'm sure kids these days could find a lot to complain about before I chase them off my lawn, but after living through an era where every year felt like a completely new paradigm, it's nice to be able to just treat even decade-old AAA graphics as a solved problem, and focus on gameplay and story.

I have a lot to say about Black Myth: Wukong, a game that surprised me at every turn and left me thinking for days about its themes, story, and just... general existence, but I need more time to put my thoughts in order. It's incredible that the thing exists at all.

Space Marine 2 next week so I can engage in the practice of adult male pillowforting, even if the game design is questionable compared to the first game's.

I'd definitely be interested to hear about black myth wukong.

Played some Kerbal Space Program 1 with mods. Had fun, but it's clunky.

Other than that, still entirely on Nebulous: Fleet Command. I'm not good at it, but I do have fun.

I'm trying to play RDR 2... I'm just so bored. The scenes are so long. I'm still in like the intro town and man every time I fk up a mission I have to repeat so much.

Kind of annoying, but I've heard such great things I'm trying to slog into it at least a bit.

The scenes are so long. I'm still in like the intro town

Skip the side missions and only focus on the story.

every time I fk up a mission I have to repeat so much.

Save after every mission.

It’s not really like most other games. It’s an immersive experience, like a form of interactive theater. It only works if you forget about game stuff like “what’s the fastest way to the next mission” and instead devote yourself wholly to thinking “what would Arthur do next?”. When it gets dark, set up camp and cook some food over the fire; in the morning brew some coffee and drink it as the fog clears, then saddle up and keep going. When you stop at a town, get a drink at the saloon, play a game of poker, overhear some conversations. Get distracted. Hunt if you spot rare game, then bring the skin back to town for sale. In between, pursue the story missions, upgrade camp as you find things, explore the towns and cities organically. Don’t obsessively overloot; looting is deliberately slow to discourage this. Your horse is fragile, you have to look after it, you can’t treat it like a ‘mount’ in other games. Speak to everyone whenever you can, your camp followers and friends have almost unimaginable amounts of incidental dialogue and there are countless little side stories, some of which you’ll miss and some you’ll be there for. Fish at sunset. Stalk a deer in a rainstorm. Read every newspaper, watching how they change as you complete quests bf meet new characters. If there’s a party in camp, do what Arthur would do; get a drink, talk to people, socialize. More than any other game of its type, Red Dead Redemption 2 needs you to buy in fully, or it will seem slow and boring. But do this and eventually every other open game of a similar type will seem like a crude facsimile of a world, a gamified, simplified, fake-feeling funfair compared to the Wild West in a setting with the industry’s best sense of time and place.

I've started playing it before our newborn came (hadn't had the chance to play it again), but my biggest problem was the immersion break on missions when suddenly dozens of mooks show up and die one after another while Arthur's crew just cuts through them like hot butter. The rest of the game is made so realistic and immersive, why did the choose to make these fighting scenes so over-the-top ridiculous like most other action games? I don't mind it as much for other action games because there it's just the way the entire world works, but for RDR2 it just seems so bizarrely out-of-place.

It only works if you forget about game stuff like “what’s the fastest way to the next mission”

I wish I could have done that, but it felt like at least early on, a lot of stuff is locked behind those missions.

Hmmm I guess I will try more to get into it, sounds like I need to dedicate some time to getting into the experience.

Idk I've never been one to get immersed in video games, any tips for getting into this mindset? Or like questions to think about as I play?

Cool! I might hop back in with you. Are there new game modes and such? I think I got tired of how stale the same old thing got after a bit.

I think two new game modes since you last played. A horde mode, and a hive extermination. I don't think I like either of those very much. I've drifted towards liking advance and secure. Because it is time limited and slightly less insane than the other game modes.

There is supposed to be a single player campaign in a month or so when the game releases.

The progression system has been changed up, 6 classes instead of 3.

Weapon progression is a thing.

I'm still trying to figure out which class I like best.

6 classes? hOLY CRAP! THAT'S A LOT

Nice man I'll check it out

Sarcasm?

From memory:

  1. Guardian (defense)
  2. Engineer (building)
  3. Ranger (scout short range)
  4. Sniper (scout long range)
  5. Medic
  6. Demolition (explosives)

Ive played all but the engineer and ranger. Different game modes fit best for each one. Medic is what I play if no one else has jumped into the match yet, or if there are less than three medics already.

nah not sarcasm. I'm just a genuine boi

New HoMM has been announced and it looks like it's being made by grognards for grognards: it's basically 3 with newer graphics and skills and other minor improvements from 5.

New HoMM has been announced and it looks like it's being made by grognards for grognards

A team of grognards already did that with Songs of Conquest.

That one has too many questionable decisions to count.

The new Necropolis look is just straight from some YA book.

/images/1725741795564061.webp

There are other art styles I would prefer but that looks tolerable to me. It could probably be improved a good bit just by improving the lighting.

Im getting Warcraft 3 vibes from that, and I'm absolutely cool with it.

Yeah, I am not a big fan of the new town screens.

That sounds great, I only ever see people playing 3 on YouTube.
There's a few franchises that had a definitive version that nothing can replace, like aoe2 and advance wars

It's kinda.. basic though. And also Rampart's special building (bank) is really nuts. I played them all but although Homm V was the best, mechanically at least.

The best 4x fantasy strategy game I ever played was Age of Wonders 2. They fucked it up with 3, they made it boring somehow. No idea how.

It's kind of like Homm except there's no stacking of units, the magical system is way more fun with domains and domain spells.

I’m still playing Star Wars Outlaws, primarily out of inertia in the hour a day between finishing with the laundry / dinner / clean-up / other chores and sleeping, and while my SO writes. The thing about Ubisoft games is they’re not exciting enough to keep you awake, but they’re stimulating enough to gently calm you down. Kind of like a mediocre drug, like microdosing shrooms or consuming low-THC weed, except possibly healthier (this is I assume debatable).

