Recommend
1 
 Thumb up
 Hide
27 Posts
1 , 2  Next »   | 

BoardGameGeek» Forums » Gaming Related » Gaming Articles » Musings On

Subject: Cheat/Bullshit and Game Theory rss

Your Tags: Add tags
Popular Tags: game_theory [+] [View All]
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
I love pyschological games where the players are trying to read each others' mind. But as it turns out, for some of these games thinking anything at all actually doesn't help in the least. Instead, you'd be "best" off playing randomly or using a set formula regardless of what you think your opponent thinks.



I was just reading a post on rock-paper-scissor, and I agree with the poster who said completely random play is the "optimal" strategy. (I put in quote because say, against an opponent who throws rock 99% of the time then random play is obviously not the best strategy. But then again he might throw scissor cuz he knows you'll be throwing paper to beat his rock. Anyways you get the point: you have the same chances of outguessing your opponent as you do of beating him by playing randomly.)

Another, more interesting article, shows that in a specific variation of poker (invented for the purpose of explaining game theory), optimal play is to follow a predetermined plan. In fact, you can tell your opponent what your plan is, and you'd still win. The game plan is foolproof no matter how the opponent plays.

So my question is, can such a game plan be applied to my 2-player variant of Cheat/Bullshit? Right now I am playing it in a purely psychological way, and it works. The game is fun, and I am actually pretty decent at reading my opponent's mind. The player who can read the other's mind better actually has a much higher chance of winning. But that's providing that the inferior opponent has a mind to be read. Would the otherwise inferior player be better off playing randomly/using a set formula of when to cheat or not than trying to read the other player's mind and outguess him?

If there is such a formula, what is it? And if there isn't, why not?

The implications of this is that, if the answer is the former, then Cheat is a broken game and I'd probably stop playing it except for game theory testing reasons.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Michael Barnes
United States
Decatur
Georgia
flag msg tools
Avatar
mbmbmbmb
Gasp! Easy there Koala bear! Don't you know they've got those buttons installed that immediately report you to the BGG Overmind if you say bad words?

"Freedom of Speech- Just Watch What You Say"
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Daniel Karp
United States
Rockville
Maryland
flag msg tools
admin
Developin' Developin" Developin!!
badge
100 geekgold for OverText, and all I got was this stupid sentence.
Avatar
mbmbmb
I hardly think Bullshit counts as excessive profanity, especially when it is part of the name of a game. If we removed bullshit, one of the tamest of "offensive" words, that would be the equivalent of banning ALL profanity, which is not our intention.

Carry on!
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Geoff Bohrer
United States
Hereford
Arizona
flag msg tools
designer
badge
Avatar
mbmbmbmbmb
Besides, how many people think Barnes' existence constitutes offensive behavior?

Come on, raise your hands!
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Matthew Gray
United States
Reading
Massachusetts
flag msg tools
admin
Avatar
mbmbmbmbmb
One key with all of these games, is they change if you are playing against non-optimal opponents.

In RPS, it's true that the "optimal" strategy of random selection with equal probabilities will win 33%, tie 33% and lose 33%. But, if I play against a suboptimal player I can do far far better. With an adaptive opponent capable of finding the optimal strategy, it will eventually converge to the optimal strategy.

But, with more complex games, even if there is an optimal strategy, and even if your opponents are smart, they can't necessarily identify the optimal strategy and therefore the "optimal" strategy may not be optimal for that game.

For example, in RPS, if I have an opponent who alternates between Rock and Scissors, I can win 100% of the time after I've figured out what he's doing. Someone using the "optimal" strategy will stay at 33%. In multi-player games (and two-player games, to a lesser extent), the key to the game is often not identifying the optimal strategy but identifying your opponents non-optimality and exploiting it.

So, even if there is a game theoretic optimal strategy for Cheat, unless it's easy to implement (ie, doesn't require massive bookkeeping/memory) and easy to discovery, it may still be a good game.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Paul DeStefano
United States
Long Island
New York
flag msg tools
designer
badge
It's a Zendrum. www.zendrum.com
Avatar
mbmbmbmbmb
dakarp wrote:
I hardly think Bullshit counts as excessive profanity,


But on the home page, as a thread title, you just moved from being a G rated site to PG.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Matthew Gray
United States
Reading
Massachusetts
flag msg tools
admin
Avatar
mbmbmbmbmb
Geosphere wrote:
dakarp wrote:
I hardly think Bullshit counts as excessive profanity,


But on the home page, as a thread title, you just moved from being a G rated site to PG.


