# 38

(not by Parker Bros., or, for that matter, Waddingtons)

A response to: 3 Levels of Rationality Verification

Related to: Diplomacy as a Game Theory Laboratory

It's a classic who-dun-it…only instead of using an all-or-nothing process of elimination driven by dice rolls and lucky guesses, players must piece together Bayesian clues while strategically dividing their time between gathering evidence, performing experiments, and interrogating their fellow players!

ROOMS:

Hematology Lab -- bring a blood sample over here, and you can find out one bit of information about the serotype…is it A or O? B or O? + or - ? The microscope knows. Don't know how to use a microscope? Try reading up on it in the Library.

Autopsy Table -- bring a body part over here, and you can take an educated guess as to what kind of weapon caused the murder wounds. (Flip over 1 of 10 cards, 4 of which show the correct murder weapon and 6 of which are randomly distributed among the other five weapons.) The error in guesses doesn't correlate across body parts, so if you personally examine enough of them, or if you can persuade your fellow dinner-guests to bust out all the body parts at the same time, you should be able to get the right answer.

Lie Detector -- bring a fellow player over here, and you can ask him/her a yes-or-no question and get some evidence as to whether it was answered honestly. Have the answerer roll a D10, add a secret constant unique to his/her character, multiply the sum by the truth value of his/her statement (1 for true, 2 for false), and then look up the number on a chart that returns the value "stress" or "no-stress."  It's up to the interrogator to figure out the correlation (if any) between stress and lying for each player! How do you get the other player into the Lie Detector room in the first place? Good question! When you figure it out, let me know…I have a paper I'd like you to co-author with me on the Prisoner's Dilemma.

Plus the usual collection of Kitchens, Billiards Rooms, Parlours, and so forth. One room is inaccurately labeled.

PIECES OF EVIDENCE:

If you spend your turn searching a room, you might find…

Blood stains -- most of them are either from the murderer or the victim, but some are not. You can take a sample so as to carry it with you to the Hematology Lab.

Body parts -- all of them belong to Mr. Boddy, and all the parts are nice and portable…just the right size to shove one in your pocket and dash back to the autopsy table to sneak a peek by yourself. Of course, if you're feeling cooperative, it might be more efficient to get the gang together and lay all your cards, er, on the table, at the same time.

Video footage of the murder -- just kidding. What kind of game did you think you were playing here, anyway?

WHERE DID THE MURDER TAKE PLACE?

The game rules chattily assure you that the murder did not take place in the Lab, on the Table, or by the Detectorbut of course this is simply disinformation coming from a source that you are likely to erroneously assume is authoritative, even though you have no firm evidence that the rulebook is a reliable narrator.

You don't need to know where the murder took place to win, as each player only gets one guess, and there are 36 weapon * character possibilities, which is a lot to sift through with just a handful of sadistic clues. However, for bonus points, you can try noticing that most of the useful clues come from the same room, and that the murderer knows where (s)he killed Mr. Boddy, so if you ask real nicely you might be able to ask him/her a few thoughtful questions over at the Lie Detector.

HOW DOES THE GAME END?

Once you realized Mr. Boddy had been killed on a dark, snowy night that shut down all travel in and out of the mansion, one of you took the precaution of activating the house's high-tech security cameras -- the murderer will not kill again this night. Rather, you will all dither endlessly until all but one of you can agree on a prime suspect, at which point you will join forces, handcuff him or her to the telescope in the Observatory, and wait for the snowplow to come through and the police to arrive, at which point you will find out just how right (or wrong) you were.

This has the distinct advantage that if most people want to stop playing they can rule-fully end the game at any time.

Note, by the way, that while I hope at least some parts of my description are funny, this is not really a joke -- I would like to design this board game and then playtest it with casual Less Wrong readers to see if it motivates us or otherwise helps us to test, develop, or practice rationality skills. If you have feedback about either the game's playability or its educational value, I'd love to hear it.

# 38

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If you did design this game,

The game rules chattily assure you that the murder did not take place in the Lab, on the Table, or by the Detector…but of course this is simply disinformation coming from a source that you are likely to erroneously assume is authoritative, even though you have no firm evidence that the rulebook is a reliable narrator.

...should be in the rulebook.

Agreed. Especially since not everyone will read the rulebook. Usually one person learns the rules and tells the other players.

As a modification for Clue, I think this will end poorly. But I think the idea of a rationalist board game is one that could end well.

Boil this down to the essentials. What is the goal of the game? What is the victory condition? What is the core mechanism?

Here's a brief guess/sketch:

The game is designed to teach reasoning under uncertainty. The victory condition could be either coming to the correct conclusion first or having come to the best conclusions at lowest cost. The core mechanism is integrating new information with old information.

The tenor of the game will be set by the victory condition. A set of reveals- say there are three cards you want to guess, and they are flipped over one by one at various stages of the game- where people place bets for victory points seems superior to a race to one correct answer.