I am very much looking forward to the new Dragon Age. I have been waiting for 10 years and will likely enjoy myself immensely even if it is bad. Because I now have actual responsibilities and a social life I am even considering taking a couple of days off to play it, but I will wait for the reviews first in case it’s very buggy.

What makes you think you'll enjoy it?

I’m a sucker for the lore and know literally everything about it. It’s probably the only fictional setting I really know everything about.

And other than Andromeda I’ve enjoyed pretty much every BioWare game to some extent, so I doubt it will be so bad as to be no fun at all.

I don't get the 'knowing about the universe' part at all. Some of the SW games and media are cool- i really liked Dark Forces game and also Tie Fighter, the one game where you could play for the right side, but the closer you look the worse it gets. I used to read the wiki they had to see the lore but it's really ..dire.

These days if I want a decent skiffy game I just play Stellaris some. Real future is just too horrific to contemplate.

But wouldn't that make you even less interested?

Bioware has not released a passable game in over 10 years, all the original or even senior writers have either left or been fired, the game has been rebooted twice with the leads fired, with EA taking more or less full control as well as cleaning house of experienced people after the lastest reboot and the trailers look atrocious.

This game being decent seems like it would be one of the greatest upsets and comebacks in gaming history.

The gameplay footage released over the last week looks pretty good to me.

Love the vocal diversity in Hank Williams Jr Cowpoke. Doesn’t sound like it’s from 1965

Totally different genre but the vocals here brought Roy Orbison to my mind, and that would be from the same era, right?

Post the floor plan of your dream house!

Some examples

Resources: International Residential Code, International Property Maintenance Code, International Zoning Code, accessibility code ICC A117.1

My dream house or a house I can afford?

There are two house plans I like a lot:

  • a basic four-square: two floors, about 10m x 10m inside. I can fit everything I want and need inside, but at 1000+ dollars per square meter I can't really afford it as a second home
  • a basic "one hall, two wings" that minimizes the hallway area and can fit three bedrooms and a study into just 120 square meters of floor area (17.4 x 9.2m external dimensions), but I keep fiddling with the design, because it's hard to end up with a living-dining-kitchen room that is neither cramped nor an obvious waste of space. It's easier when the house is 18.0 x 9.8m (or about 140 sqm inside), but that's 20 square meters I would have to pay for.

I'm at my summer cabin, so I'll post the plans when I get home.

Some examples

Whats up with the separation of kitchen, dining and living rooms? Is this how modern apartments/houses in the US are designed right now?

I strongly dislike it, especially the cases where the dining room is "across" the hallway from the kitchen. I would always choose an eat-in kitchen, probably open floor with the living room.

What's up with the separation of kitchen, dining, and living rooms? I strongly dislike it.

I personally like explicitly separating the different rooms. Even if zoning is bad, having individual blocks (not entire neighborhoods) dedicated to residential, commercial, industrial, and office uses still looks more elegant on the map of the city.

Is this how modern apartments/houses in the US are designed right now?

At a glance, no.

Reject hallway, return to tradition.

I lived in a railroad apartment in college and for a few years after. It was fine for just my wife and I in a 1bd, an entire large house seems less workable.

Is there any comedy more implicitly moralistic than Napoleon Dynamite? The humble hard-working Napoleon finds esteem in his dance performance, with his class looking past his oddities; the pure of heart Pedro becomes president of the class; the protagonist finds innocent love; his deficient-in-character brother finds a partner which balances his flaws. Maybe Nacho Libre?

I don't see it as a moralistic movie. The logic of 2/3 of those beats rest entirely on Napoleon's insane dance performance. It's not by being a good person that Napoleon succeeds, it's by doing something totally out of character and ubermenchian that wins everyone over. Note how in the final scene he hits the thetherball as hard as he can over and over.

Is Forrest Gump a comedy?

Developmentally delayed bildungsroman.

Bildungslowman

Am I allowed to nominate a one word replay for an AAHQ

We’re still implementing the Actually A Hilarious Quip system, sorry.

I'd just disagree on them being comedies.

What would you call them?

Not funny

Football season kicked off last night. I missed the game, at work all night, but I'm excited for my Philadelphia Eagles to kick off in Brazil tonight.

How're my fellow sports fans on the motte feeling about their teams this season? Any degens placing longshot parlays this week?

I'm thinking that by week 8, most predictions in this Eagles team are going to look pretty stupid. Last season they were the best team in the sport for half a season and the worst team in the sport for half a season. The spine of the team is pretty much the same. They swapped out OC and DC but kept the same head coach. They've added several young defensive backs and a few veteran linebackers, lost their most dangerous edge rusher and a team legend; they swapped out a Hall of Fame center but they had an in house heir so they just needed a new right guard, and signed a star running back they're hoping isn't old. At the end of the day the most important question is at quarterback, has the league figured out Jalen Hurts? If he collapses under blitzing every time, the rest is academic. Their outcomes seem likely to again be binary, but a lot of power rankings hedge by placing them in the middle. I wouldn't bet the o/u of 10.5 wins either way comfortably, but one could probably make money betting tail odds of over 12.5 wins and under 6.5 wins. This is either a team with a ridiculous unguardable number of offensive weapons or a team with no answer to extra pressure.

Reading the responses to this post makes me think The Motte should have a weekly NFL thread.

I'd probably enjoy it.

College football is probably the only American sport I still follow (I suppose international soccer involves the Yanks?), and I'm not sure how to feel this season. Vanderbilt is an academic school in a group full of football powerhouses, but this year we seem to be somewhat not-incompetent? I'm waiting for reality to catch up, but it's not implausible that we have our best season in the past decade.

I was at the UNM Lobos football opener, first game for their new coach.

A sudden windstorm blew a camera off the stadium roof and almost injured spectators in the crowd below, but one data cable held firm and didn’t snap. Someone on the second story pulled it inside safely.