I agree with Daniel, that as moderators, we're not going to come down on this kind of usage. It's a game name, it wasn't put there intentionally to antagonize, etc.

but...

I agree with Paul, it does make the site something that is more likely to be blocked by parents, corporate filters and otherwise disincline people from using the site. As a community member (NOT as a moderator) I think it would be nice to change the thread topic to "Cheat/I Doubt It and Game Theory".
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Michael Barnes
United States
Decatur
Georgia
flag msg tools
Avatar
mbmbmbmb
"Maybe if you guys could change it to 'Girl, we can't get much better' " ?
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
J C Lawrence
United States
Campbell
California
flag msg tools
designer
badge
Avatar
crackedlcd81 wrote:
"Maybe if you guys could change it to 'Girl, we can't get much better' " ?


The VP of Marketing at one of my prior startups had the simplest and best way of putting it:

Open legs for open wallets
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
You are right Matthew, but it's just not as fun exploiting other people's pyschological weaknesses when you know they can be better off and immune to your mind reading advantage if they'd just played randomly. For example, the inferior player in RPS can just choose to play randomly and give up trying to think at all.

Lets say a round of sevens is in play, and for simplicity each player can only play 1 card at a time. Each player has 2 sevens, and player A goes first.

On each of his playing turn, player A tosses a coin to decide whether to cheat or not. On his calling turns, he tosses a coin to decide whether to call or not.

If you were player B, what strategy would you use to beat player A's strategy?

 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Marc B.
United States
Palm Bay
Florida
flag msg tools
badge
Avatar
mbmbmbmbmb
mkgray wrote:

but...

I agree with Paul, it does make the site something that is more likely to be blocked by parents, corporate filters and otherwise disincline people from using the site. As a community member (NOT as a moderator) I think it would be nice to change the thread topic to "Cheat/I Doubt It and Game Theory".


This is where the parent/considerate human side of me agrees. I personally don't have issues with this type of language, when used in appropriate company. As a subject header that is on the front page of the site, I don't consider appropriate. I use mild words like this myself when I am among company that I KNOW won't be offended by it.
I personally don't use the F-bomb, and as a Christian will not take "my Lord's" name in vain ( quoted because I don't want anyone to think I'm preachin'). But most other words are basically rude by social standards only. Within the post bodies themselves is fine within reason. Spewing profanity every other word just makes me hit the back button.

I view it this way: The subject headers should be treated the same as something said in a crowd of strangers. If you are at all courteous of others why would you use profanity at an audible level with children/strangers around? The only reasons I can imagine is you have no respect for others and feel you need to prove it. Or you're just an ass. (see I use them)

So, I personally wish people were more considerate of others, but I also understand people who feel it is their right of "freedom of speech" to do it, though dropping loud fbombs in the line at the grocery store with children 2 feet from you doesn't make a positive case for you as someone to "look up to". It just means that as I see more and more of it, I can no longer allow this site to be a part of my families entertainment venues. Just like sports games, concerts, and most things that have many people gathered together.. Sad when a site about games can't be accessible to children.

Sorry, rant over. I'll leave the room now. Topic struck a cord in me.

arrrh
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Alex Rockwell
United States
Lynnwood
Washington
flag msg tools
designer
badge
Avatar
mbmbmbmbmb
Choosing truly randomly in RPS is only better if your opponent is better than you. Its worse if you are better than your opponent. It guarantees average results.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
David Fair
United States
Damascus
MD
flag msg tools
designer
Or maybe PowerGrid?
badge
Yeah, that's me. Handsome devil, I know.
Avatar
mbmbmbmbmb
Alexfrog wrote:
Choosing truly randomly in RPS is only better if your opponent is better than you. Its worse if you are better than your opponent. It guarantees average results.


At the World Series of Poker, they hold an RPS championship (proceeds go to cancer research, IIRC) every year. This year's winner was Annie Duke, who kept using different dollar bills to pick her next "throw", thusly:

Roll the bill so you can't see the serial number, then unroll it slowly so you reveal just one number. If it is 1-3 throw rock, 4-6 throw paper, 7-9 throw scissors, and on a 0, skip to the next number.

 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Mark C
United States
Ypsilanti
Michigan
flag msg tools
Avatar
mbmb

The bluffing article referenced in this thread is actually inaccurate in it's causation. You do not win the game because you are bluffing. You win because you have perfect information. By having perfect information, you are not truly bluffing, but using that information to limit your loss on the hands that you are going to lose.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tyler Sigman
United States
Seattle
WA
flag msg tools
designer
Avatar
mbmbmb
I used to teach Game Theory, and here's the brief take:

In games of pure equality, your best play would be as follows.

