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Subject: Is "She knows that I know that she knows that I..." simply a randomness? rss

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Maxim Steshenko
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Prediction of opponents' actions always benefits you. And I heard/read "I know that he knows that I know" phrase in game reviews from time to time. Sadly, I can't recall specific title right know. Usually this phrase is in a context when player guesses opponents' action and counters it with his own action. But there is a problem...
Let's take for instance Citadels. After first player picked a character and banned another one, second player may analyse other six characters and figure out opponent pick... or simply guess it with 50% chance.
I worked on a game where explicit prediction was a part of a gameplay and correct guess influenced on a turn outcome. And it worked until one of testers mentioned that "It simpler to guess rather that do this mindgames." Instead of puzzling out opponents' way of thinking you can make a choice in a split second with good chance to guess correctly. So, technically you can shuffle five cards, do mental exercise "She knows that I know..., make a prediction, reveal top card and it will be meaningful to you. Yes, as an optional "part" of a gameplay this mindgame may slightly benefits you, because occasionally analysing will be more accurate than blind guess. But what about using this as a core element of a game, when player must indicate opponents' choice?
Increasing number of choices makes prediction even less attractive and decreasing makes it easier to guess. Clues or any open information simply decrease number of choices rather than make prediction procces more interesting. For example, when opponent has 12 options to choose from and 10 of them are meaningful for current round, it's damn hard to predict his logic. And any clues like "Reveal green token if you choose one of this 5 options" ether narrow down number of options to guess or act as decoy and in the end will be always ignored.
Well, are that mindgames just an over-thinking over simple random choice or there is a way to make them more meaningful? I humbly ask for second opinion.)
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Yao-ban Chan
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I do wonder about this from time to time. In theory, when faced with what I call a "Princess Bride" situation (which is the same as the one you describe - I refer to the famous Vizzini battle of wits scene), optimal play is indeed to act randomly. And of course, if your opponent acts randomly, there's nothing to guess.

But here's the thing: it's well-established that humans are really bad at acting randomly. So psychological guessing can still be effective.

Regarding your second question, I'm not sure if there is a way to make the choices more meaningful. David Sirlin had this problem when he designed Yomi (which is basically built on Princess Bride/rock-paper-scissors situations). I recall that he implemented two things to address this: uneven valuations (each option is not worth the same) and incomplete information (regarding the valuation of each option). It seems to work quite well, although the basic charge of "random play is optimal" still applies.
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Andrew
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There's some empirical research that a particular fraction of people think one more level deeper each time - I can't remember the source but I believe Geoff Engelstein mentions it on one of his podcasts.

Within a game, simultaneous decisions fall into the field of Game Theory and "mixed strategies", where the optimal approach is to pick randomly according to probabilities that depend on the payoffs. Incidentally, humans are really bad at picking things randomly so people's "blind guesses" often aren't so random.

Doublethink becomes more interesting when payoffs are asymmetric and bluffs aren't free. In Citadels this comes from the characters' special powers.
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Eric Brosius
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If you introduce some asymmetry so that randomly picking one of several options is not an optimal "mixed strategy" (to use the game theoretic term,) it is very difficult for human beings to identify the correct random mixture of choices and then select the choices in a way that cannot be predicted by a canny opponent.

This makes it a real game, at least for humans.
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Russ Williams
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Orntt wrote:
But here's the thing: it's well-established that humans are really bad at acting randomly. So psychological guessing can still be effective.
Still, a half-way competent player can often act sufficiently randomly/unpredictably for practical purposes even if they're not acting highly randomly.

And a more competent player can unpredictably randomize genuinely well, e.g. simply by shuffling their action cards / tokens / etc and picking one, or by rolling a die, or by looking at the second hand on a clock and taking that mod N, or similar easy randomizing methods.

Quote:
Regarding your second question, I'm not sure if there is a way to make the choices more meaningful. David Sirlin had this problem when he designed Yomi (which is basically built on Princess Bride/rock-paper-scissors situations). I recall that he implemented two things to address this: uneven valuations (each option is not worth the same) and incomplete information (regarding the valuation of each option). It seems to work quite well, although the basic charge of "random play is optimal" still applies.
Agreed. Typical games of simultaneous decisions are simply fancied-up classical game theory situations, for which the optimum strategy is in general some random mixed strategy. Trying to outguess the opponent only seems realistically viable to me if the opponent is somewhat incompetent (e.g. Bart Simpson always playing "rock" in rock-paper-scissors.)

(Of course it might not be obvious what the optimal assignment of probabilities to options is... but mathematically solving for the optimal probabilities is probably not the kind of skill which the game designer was hoping to make the game depend on...)
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Big Lebowski
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yeah? well… y’know, that’s just like, uh… your opinion, man…
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if doublethinking was randomness, there would be no poker champions.
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Russ Williams
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woodoo03 wrote:
if doublethinking was randomness, there would be no poker champions.
The presence of randomness does not imply that skill has no relevance.