We were ahead of the other team for all but thirty seconds of the game. Too bad it was the final thirty seconds. On the way out of the stadium, we heard some hate-watchers saying they knew it all along that the new coach was never going to cut it, and he should just quit now.

So, business as usual for the Lobos.

Things are looking up for the Texans, which is always when shit goes South and we completely capsize.

I mean the good news is that the AFC South blows, so the Texans have a clear shot to win the division with only mediocre play, and then, who knows.

Professional football prognosticators seem to be more fickle than normal lately. The Eagles had a bad end to the season but I'm not going to throw them under the bus and say that a season and a half (plus the improved season before that) was all a lucky fluke just because of a half-dozen games. The Gnats are terrible. The Commanders get hyped every year but never seem to go anywhere. That leaves the Eagles and the Cowboys, and the Cowboys will probably choke. At the very least, they don't deserve to win anything. For some reason their fans hate Dak. Everyone keeps saying Zeke is washed, but he's still better than the guy backing him up. They have a good defense, but Micah Parsons is unhappy. I don't know what to make of this. The Eagles have as good a chance as they do.

I'm going to ping @Walterodim so I can consolidate my responses here. I have Josh Allen as my dynasty league QB so I'm totally biased, and I've always liked the Bills. I have a theory about QBs like Allen and Mahomes; when you combine guys this good with really good coaching, it doesn't matter who the receivers are. In a sense this is the ideal play because they can't just shadow your top guy all day. Tom Brady won all of his Super Bowls in such a system — everyone forgets this, but the only wideout to ever make the Pro Bowl on a Patriots Super Bowl team was Troy Brown in 2001 (and that was his only Pro Bowl). Randy Moss and Wes Welker had better careers, but neither won a Super Bowl. The Bills' defensive injuries are more of a concern but it seems like they always have a ton of defensive injuries. Speaking of the Patriots, they're in a rebuild and are expecting to be so bad that they're easing Drake Maye into the QB role even though he's obviously better than Brissett. The Dolphins are the kind of team with an "explosive" offense that wins games by hanging a ton of points on shitty teams. But they can't beat anyone good. Their defense relies on the offense keeping them off the field. As for the Jets, it's all hype. The offense assumes a 76-year-old Aaron Rogers will be back in hall-of-fame condition after being injured for a year. I predict he gets injured again and we get to see Tyrod Taylor. Their defense boils down to "we have Sauce Gardner", and they can't stop the run. Breece Hall is good, but so was Travis Henry. Bills win this division easily.

Pinging @Hoffmeister25. The only thing the Chargers have going for them is that they're clearly better than the Raiders and Broncos, so they should coast to an easy second place finish. If two things are certain it's that Jim Harbaugh will run the ball, and J.K. Dobbins will get injured, so be ready to see a lot of the Gus Bus. The Jags briefly looked like they had their act together, but that remains to be seen. The Texans should easily win this division, but their only two years removed from being the second worst team in the league, and as a Jags fan you should know what that means. Hell, as a Chargers fan you should know what early hype combined with limited success can lead to. Granted, the Texans looked more put-together last year than the Jags or the Chargers ever did, but I'm not about to crown them kings of the division, either. The Colts could also pose a problem, but I'm not a fan of overhyped QBs like Anthony Richardson and Michael Pittman, Jr. always underperforms expectations in fantasy, so I'm rooting to see Joe Fluke-O lose another wild card game. The Titans are an interesting story. They deserve to lose for tearing down a stadium that isn't that old to build a taxpayer-funded dome in a city with mild weather. They also have a history of disrespecting the Terrible Towel, and their best season in the past 20 years was with Kerry Collins at quarterback. Honestly, this division could go in any direction.

And now for my Steelers. Over the offseason, they took the bold step of replacing the frustration of a mediocre quarterback with the frustration of two mediocre quarterbacks. As they can't help but repeat in every broadcast, Mike Tomlin has never had a losing season. Every year some edgy sportswriter picks them to go 5–12 or some bullshit without realizing that that isn't possible. No matter how dire things seem, if there's one thing the Steelers are capable of it's battling back from a terrible season to have a chance to make the playoffs with a Steelers win AND a Jaguars loss, AND a Chargers loss, AND a Browns–Bengals tie, only for every leg of this impossible parlay to happen except the part where the Steelers beat the 2–14 Texans. Or, alternatively, they make the playoffs but are so outclassed they lose 45–15. After experiencing two Super Bowl wins I have resigned myself to this fate. But the sportswriters are still idiots; this team is better in every dimension than they were last year, but they're predicted to do worse. Some of this has to do with the brutal schedule, but they have one of the best defenses in the league and everyone forgets that last year they were 7–4 after Thanksgiving despite not scoring any points and would have easily cruised into the playoffs if it weren't for three fabulous weeks of Mitch Trubisky. The idea that Russell Wilson and Justin Fields can be written off entirely after a combined three minutes of preseason play is absurd. Seriously, there's absolutely no correlation between the preseason and regular season so commentators just need to stop acting like there is.

The division is interesting. The Ravens are clearly the best team, but the Steelers should have no problem beating them twice so long as Lamar stays healthy. I used to like Joe Burrow but I lost all respect for him when he showed up to the Super Bowl in that horrible suit (and had to wear it to the press conference since he forgot to bring anything else). Supposedly he's oblivious to fashion so he lets Ja'Marr Chase pick his clothes for him. Most people know that there are certain clothes that white guys can't pull off. Unfortunately, "most people" does not include stylish black guys, who tend to uncritically assume that their approach works for everybody. When Ryan Fitzpatrick showed up at a press conference wearing DeSean Jackson's clothes everybody in the press laughed because they knew it was obviously a joke. No one laughs about Burrow's sartorial choices because they know he's oblivious and it would just hurt his feelings. Anyway, they have a questionable running game and their defense might be worse than the Chargers. These are the kinds of teams the Steelers beat easily since they can't stay competitive unless they score 500 points. The Browns are always the Browns. I'll admit that they have a good defense. But DeSean Watson is terrible enough that they signed ALL the quarterbacks. Nick Chubb won't be his old self coming off of injury and will be worse than Jerome Ford was in his last game before Chubb came back, but not so much worse that they can make Ford the starter. These defensive battles are tossups so the Steelers should split this with them. You can throw darts at a board for the rest of the games because some bullshit always happens.