Condition A (your opponent is inferior; in other words, you can predict them better than they predict you): You should employ your advantage by trying to outwit. Choose your actions consciously.

Condition B (you are inferior; in other words, your opponent can predict you better than you can predict them): You should employ random decisions.

Employing random decisions is known in Game Theory as a "mixed strategy." Annie Duke's RPS tactic is a good example. In contrast, a "pure strategy" would be a strategy built up through conscious decision(s).

The classic example that illustrates the importance of a mixed strategy is this:

Imagine we are playing a game of "odds/evens". We each choose odd or even secretly, then reveal. If we choose the same thing (even-even or odd-odd), then I get $1. If we choose opposite things, then you get $1. From a game theory standpoint, this is a zero-sum game with a value of $0.

Now imagine that you are unbelievably smarter than me (probably true!) and can consistently outwit me by predicting my play. Theoretically, assume you can do it 100% of the time. Now I'm hosed: I'll lose $1 every time we play.

If I employ a randomized strategy, however, now there is no possible way for you to employ your skill. By using a mixed strategy of 50% Odd / 50% Even, I can bring the value of the game back to its theoretical $0. I will win as often as I lose.

Applying this to a Rock-Paper-Scissors tournament (or to "Cheat/BS"), you should use your skill if you think you have an edge, or resort to a purely randomized approach if not. The randomized approach won't guarantee a win, but it will theoretically neutralize your opponent's advantage if they have one.*

*In the book "The Banker, the Professor, and the Suicide King", Andy Beal (billionaire who takes on pro poker players in high stakes games) employs just such a mixed strategy to attempt to negate the skill edge of the poker pros. He keeps a randomizer in his pocket, and allows it to make some of his decisions for him. That way, the pros cannot use their skill to "read" him.

For some good reading on this subject, see "Game Theory: A Nontechnical Introduction" by Morton D Davis. There is a passage from Poe's "The Purloined Letter" which discusses an even/odd game where one child can predict his opponent 100% of the time.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
Well put Matthew, Alex and Tyler, what you said is what I meant to say.

Optimal strategies can be used by the inferior player to break even. If you want to win you have to 1)read his mind better than he can read yours and 2)he actually has a mind to be read (he's playing trying to out think you--the irony--rather than using a set randomnizing formula).

Either that or, he is using a formula but that formula isn't optimal, in which case you can also use your own formula to beat him (assuming you know what his formula is).

So for an inferior player, what would be the optimal formula in Cheat?

 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
Now supposing we are playing RPS for $1 per win, except that a win with a rock nets you $2. What would be the optimal strategy?

In case your opponent always plays rock, you playing: paper = +1 and scissor = -2. So your paper:scissor ratio has to be 2(or more):1.

Him playing paper. Rock = -1 and scissor = +1. Rock to scissor ratio must be 1:1(or more)

Him playing scissor. Rock = +2 and paper = -1. Rock to paper ratio must be 1(or more):2.

So I think the optimal strategy for rockaper:scissor ratio is 1:2:1. Interesting how it's paper that you should play more as opposed to rock.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Eric Haas
United States
Edgewood
Maryland
flag msg tools
badge
Avatar
mbmbmbmbmb
Alexfrog wrote:
Choosing truly randomly in RPS is only better if your opponent is better than you. Its worse if you are better than your opponent. It guarantees average results.


So, in any RPS match, the inferior player should always choose to play randomly, forcing the superior player to play randomly as well.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Barry Figgins
United States
Woodland
California
flag msg tools
badge
http://lyrislaser.com
Avatar
mbmbmbmbmb
Eric Haas wrote:
Alexfrog wrote:
Choosing truly randomly in RPS is only better if your opponent is better than you. Its worse if you are better than your opponent. It guarantees average results.


So, in any RPS match, the inferior player should always choose to play randomly, forcing the superior player to play randomly as well.


If the inferior player is truly playing randomly, it doesn't matter how the superior player plays. Anything he throws has even chances of winning, tying, and losing.

By the way, this whole thread is exactly why I hate the 'rock-paper-scissors' resolution for the Vampire: The Masquerade LARP. It's not really random.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Andrew Prizzi
United States
West Newton
Pennsylvania
flag msg tools
Avatar
Quote:
Another, more interesting article, shows that in a specific variation of poker (invented for the purpose of explaining game theory), optimal play is to follow a predetermined plan. In fact, you can tell your opponent what your plan is, and you'd still win. The game plan is foolproof no matter how the opponent plays.