For example, let us consider a three player game. There are color cards, shape cards, and material cards. There are three cards of three types (red, blue green; circle, triangle, square; wood, metal, glass). Each deck of 9 cards is shuffled, and one is removed at random and placed in order (so there is a color then a shape then a material). The remaining 24 cards are shuffled together and 8 cards are dealt to each player. Players now have incomplete and uncertain information- even if I hold 2 blue cards in my hand, the removed card might be blue. I can be certain it's not blue if I hold 3 blue cards, but that doesn't help me figure whether to bet on red or green.

Players share information somehow. How can be worked out later.

Players start off with, say, 6 tokens. After a set amount on information sharing, players must bet at least 1, but up to as many as they have, tokens on what the color card may be. The amount of the bid is not secret, but the color selected is (and they can bid on as many colors as they would like). A correct bet is doubled. Then there is another information-sharing phase, then the players bet on what shape was pulled out. Another information-sharing phase, then the players bet on what material was pulled out.

I think this would work best with fewer information-sharing rounds but high-quality information.

 Note that this doesn't really deal with the Bayesian issue of integrating new and old information, unless the information-sharing is built that way. It should be something better than just showing people cards.

[2023 edit]: A better game than my suggestion here is Figgie.

[-][anonymous]13y4

There's definitely an idea here for an enjoyable, playable game. I've had a go at fleshing out the rules, but not got anything entirely to my satisfaction, so instead I'll list what I consider to be some important design questions.

The first is whether or not the murderer should know who they are. If they do, there's a risk that the game turns into Mafia, with an emphasis on dealing with deception rather than assessing evidence. This is not necessarily a bad thing, but it's something to be aware of. If not, or if the murderer is not a player character, then some sort of time pressure needs to be introduced to force the kind of trade-offs you wanted to see.

Under what circumstances are players allowed to ask each other questions, and is this done in public or in private? With a cooperative game there would seem to be little point in keeping secrets, but with a rogue murderer opportunities for misdirection would add useful complexity.

There's a risk that the randomisation aspect become sufficiently complicated that it would really need to be done by computer, but a game that could be played by people sitting around a table would be much more useful, and enjoyable.

This could be a fun and educational game. Possibly even commerically exploitable.

The first is whether or not the murderer should know who they are. If they do, there's a risk that the game turns into Mafia, with an emphasis on dealing with deception rather than assessing evidence. ... [If they don't] there would seem to be little point in keeping secrets [and] ... some sort of time pressure needs to be introduced.

Spot on, all all counts. There are other ideas that just got posted that might help with this; if players had a limited number of chips and were playing to maximize their chip count, then sharing info would only make sense if you thought it would give you a relative advantage. If the murderer was given weak evidence that he/she was the murderer, that might create a bit of deception without encouraging a Mafia dynamic. Accusations could be made expensive relative to other activities (i.e., you have to go to the Control Room, or gather everybody together, etc.).

Under what circumstances are players allowed to ask each other questions, and is this done in public or in private?

I had imagined that you can talk whenever your characters are in the same room, but you can't ever physically flip over your clue cards to show people what they say. E.g. if you did an autopsy on the left leg and it revealed lead-pipe-impacts, you could say "It was a lead pipe, I swear!" but you couldn't actually give the person your "lead-pipe-impact" card. Just like in real life, we don't have provably-secure mind-bridges. You could, however, give the person the left leg, and then they could do their own autopsy.

There's a risk that the randomisation aspect become sufficiently complicated that it would really need to be done by computer.

I agree, and I'll find ways to avoid that risk. It happens to be one of my talents.

This could be a fun and educational game. Possibly even commerically exploitable.

Thank you! I'm glad you think so.

I'd love to play this game. It looks awesome and will likely lead to either learning or hilarity.

I think the lie detector schema is overly complicated, but that may be because I don't have access to the stress/no stress table. If the table is non-random, and the questioner can see the d10, it should be okay.

Also, what exactly is the win condition? Figuring out who done it and handing them over to the cops? That plus knowing which weapon and room?

I'm pretty sure the point of the lie detector that it conveys essentially no information. Real lie detectors are notoriously unreliable.

I thought it was a nice touch.

I was looking at it from a game perspective, but from a realist perspective it's good.

Worse than unreliable - they read "stress" pretty much whenever an accusatory question is asked (since being accused of things, even falsely, is stressful), which means that ignorant users will pretty much always conclude that the person being questioned is guilty.

I imagine the "stress table" is just a threshold value, and dice roll result is unknown. This way, stress is weak evidence for lying.

Also, what exactly is the win condition? Figuring out who done it and handing them over to the cops? That plus knowing which weapon and room?

Correct, and in that order.

I'd like to play it. This could work by email, turn-based. All players could move simultaneously on each turn.