Prediction: They enter divisional play in last place with a 3–6 record against a shit schedule and everyone starts talking about how the schedule is so tough (all divisional plus Eagles and Chiefs) that there's no way they can possibly come back and Tomlin needs to go, etc. This whole affair involves repeated benchings of both Wilson and Fields and at least one disastrous Kyle Allen start. And then they sign Ryan Tannehill because he knows the "Arthur Smith offense" and they win 7 of their last 8 thorough some combination of the following: Injuries to opposing QBs who aren't Lamar Jackson, fluke plays, missed field goals, questionable penalties, TJ Watt fumble recoveries for TD, Minkah pick-6s, the Eagles starting Kenny Pickett, and at least one Calvin Austin jet sweep. They will then lose to the Browns in the first round of the playoffs in a game so badly played it's nearly unwatchable.

Over the offseason, they took the bold step of replacing the frustration of a mediocre quarterback with the frustration of two mediocre quarterbacks.

Replacing three mediocre quarterbacks.

Trubisky was well below mediocre.

I have a lot of affection for the Steelers as a franchise. Always play hard, never a team that pisses me off, does it the right way.

Also, false alarm, the eagles are undefeated, despite their best efforts. Saquon is doin' it for the keystone state. Never in doubt.

Also, false alarm, the eagles are undefeated, despite their best efforts.

They are, but good God, if Hurts is going to play like that then you guys better get used to the idea of Kenny Pickett starting.

Why would they start Kenny Pickett? Hurts threw a third as many touchdown passes last night as Kenny Pickett threw in 12 games in last year. They would have no chance of getting anywhere in particular with Pickett, no matter how poorly Hurts plays there is no point in putting in Pickett if Hurts is healthy. They're at the point in the carousel where if Hurts plays poorly, Sirianni is next on the chopping block, and only then after another bad season will Hurts be cut loose, probably as part of a down-to-the-studs rebuild with no more than a half dozen players on this team seeing the next competitive Eagles season.

After the Donovan McNabb experience, if I were a black quarterback signing a big contract, I'd require a secret written agreement from the team that they will never, under any circumstances, sign a white backup QB. All my backups must be black. I've never seen any black QB other than Mahomes who didn't get talk radio "questions" about replacing him with the white backup after a mediocre game. It's inevitable.

I wasn't suggesting they'd ever consider benching Hurts for Pickett. The way he was playing made it look like he was eventually going to get injured.

Edit - If you think having a black QB is bad, try having a black coach. Tomlin haters not only call for his firing on an annual basis, regardless of what the team does, but also refuse to give him credit for his successes which include winning a Super Bowl. This is discounted because it was allegedly done "with Cowher's players", as though there's no GM or front office involved. Never mind that the team was 8–8 Cowher's last year. Never mind that literally every coach who won a Stanley Cup with the Penguins had less time with the team than Tomlin. This is logically contradictory with the other criticism they have, which is that the teams with Bell and AB should have done more. Isn't that admitting that the guy can put a team together? So either he's a bad team assembler or he's a bad game day coach. I could excuse this as just general sports fan stupidity but, in person, they always have to bring up that he was only hired so Dan Rooney could "walk the walk" when it came to his rule. The only conclusion I can draw from this is that they think the Steelers would have been better had they hired the other leading candidate, Russ Grimm, who, as far as I know, was never considered for a head coaching position after that.

The other thing they like to bring up is that winning seasons don't matter if you don't go anywhere in the playoffs. They may have a point, but I suspect this is influenced by how long it's been since we've seen a truly dreadful season. If we were to start going 6–11 every year they'd long for the days when Tomlin was coach and there was at least a reason to watch. A couple years ago I actually did an analysis where I looked at every NFL head coach since Tomlin was hired and, giving the other guy the benefit of the doubt, graded every one as either better, the same, or clearly worse. 7 were arguably better, 10 were about the same, and 80 were unarguably worse. Some of those guys were obvious mistakes, but most of them were guys with good resumes who fans were excited about. Suggesting Tomlin should be fired after a winning season is one of the stupidest sports takes out there, and at least half of the people making the argument don't even pretend that it isn't because he's black.

One final dumb criticism that's always brought up is his lack of a coaching tree, as though this matters. The only one of his assistants this even applies to is Matt Canada — he inherited Bruce Arians and Dick LeBeau, Todd Haley had been a head coach previously, Keith Butler retired (and was in the organization longer than Tomlin), and Randy Fichtner would have stayed with the team if they hadn't been mesmerized by Canada. And if Arthur Smith coaches elsewhere he won't count as part of Tomlin's tree, either. It's a dumb argument anyway.

My fault for misunderstanding! Hurts is either going to make it or he isn't, injury and talent wise. Trying to play him at half his power level is mostly pointless, though the brotherly shove play might be gone after the shambles last night which might save him a few hits.

Tomlin is serially underrated across the game. I'm not sure why. No other coach comes close on steady Eddie record, there has never been an unwatchable Steelers season under Tomlin. Maybe this will be the year but I doubt it. In the NBA where the regular season itself is mostly unwatchable anyway, I understand the championship or bust mentality. But I'd sooner have an NFL team that plays good entertaining football 17 games a season every year than a rebuild, most of which completely fail anyway.

No other coach comes close on steady Eddie record, there has never been an unwatchable Steelers season under Tomlin.

Just good enough is a dangerous trap in the NFL. For the record I love Tomlin, but you can see why people might be upset when you have teams like the Eagles that do repeated tear down and rebuilds, especially given how hard it is to land a good QB in general but when you are mildly above average in particular.