Otherwise there would be no champions in many games of chance, e.g. Backgammon, Scrabble, most euros and wargames, etc.
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Big Lebowski
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yeah? well… y’know, that’s just like, uh… your opinion, man…
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russ wrote:
woodoo03 wrote:
if doublethinking was randomness, there would be no poker champions.
The presence of randomness does not imply that skill has no relevance.

Otherwise there would be no champions in many games of chance, e.g. Backgammon, Scrabble, most euros and wargames, etc.
I agree with you. Nevertheless I regard the doublethinking in Poker as the non-random part of the game (luck of cards being the random one).
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Sturv Tafvherd
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russ wrote:

Still, a half-way competent player can ...

Wait ... how do we measure competency, and what's "half" of that?

Yeah, I'm trying to be funny.

On a more serious note (to the op) ..., consider this: random action is a strategy.
 
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Matteo Perlini
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Orntt wrote:
Regarding your second question, I'm not sure if there is a way to make the choices more meaningful. David Sirlin had this problem when he designed Yomi (which is basically built on Princess Bride/rock-paper-scissors situations). I recall that he implemented two things to address this: uneven valuations (each option is not worth the same) and incomplete information (regarding the valuation of each option). It seems to work quite well, although the basic charge of "random play is optimal" still applies.
I did a similar thing with my minimalist game Experior.
One part of the game is to read your opponent (and to avoid the opposite), the other part is to find the optimal play and manage your exp points.
 
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Justin R
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woodoo03 wrote:
russ wrote:
woodoo03 wrote:
if doublethinking was randomness, there would be no poker champions.
The presence of randomness does not imply that skill has no relevance.

Otherwise there would be no champions in many games of chance, e.g. Backgammon, Scrabble, most euros and wargames, etc.
I agree with you. Nevertheless I regard the doublethinking in Poker as the non-random part of the game (luck of cards being the random one).

Odds calculations and mathematically correct betting are nonrandom. So if the doublethink is random, there would still skill elements to poker. In fact, the lesson there is that a single hand applying doublethink is much less important that the macrocosm of trend recognition as informing one's play. So I'm not sure poker is proof that doublethink is not random, because the trend recognition is the skill.
 
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dennis bennett
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How do humans even "pick" "randomly"?
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Beau Bocephus Blasterfire
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I think it can be a big part of games, like in poker. In the end it does come down to a guess, but there is a human element as well when it comes to many of these situations. Some people are easier to read and can't bluff to save their lives, others are impossible to read.
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Ben Smith
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This makes me think of the game Revolution!. In this game, players all secretly and simultaneously bid to control a number of town leaders. Everyone has at least 5 resources to bid with, though they can put it all on one or spread out as they see fit. And there are a dozen different places (leaders) where you can bid. The catch is that if someone outbids or even ties you on a certain leader, then you get nothing for your bid. So what do you do?

If you try out the game you will likely get some insight into your question of how to make the choices interesting and strategic.

For one thing, there are certain optimal strategies based on the resources you win from certain leaders, so often you'll bid one turn on the guy who gives you more Force (a resource), and then use that Force next turn on the guy who gives you Blackmail (another resource), and go back and forth. BUT, because that is an optimal strategy, others know that you are likely to try it and can try to block you. So then you must decide, do I push for my "optimal" strategy, or abandon it in order to be random and thus unpredictable and harder to (purposely) stop.

One other thing that comes out of this game is that the longer you play these "She knows that I know..." kind of games with the same people, the more the human tendencies come out. People start to become more predictable and play in patterns. Certain of my friends prefer certain strategies in Revolution; and as soon as you detect these patterns in people you have a better chance to capitalize on that knowledge, even if it's only an increased probability of success and not a sure thing.

All that boils down to two things, in summary:
d10-1 Getting to know your human opponents is part of the fun of these games, and in some ways the test becomes "How well do you KNOW this person?" So a game skill becomes understanding a human, which is always a challenge.
d10-2 If you create a clear optimal strategy for someone, but allow others to stymy them if they act predictably, then you give people the interesting choice of whether to pursue their ideal strategy, or abandon it in favor of being "unpredictable."
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Brook Gentlestream
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I believe you are discounting the importance and subtelty of open-information hints far too easily. There's more to this genre than just Citadels, and yet more even than the theoretical "correct the right card and play the perfect counter to it".

This is actually one of my favorite styles of games and can be found in most games, but is especially prevalent in Citadels, Race for the Galaxy, Mission: Red Planet, The Ares Project, BattleCON: War of Indines, BattleCON: Devastation of Indines, Star Wars: X-Wing Miniatures Game, Star Trek: Attack Wing, and Chaosmos.

Try out any of these games. Each of these games makes use of open-information and the importance of prediction in entirely different ways. BattleCON, in particular, is like an extension course in the science and art of double-blind deduction.
 
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Jeremy Lennert
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silencewalker wrote:
Increasing number of choices makes prediction even less attractive
In what sense?

Increasing the number of options makes it less likely that you will predict your opponent correctly by blind guessing, and therefore increases the difference between a successful predictor and a mere guesser. It therefore offers greater rewards for demonstrations of predictive skill.