I'd like to give it a shot too

All right, Phil, I'll PM you if I get the rules and maps and cards together.

Can I be in too?

[-][anonymous]13y2

I'd be interested, but couldn't make a firm commitment to be available at this stage.

Lol, yes, of course. Quiver, you don't need a firm committment yet -- there's another game I'm designing first, so this one won't be ready until March 1st at the earliest.

I clicked on the title of this post expecting that you had made some sort of rationalism-specific clue-by-four, and had pictures.

This is pretty cool too, though. :-)

Activating the security cameras does not, in and of itself, prevent further murders. It's a deterrent, not a shield.

If that's how you want to play it, I'd recommend having a game mechanic for assaulting another player's character with one of the murder weapons, which forces them into cryostasis or uploading. Cryostasis is, from an out-of-game perspective, "Screw you guys, this sucks, I'm gonna go do something else." Uploading means you can continue to play, in a robotic telepresence body, but (due to the inadequately-secured wireless signal) can no longer keep secrets, and possibly have other restrictions.

The security system, having been put on alert, cannot be quickly and non-destructively shut down without a set of codes that Mr. Boddy was clever enough to not keep written down on-site. It is possible, however, to spend a turn's action functionally disabling the surveillance in a given room, either by taping opaque obstructions over lenses (which can be easily reversed by anyone else in the room) or by destroying the cameras outright. Either is enormously suspicious, there's a chance you missed one, and you have to be in the room in question to even make an attempt. Alternatively, from the security system's control room, it's possible to recalibrate a given room's cameras into uselessness: pivot them to face walls, turn up the gain to record only whiteout, etc. This is always impermanent, but makes it safer to break the cameras. From the control room, it's possible to review recordings (look at the notes other players have secretly exchanged) but not destroy them, since there's an off-site backup.

It would make sense for at least one person to sincerely remember being the murderer. That's strong evidence, but far from perfect. If a person who remembers actually is the murderer, their memories of how it happened and where are also useful. Everybody knows what they remember, nobody knows The Truth... until it's over.

It's the same basic genre as Mafia or Diplomacy. Might as well admit it and learn from what came before.

I think the tricky Bayesian-specific part would be the probability estimates. What about giving everyone chips, like for roulette? Start with a pile, expend them on certain in-game actions. When the game ends, if there's a spot that turns out to be true but you didn't put any chips on, you lose outright, but the highest possible score is to have exactly one chip on each correct answer and none on any others, regardless of how many you spent, representing peoples' willingness to put up with annoying behavior from someone who turns out to be an oracle.

What about giving everyone chips, like for roulette? Start with a pile, expend them on certain in-game actions. When the game ends, if there's a spot that turns out to be true but you didn't put any chips on, you lose outright, but the highest possible score is to have exactly one chip on each correct answer and none on any others\

You mean, like Wits & Wagers?

About three questions worth of W&W for the endgame, yeah. One big difference, though: failure to bet on a winner in a given round normally just means you win nothing, and lose as much of your stake as you bet that round. In Bayesian probability, assigning probability zero means there's no going back, so it's important not to do that unless you're unreasonably sure. Of course, the goal of the game is to be rational, and rationalists should win, so it's good to have an ultimate victory condition that someone who's blatantly irrational can achieve occasionally by dumb luck, to keep the ones who are as skilled at the game as is reasonably possible craving opportunities to improve further.

I like the idea a lot. I'm not nearly as crazy about your analysis, but, then your analysis is maybe 100 x more complicated than the idea itself in terms of Kolgormoioff-who's-his-face-complexity, so that's not too too surprising.

I think if we're going to apply strict Bayesian religious payoffs, we'll need to give each player more chips to drive the point home. With six chips and three choices, e.g., it's trivial to learn to bid 3:2:1 or 4:1:1 (the only combinations that don't leave a zero anywhere), depending on whether you're "sure" or not that your #1 pick is correct. It's also suboptimal: if you're only going to play, say, 3 or 4 games with the same group of people, and each game has 3 rounds, and you are rationally 95% confident that your #1 pick is correct with 3.5% in your #2 pick and 1.5% in your #3 pick, then you could bid 5:1:0 and expect to beat all your friends until they got bored with the game. It teaches the wrong lesson, maybe. Life offers more iterations than one-off Clue.

With six weapons and six characters and, say, 40 chips, there is still a temptation to play zero chips on some weapons, but the dangers of this strategy are likely to become vividly apparent in only a few games...because you don't need to leave a tile open in order to win (you can win by outguessing others with your distribution, maybe putting 15 chips on a weapon that you are quite sure of, and only 5 on the character you are most sure of, because you are well-calibrated and know what you know), the downsides of leaving a zero open are fairly apparent. Your final score could be the chips you bid on the winning weapon times the chips you bid on the winning character.

[-][anonymous]13y0

Instead of making one guess, each player submits a probability distribution and the one with the best log score wins.