Many fans (maybe foolishly) would choose ups and downs instead of consistency.

I guess the shame of it is that you don't get to pick which team you root for, for the most part, so you're stuck with the style of whatever team you like.

In the NFL I actually watch a lot of regular season games with my family, and I'd sooner pick a competitive if unspectacular team every year over unwatchable year after year while hoping for the future. MLB I understand tanking because it takes years of playing lots of young players for some of them to hit and start to build a core, there's value in playing the kids live. The star centric nature of basketball makes it, for most teams, an unfortunate necessity in the NBA.

But in the NFL, there's a confluence of short careers, limited and uneven development of players in the league, complicated salary cap rules, and the randomness inherent in player selection. Yes, you need to tank if you want to draft a Joe Burrow. But sometimes you go all in to get #1 overall and you get nothing. The Jets have spent the last six seasons starting a second overall and a third overall pick, they've never had a winning record in that time.

Good teams with good coaches and GMs and systems might have missed picks, down years, and problems, but they're able to reset quickly without years of losing by making good selections in later rounds and developing players well. Glancing over the QB rankings at TheRinger for a quick reference, out of the top 20: Hurts, Purdy, Love, Smith, Prescott could all have been drafted by basically any team in their draft year. I'd sooner bet on a good organization developing a fresh player than I'd bet on a bad organization turning things around. For every CJ Stroud there's a Bryce Young. And sometimes you tank for the top pick and end up with a Baker Mayfield or a Trevor Lawrence, whose best seasons have looked like the ones Tomlin's detractors are complaining about.

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Last season they were the best team in the sport for half a season and the worst team in the sport for half a season.

Nitpick here - none of the advanced metrics liked them even with the strong W-L record. They kept showing up at like 10th in DVOA and Aaron Schatz had to keep explaining that they're just not all that good on a play-to-play basis. As a massive Bills homer, I will also note that they needed absolutely absurd officiating to fluke their way to that win. I'm not an unbiased source and remain very salty :-|

On the topic of my beloved Bills, they're pretty clearly talent depleted due to a combination of some bad injury luck and poor contract choices. After Josh Allen, the next three biggest cap hits this year are Stefon Diggs (no longer on the team), Matt Milano (torn bicep, out till December), and Von Miller (old, injured, washed). You're just not going to have a talented and deep roster when you screw up like that. Even so, I'm excited to watch the young offensive core - James Cook, Dalton Kincaid, Khalil Shakir, and Keon Coleman are all at least enticing players with upside. Curtis Samuel is probably going to be useful in a limited role. Some of the defensive losses are overblown in the media (Poyer and Hyde were old and didn't look great last year, Tre White only played 3 games anyway), but there are enough talent gaps to have real concerns about them staying above water. I did bet them to win the AFC East because I think the Jets hype is just plain stupid and I ultimately trust the McDermott/Allen alliance much more than any other team in the division. Realistically though, they're not going to be on the same level as the teams we watched last night.

I was at that Bills Eagles game. I picked it to see Allen play. The Eagles kept coming up with one desperate play when they needed it. After on SEPTA heading home a bills fan told me he just wanted the bills to WIN the game of the year for once. After that one every power ranking i followed had the Eagles at one, and it was all downhill from there.

I want to see Josh Allen win a super bowl so bad. Maybe more than I want to see the Eagles win another.

I was at that Bills Eagles game.

Oh man, that's pretty cool. Wild game to be at. I was visiting my family back home, in a bar with quite a few people that shared my displeasure!

But anyway - my inclination is to think the Eagles arrow tilts back up this year. I'm unclear why the Matt Patricia experience happened to yet another team, but simply moving forward with actual competent coordinators should be a tremendous difference. If I was going to be pessimistic, it would largely about Kelce, because I'm a long-time center enthusiast. Usually the huge problems there are from mid-season changes though, so I'll be surprised if there's actually a disaster. You're absolutely right that there needs to be some sort of consistent answer to blitzes, but I tend to think they'll sort out some sort of plausible counter.

Update: Eagles are going 0-17.

Least emotionally-unstable Birds fan.

Update: never mind, Jalen Hurts is bad at football

Listen the worst part about modern rechargeable electronics is the lack of batteries to throw.

That game was so rainy. My wife is hoping she'll finally go to a dry game this year.

My NFL loyalties are split, in a complicated dance, between the Chargers and Jaguars. (The 2022 AFC Wild Card game was one of the strangest sports watching experiences of my life.) Both teams are in a somewhat similar position, and my excitement for the upcoming season is about the same for either team.

In terms of QB, the Chargers have the obvious advantage; Justin Herbert is a more experienced, more proven, more well-rounded, and significantly less turnover-prone than Trevor Lawrence. The Chargers also have the clear advantage on the offensive line, with maybe the best young tackle tandem in the AFC. The Jaguars’ offensive line, while they’ve hopefully patched the disastrous liability at center, is still a bottom-6 O-line, which risks yet another year of Lawrence scrambling for his life and unable to manifest his sky-high potential. The Jaguars do, though, have a very impressive group of offensive weapons around Lawrence, and if the O-line play is even league-average I expect a very effective passing offense. The Chargers’ passing game, on the other hand, is a giant question mark. Having lost veteran pass-catchers Keenan Allen and Mike Williams in the off-season, Herbert will be offloading passes to… Josh Palmer? Rookie Ladd McConkey? First-round-bust-in-the-making Quentin Johnston? With the addition of Jim Harbaugh as head coach - a move which increased my confidence in this team by about 5000% - and Greg Roman at OC, I expect the Bolts to run the ball approximately 900 times a game; they even directly imported the RB duo from the Ravens’ last few seasons.