I suspect what you mean is that increasing the number of options makes trying to predict your opponents more discouraging, because it means you will be correct much less often--but if so, that's probably because your successes in the "easier" example were mostly attributable to luck.

Of course, if the player you are trying to predict is specifically trying to avoid being predicted, and you are roughly equal in skill, one would expect your odds of success to be pretty close to blind chance even if that shared skill level is rather high. Maybe it would be more interesting to employ prediction in a setting where the target isn't trying to avoid prediction (or at least cares about something else significantly more than avoiding prediction).
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Russ Williams
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dennisthebadger wrote:
How do humans even "pick" "randomly"?
There are many possible ways; I mentioned some explicitly in an earlier comment.

Unless you want to get all philosophical and play the "but nothing is truly random" card.
 
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Christopher Dearlove
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Orntt wrote:
In theory, when faced with what I call a "Princess Bride" situation (which is the same as the one you describe - I refer to the famous Vizzini battle of wits scene), optimal play is indeed to act randomly.

Of course in The Princess Bride the optimum play was not random, but to step outside the game. Cheat if you like.
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Christopher Dearlove
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dennisthebadger wrote:
How do humans even "pick" "randomly"?

Best way is with an external source. A coin (or dice, cards etc.) is good. If you can't do that then for a one-off value a sneak peak at a clock and use the seconds digits is good. Or the least significant digit of many things such as the stock market index. If no one knows what you are doing, and you happen to have memorised the digits of pi, use them.

(There are even real world applications of at least two things I've mentioned.)
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dennis bennett
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But that means you're using something outside of the game for help.
Potentially unfair.

 
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Russ Williams
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dennisthebadger wrote:
But that means you're using something outside of the game for help.
Potentially unfair.
A subject of occasional debate in these threads. I personally see nothing inappropriate/unfair/illegal about a player e.g. choosing one of their cards or tokens without looking, and I've never seen a convincing argument why it should be considered inappropriate/unfair/illegal.

The idea of randomizing by some mechanism outside your own mind is objectively unenforceable in any case. E.g. you could decide to generate a random number by counting in your mind until another player talks and use the number which you reached as your random number.

Or you could generate a sequence of effectively unpredictable random numbers wholly within your mind by using the numbers of letters in successive words of some arbitrary sentence which you made up and remember.

Or remember the digits of your old telephone numbers. Etc.

===

Possibly related example/idea: in many bluffing games you are supposed to make a statement about a card or some dice which other players can't see but which you yourself are allowed to see. I don't see anything wrong with making the statement without looking at the hidden info yourself. E.g. in Cockroach Poker sometimes a player hands me a card and says "That is a roach" and without looking I immediately pass it to another player and say "Yes, that is a roach". In some sense, I have made a random decision. I don't think there's anything wrong with doing this; do you?
 
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dennis bennett
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russ wrote:
dennisthebadger wrote:
But that means you're using something outside of the game for help.
Potentially unfair.
A subject of occasional debate in these threads. I personally see nothing inappropriate/unfair/illegal about a player e.g. choosing one of their cards or tokens without looking, and I've never seen a convincing argument why it should be considered inappropriate/unfair/illegal.

The idea of randomizing by some mechanism outside your own mind is objectively unenforceable in any case. E.g. you could decide to generate a random number by counting in your mind until another player talks and use the number which you reached as your random number.

Or you could generate a sequence of effectively unpredictable random numbers wholly within your mind by using the numbers of letters in successive words of some arbitrary sentence which you made up and remember.

Or remember the digits of your old telephone numbers. Etc.

===

Possibly related example/idea: in many bluffing games you are supposed to make a statement about a card or some dice which other players can't see but which you yourself are allowed to see. I don't see anything wrong with making the statement without looking at the hidden info yourself. E.g. in Cockroach Poker sometimes a player hands me a card and says "That is a roach" and without looking I immediately pass it to another player and say "Yes, that is a roach". In some sense, I have made a random decision. I don't think there's anything wrong with doing this; do you?

I'm not sure about how Kakerlakenpoker works but in most games of bluffing (where people can call you out on your bluff) it's a suboptimal stretegy to deny yourself information and not look at the card.

In most games, having any specific card will be less likely than having "any other card", so being called on your bluff will give your opponent more than a 50% chance of winning.

I personally just don't see the point of playing against people who play like that. what i'm looking for is some human/social interaction. If you're using some form of generating random numbers you're essentially denying me that human factor. I might as well play against a computer or play a game of solitaire.
 
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Martin G
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See also: http://boardgamegeek.com/thread/1101630/anyone-else-experien...
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dennis bennett
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qwertymartin wrote:

LOL. I just thought of that thread but didn't go to the trouble of looking for it/quoting it. thanks!
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Yao-ban Chan
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Dearlove wrote:
Orntt wrote:
In theory, when faced with what I call a "Princess Bride" situation (which is the same as the one you describe - I refer to the famous Vizzini battle of wits scene), optimal play is indeed to act randomly.

Of course in The Princess Bride the optimum play was not random, but to step outside the game. Cheat if you like.

Good point. But that's not going to stop me trying to get the name accepted into the general vernacular.
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