Isn't that the definition for a broken game? Sounds like the old "let's flip a coin. Heads I win. Tails you lose." game. What's interesting about a game with a 100% unbeatable strategy?

Unless, of course you need such a game to convince a computer not to obliterate Russia with nuclear weapons.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Andrew Prizzi
United States
West Newton
Pennsylvania
flag msg tools
Avatar
Quote:
I used to teach Game Theory, and here's the brief take:

In games of pure equality, your best play would be as follows.

Condition A (your opponent is inferior; in other words, you can predict them better than they predict you): You should employ your advantage by trying to outwit. Choose your actions consciously.

Condition B (you are inferior; in other words, your opponent can predict you better than you can predict them): You should employ random decisions.


The strategy for condition B doesn't make any sense. The only "unequal" part of the game chess is that white gets to move first. We can eliminate this inequality by having the two players flip a coin, roll a die, play rocks paper scissors, or whatever else you want before the game- the winner gets to choose which to be: black or white. The assignment of sides is now a part of the game- that each player has an equal shot at.

So now, you're telling me that if I'm not as good a chess player as my opponent, my best strategy is to randomly select moves from all of my possible choices??? I'm pretty confident I'd get trounced in short order.

I can see the "play randomly" strategy working for some games- rock, papers, scissors for one, but there are lots of other games where the players start out equally in which random play would be anything but optimal- whether you're the inferior player or not. If you are the inferior player in such a game my advice would be "play as best you can. Hope the other guy screws up." I think that strategy will be much more succesful than the random selection of moves strategy. Plus, in the long run, you'll become a better player because you've been thinking about the strategy of the game instead of just pulling moves out of a hat.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
John Cataldo
United States
Somerville
Massachusetts
flag msg tools
Avatar
mbmbmbmbmb
prizziap wrote:
Quote:
Condition B (you are inferior; in other words, your opponent can predict you better than you can predict them): You should employ random decisions.


The strategy for condition B doesn't make any sense. The only "unequal" part of the game chess is that white gets to move first. We can eliminate this inequality by having the two players flip a coin, roll a die, play rocks paper scissors, or whatever else you want before the game- the winner gets to choose which to be: black or white. The assignment of sides is now a part of the game- that each player has an equal shot at.


You are clearly and obviously correct. However, "Game Theory" refers to a specific kind of math, not theories which apply equally to all games.

Everyone so far is right, when the right context is considered.

In particular, the random-play element requires unknown information (often being the opponent's decisions, as in RPS, but also sometimes like cards in Poker). The short version is that you don't want to play too consistently, or your opponents will always be able to react appropriately (in ways that disadvantage you). This doesn't really apply to games without unknown information ("guessing").
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
beri wrote:
Eric Haas wrote:
Alexfrog wrote:
Choosing truly randomly in RPS is only better if your opponent is better than you. Its worse if you are better than your opponent. It guarantees average results.


So, in any RPS match, the inferior player should always choose to play randomly, forcing the superior player to play randomly as well.


If the inferior player is truly playing randomly, it doesn't matter how the superior player plays. Anything he throws has even chances of winning, tying, and losing.

By the way, this whole thread is exactly why I hate the 'rock-paper-scissors' resolution for the Vampire: The Masquerade LARP. It's not really random.


All true, but if the other player is playing randomly, there is nothing to be gained by playing non-randomly, and you are risking having your play pattern being exploited and becoming the "inferior" player yourself.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
Quote:
So now, you're telling me that if I'm not as good a chess player as my opponent, my best strategy is to randomly select moves from all of my possible choices??? I'm pretty confident I'd get trounced in short order.


I don't know where you got that from. Nobody is saying/thinking that. Obviously we aren't talking about games like chess but purely luck and/or psychological games such as poker, cheat/bullshit, liar's dice, etc.


 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Tony Chen
Taiwan
flag msg tools
designer
badge
Avatar
mbmbmb
prizziap wrote:
Isn't that the definition for a broken game? Sounds like the old "let's flip a coin. Heads I win. Tails you lose." game. What's interesting about a game with a 100% unbeatable strategy?


On a side note, all perfect information games has a 100% unbeatable strategy. But we are not talking about perfect information games here.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
1 , 2  Next »   | 
Front Page | Welcome | Contact | Privacy Policy | Terms of Service | Advertise | Support BGG | Feeds RSS
Geekdo, BoardGameGeek, the Geekdo logo, and the BoardGameGeek logo are trademarks of BoardGameGeek, LLC.