Both teams suffer from the same fundamental flaw, though, which is that they stand almost no chance of being the best team in their respective divisions. The Chiefs are the undisputed best team in the AFC, and nothing I saw from them last night caused me to question this. The odds of the Chargers making it out of that division intact, let alone out of the AFC playoffs, are nonexistent. The Jaguars do not have to compete within their division with a buzzsaw quite as comprehensively unstoppable as KC, but they will be facing the seemingly ascendant Texans - freshly bolstered by the additions of Stefon Diggs, Joe Mixon, and the expected stratospheric second-year leap by CJ Stroud (the centerpiece of my fantasy football team, which is projected to win my league) who have all of the pieces to challenge for the upper echelon of offenses in the entire league. I just don’t think the Jags can measure up against that, especially not with our piss-poor defensive backfield.

I expect an encouraging leap from both teams in the regular season, dashed hopes in the early round of the playoffs, and a spectacular triumph for my fantasy team.

How did you end up with those teams? Do you think the jags will ever pull off moving to London like they've wanted to for years?

How did you end up with those teams?

I was raised a San Diego Chargers fan, but in college I started to drift away from the fandom; the team was bad, enthusiasm for them in the city was waning, and frankly I was just a young contrarian who wanted to forge my own path and pick a team for myself instead of just inheriting an unchosen fandom. Then when the Chargers moved to LA I fully severed myself from them. I needed a team, and a lot of things about the Jags attracted me: underdog/hipster appeal, cool uniforms, the uniqueness of being the only Jaguars fan I know, no history of success I needed to acquaint myself with or pretend to be emotionally invested in, etc.

I dove into the fandom feet-first, and within a few years I was riding high on the 2017 Sacksonville team that made it all the way to the AFCCG (and should have gone to the Super Bowl - Myles Jack wasn’t down, and that wasn’t a PI by AJ Bouye). Then everything fell apart from there; the Sacksonville defense immediately imploded, Jalen Ramsey gave in to his inner diva, the Nick Foles experiment exploded on the runway, the Minshew Magic meme seasons stopped being funny very quickly, and the Urban Meyer trainwreck especially seemed to prove just how awfully-run this franchise is.

Right around that same time, the sting of the Chargers abandoning San Diego started to fade, my diehard Chargers fan buddy started haranguing me to come back home to the team, and a lot of things about the Chargers were trending upward. (Justin Herbert, in particular, is just a very appealing guy to root for.) Simultaneously, I started regretting abandoning the team I was raised with, and as I began planning to move out of San Diego, the prospect of bringing my hometown team fandom (sorry, they will always be the San Diego Chargers, and nobody in Los Angeles will ever organically care about them) with me wherever I go started to become very appealing. Plus it will give me something to share and discuss with my mom, who never wavered in her fandom. So, now I’m sort of caught between two fandoms, uneasily hoping that I don’t have to witness the two of them directly competing for anything meaningful anytime soon.

Do you think the jags will ever pull off moving to London like they've wanted to for years?

Oh god, this again. The team is not moving to London, and it is not leaving Jacksonville. Shad Khan has poured obscene amounts of money into the city, the stadium renovation, the entertainment complex around the venue, etc. I think that maybe early on when he bought the team he genuinely hoped to move it to the UK, but in the intervening years all evidence points to him making peace with the fact that the move will never happen, and embracing making Jacksonville a more attractive destination for both players and fans. I’ll be shocked if the team ever plays more than four games a year in the UK, for the reasons I’ve listed, and for pure logistical reasons as well.

Before you are three closed, identical boxes. The first box contains two silver coins and nothing else. The second box contains two gold coins and nothing else. The third box contains two coins (one gold and one silver) and nothing else. You have no idea which box is which, you cannot see inside the boxes, and they are mounted to the wall so you cannot lift them to estimate their weight.

You reach your hand into one of the boxes and withdraw a gold coin. If you reach into the same box to withdraw the second coin, what is the probability that that coin is also gold?

It's 66%. You know that the box you withdrew the first coin from can't be the box with two silver coins in it, so it must be one of the other two boxes. There are exactly three coins remaining in these two boxes combined, one of which is silver and the others gold. Ergo the odds of you withdrawing a second gold coin are 2/3.

This puzzle was shared on a Facebook meme page I follow. I'm not trying to flex or anything, but I solved it instantly and the solution seems incredibly obvious to me. I was very surprised to see the comments full of people asserting that the answer is 50%. There's even a Wikipedia article about it, and it's referred to as a "paradox". One of my pet peeves is when the word "paradox" is used to refer to mathematical problems with counterintuitive solutions, or counterintuitive findings from the sciences - as opposed to contradictions in logic. Russell's paradox is a legitimate paradox: there is no good answer to the question "if a barber only shaves men who do not shave themselves, does he shave himself?" The "twin paradox" in general relativity isn't actually a paradox, but I can see how it runs counter to our human intuition of how things work in Mediocristan. But in this case, I don't think this particular puzzle even rises to the level of "mathematical problem with a counterintuitive solution": the solution seems incredibly obvious and straightforward. The word "paradox" gets used far too freely.

Bayes to the rescue: If you pull a gold coin from a box, that is strong evidence that the box is pure gold (because with a gold box, you will always get that measurement), neutral evidence that it is mixed (because with a mixed box you /can/ get that measurement) and rules out that you have the pure silver box.

If you start with a uniform prior, then you should end up with 2/3 pure gold, 1/3 mixed, which will give the probability you said.

So what would you say is your probability of withdrawing a gold coin if everything else is the same, but the third box has one gold coin and 10 silver coins, instead of just one gold and one silver coin?

In that case, since we know he drew one gold coin, it also rules out Box 1, so we’re left with Box 2 and 3. We know that initially there were 13 coins here (3 gold, 10 silver) so now there are 12 coins left (2 gold, 10 silver). So 2 gold out of 12 remaining coins = 1 in 6 chance = 16.66%?

[Of course, the chances of him plucking a gold coin in the first place would have been much less than the 50% in the first question – it would actually have been just 20% 2 silver 2 gold 1 gold, 10 silver = 3 gold vs 12 silver = 20% But since we know he did actually pick a gold coin first, the chances of him also picking a gold coin second are 16.66%.]

Of withdrawing another gold coin? 2/3

Why 2/3?

OP's intuition says that once you pick one gold coin, you know that you have one of two boxes, and that there are exactly 12 coins in those two boxes combined, two of which are gold, so that would put the probability of getting another gold coin at 2/12.

Wait, I am wrong.

The probability of picking the two-gold box is 1/3. The probability of picking the mixed box and finding gold on the first draw is 1/3*1/11=1/33.

11/33 vs 1/33, I am 11 times more likely to find another gold coin, not two times.

Because you know that you picked gold initially. The odds of the second coin being gold is the odds that you didn't pick 1/3 boxes with with both gold and silver coins, meaning 2/3. The only way the second coin isn't gold is that the initial choice was the box with both silver and gold coins in it, the number of silver coins in that box do not matter because of the precondition of having picked a gold coin.

Of course they matter, they increase the chance that the gold picked in round one was from the double gold box dramatically, which itself hugely increases the odds of round 2 is also gold.

They dont matter because the question is conditioned on that we already picked a box with a gold coin.

The question is what the odds are that we picked the box with both gold and silver, given that we have a box with at least a gold coin in it. There is 1/3 with gold and silver, hence the probabilty of the second coin being gold is 2/3. You could increase the amount of silver coins by infinity and it wouldn't matter. You're picking boxes, not coins.

Yes. But the fact that w already picked a box with the gold coin tells us that it was almost certainly the double gold box and therefore that the probability of the gold second coin is even higher.

No, it tells us nothing. The question is conditioned on a gold coin having been picked.

We didn't pick a box at random, the gameshow host did and revealed a gold coin.

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I think this checks out but someone else will need to check for me.

It's probably good that you're not trying to flex too much about how smart you are due to finding the solution to this problem incredibly obvious, because it seems that you got the answer correct the same way that a broken clock gets the time correct twice every day. ;)

Okay, rude.

I disagree. Maybe this is the reason I "always forget" the simple route; because I'm not sure it's actually right. I did this two different ways, my renormalization route (thinking of things as a tree with info sets) and just brute reproducing the wiki entry on using Bayes to solve it.

Method 1: Renormalization

There's a 1/3 chance of picking each box, one which has a 100% chance of giving you a gold on the first draw and the other has a 1/11 chance (ignoring the option with zero chance of getting a first gold), so the chances of me being in each relevant box at the current state are 1/3 and 1/33. To renormalize, I need to multiply by the reciprocal of their sum, 1/3 + 1/33 = 12/33.

So my chance of being in the GG box is 11/12 and my chance of being in the G10S box is 1/12.

Method 2: Straight Bayes, yo

Just shutting up and calculating, reproducing the wiki article directly.

P(GG|see gold) = P(see gold|GG)*(1/3) / [P(see gold|GG)*(1/3) + 0 + P(see gold|G10S)*(1/3)]

P(GG|see gold) = (1/3) / (1/3 + 0 + 1/33)

= (1/3) / (12/33)

= 11/12

I'd say law of conditional probability is the simplest route here. P(2nd Coin Gold | 1st Coin Gold) = P(Both Gold) / P(1st Coin Gold) = 1/3 / (1/3 * 1 + 1/3 * 1/11) = 1/3 / (1/3 + 1/33) = 1/3 / (12/33) = 1/3 * 33/12 = 11/12.

This is obviously correct, I have no idea what the other people are saying.

Two intuitive ways to formulate this come to mind.

First, law of conditional probability. P(A | B) * P(B) = P(A and B), or alternatively, P(A | B) = P(A and B) / P(B). P(2nd Coin Gold | 1st Coin Gold) = P(Both Coins Gold) / P(1st Coin Gold). P(1st Coin Gold) is 50% or 1/2, the probability of selecting the box with both gold coins (1/3) plus the probability of selecting the mixed coin box times one half (1/3 * 1/2 = 1/6). Probability both coins are gold is 1/3, as it can only occur if you pick the one box of three with two gold coins. 1/3 / (1/2) = 2/3.

Second, just thinking of all the possible outcomes before any coins are picked. Let's arbitrarily designate one coin in each box X, and the other Y. So boxes one to three contain coins Gold X and Gold Y, Gold X and Silver Y, and Silver X and Silver Y, respectively. There are only six possible outcomes for first and second pick, comma separated:

  1. Gold X, Gold Y
  2. Gold X, Silver Y
  3. Silver X, Silver Y
  4. Gold Y, Gold X
  5. Silver Y, Gold X
  6. Silver Y, Silver X

If you picked gold first, you know you can't be in outcomes 3, 5, or 6. Out of outcomes 1, 2, and 4, two of those have gold as the second pick. Thus, 2/3 once again.

I’m convinced this is easy to explain to pretty much anyone, just by making clear that the fact that you chose gold first makes the double-gold box more likely than the mixed box because coins of the same type are fungible.

Like the Monty hall problem, people who make the mistake do so not (necessarily) because they’re stupid, but because they just haven’t been taught to think carefully about the “given that” aspect of these probability questions.

If you pick a gold coin in box A, you have a 100% chance of getting a second gold. If you pick a gold coin in box B, you have a 0% chance of getting a second gold. (100+0)/2 does indeed equal 50. But the first gold was clearly twice as likely to come from the double-gold bucket as the mixed bucket, which means that the chance of a second gold is obviously also higher.

I got the right answer, but I always forget the simple way of thinking about it that you mentioned and do these problems the hard way.

There's a 1/3 chance of picking each box, one which has a 100% chance of giving you a gold on the first draw and the other has a 50% chance (ignoring the option with a zero percent chance of getting a first gold), so the chances of me being in each relevant box at the current state are 1/3 and 1/6. Renormalize, and you get a 2/3 chance of getting another gold. I think this renormalization reasoning works for these particular problems, but I'd probably have to sit with Bayes rule for a minute to convince myself that it does generalize. I've been doing game-theoretic information sets on extensive form games more recently, so I'm picturing a tree in my mind and an information set across states.

I almost said 50%, but 2/3 is easy to prove by enumerating every possibility: uppercase coins are gold, lowercase coins are silver:

  • boxes contain AB, Cd, ef
  • there are six potential outcomes:
    • A, then B
    • B, then A
    • C, then d
    • d, then C
    • e, then f
    • f, then e
  • the last three are not what happened, so you're in one of the first three potential timelines, two of which result in a second gold coin

I prefer the boy or girl paradox, which is much less straightforward.

So, if you treat the coins as not being fungible, this makes sense. But they are fungible? So why wouldn't it be 50%? The question isn't about pulling a specific gold coin, but any gold coin. Like I'm pretty sure I could bang out a quick script that will run this 1000, or 10,000 times, or however many you want, and the observed results will be 50% and not 66%.

Edit: Huh, I'll be damned, it is coming out 66%

"Fungible" is misleading. There are 3 boxes, therefore each box has 1/3 of the possible outcomes. If you start with that, everything else falls into place.

function randint(n) {
	return Math.floor(Math.random()*n);
}

function draw_twice() {
	let boxes = [[0,0],[0,1],[1,1]];
  let box = boxes[randint(3)];
  let first_coin = randint(2);
  let second_coin = 1 - first_coin;
  if (box[first_coin] == 1) {
  	return box[second_coin];
  } else return -1;
}

cases = [0,0,0];
for (let i = 0; i < 10000; i++) {
	cases[draw_twice()+1]++;
}
console.log('Silver picked first: '+cases[0]+' times, gold->silver: '+cases[1]+' times, gold->gold: '+cases[2]+' times');

Console output:

"Silver picked first: 4893 times, gold->silver: 1731 times, gold->gold: 3376 times"

Note that if I drew the coin with box.pop(), I'd get 50% because I'd only be drawing the gold coin from [0,1] every time.

Yeah, mine was a bit different.

class box
{
    public bool[] coins = new bool[2];
}
class Program
{
    static void Main(string[] args)
    {
        box[] boxes = new box[3] { new box(), new box(), new box()};
        boxes[0].coins[0] = true;
        boxes[0].coins[1] = true;
        boxes[1].coins[0] = true;
        boxes[1].coins[1] = false;
        boxes[2].coins[0] = false;
        boxes[2].coins[1] = false;

        int discard_count = 0;
        int firstcoin_count = 0;
        int secondcoin_count = 0;

        Random rand = new Random();

        for(int i = 0; i < 100000; i++)
        {
            int boxnum = rand.Next(0, 3);
            int coinnum = rand.Next(0, 2);

            bool firstcoin = boxes[boxnum].coins[coinnum];
            if (firstcoin)
            {
                firstcoin_count++;
                bool secondcoin = boxes[boxnum].coins[(coinnum + 1) % 2];
                if (secondcoin)
                {
                    secondcoin_count++;
                }
            } else
            {
                discard_count++;
            }
        }
        Console.WriteLine(string.Format("discard_count = {0}", discard_count));
        Console.WriteLine(string.Format("firstcoin_count = {0}", firstcoin_count));
        Console.WriteLine(string.Format("secondcoin_count = {0}", secondcoin_count));
        Console.WriteLine(string.Format("chance of second coin given first coin = {0}", (double)secondcoin_count / (double)firstcoin_count));
    }

With output of

discard_count = 49935

firstcoin_count = 50065

secondcoin_count = 33440

chance of second coin given first coin = 0.6679316888045541

1/2, because given that I've withdrawn a gold coin, the only possibilities are that I'm drawing from either 1g1s or 2g, so after I've drawn for the first time, the box I'm drawing from is either 1s or 1g. Equal chance between those. If we work through this from the very beginning, I have a 1/3 chance to pick either of the three boxes, but the p(1/3) case to draw from 2s is discarded according to the premise.

I see where my mistake is after reading the explanation: I've assigned separate cases to each box rather than each coin.

I made the same mistake.

Your mistake is that upon drawing a gold coin, you concluded you’re equally likely to have drawn from 1g1s and 2g. The latter is twice as likely as the former. Interesting that more people would have understood this if the numbers were 100s, 99s1g, and 100g.

1/3? Unless I'm missing something, it's another variant of the Monty Hall thing.

Damn. I'll claim half a point for getting the opposite of the right answer.

Fun and mysteries with maps and money.

This map on Wikipedia is almost not surprising. Metropolises and mountain retreats for billionaires are in dark green (as is oil-rich Midland County, TX), everything else literally pales in comparison. But there's this dark green square in Nebraska that is completely out of place.

It's Wheeler County, and it has less than a thousand residents. And for some reason its per capita personal income shot up in mid-2010's but is now similar to the nearby Garfield County. What's going on? It's small enough that a big sale should effect the per capita ranking (an increase of 61k times 800 residents means someone earned 50 million dollars), but it's not a peak, it's a hump. Who has spent several hundred million buying up land in the middle of nowhere in 2011-2016? Bill Gates? Ted Turner?

And there's Union County, the coccyx of South Dakota. There's no hump, it's just rich and growing richer. If there was a major booming company there, the whole Sioux City metro area would've been darker, but only Union County is an outlier. It's not that small (16k people) that a single rich family would skew the per capita income either. It it because every person of affluence from Sioux City has moved to Dakota Dunes? Just how many people earning hundreds of thousands can the meat packing industry support?

Does wheeler county have a jackpot winner? Like it’s 1000 people, can skew it pretty easily.

It's not a spike, it's a hump. Multiple years of increased income followed by a return to normalcy.

Lotteries do that lump sum vs. payment plan thing. I wouldn’t rule them out.

Or some other sort of windfall. Promising mineral assay? Intellectual property? Messy divorce? I dunno.

Couldn't it be slightly more senior oil/gas workers that for some reason have their families there?

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