The mathematical modelling of popular games by Nick Berry
April 7, 2012 10:16 PM Subscribe
H _ _ _ m _ n, Y a _ _ _ e e, _ _ t t _ _ _ h i p, _ h u t _ s & L a _ _ e r _ , R _ _ k , _ _ n d y _ _ _ _ , and _ _ r t s.
M _ _ t e _ y m _ a t.
posted by Brocktoon at 11:45 PM on April 7, 2012 [2 favorites]
posted by Brocktoon at 11:45 PM on April 7, 2012 [2 favorites]
Interesting.
It actually occurred to me the other day that I've been playing hangman wrong the entire time as a child, but for entirely different reasons. At least as the player selecting the word. When selecting a word, for some strange reason, I (and many other kids I played) tended to select comparatively long words (say "appendectomy" or "idiosyncratic"). Which means that there are fewer misses for the calling player. A better strategy would probably be to select extremely short words, and ones rhyming with many others at that, such as "zit" or "van". Or with few vowels like "thyme". Never got to put that theory to the test, though.
posted by sour cream at 11:52 PM on April 7, 2012
It actually occurred to me the other day that I've been playing hangman wrong the entire time as a child, but for entirely different reasons. At least as the player selecting the word. When selecting a word, for some strange reason, I (and many other kids I played) tended to select comparatively long words (say "appendectomy" or "idiosyncratic"). Which means that there are fewer misses for the calling player. A better strategy would probably be to select extremely short words, and ones rhyming with many others at that, such as "zit" or "van". Or with few vowels like "thyme". Never got to put that theory to the test, though.
posted by sour cream at 11:52 PM on April 7, 2012
There's no easy way to say it. You've probably been playing Hangman wrong your entire life.
I eventually figured out on my own that kicking away the chair wasn't the optimal strategy.
posted by dhartung at 11:58 PM on April 7, 2012 [5 favorites]
I eventually figured out on my own that kicking away the chair wasn't the optimal strategy.
posted by dhartung at 11:58 PM on April 7, 2012 [5 favorites]
Depends on the goal. In particular, if you want to win without making the other guy think you're some sort of total weirdo asshole, then playing ordinary garden-variety "hard" words — you know, the sort of reasonably common polysyllabic word that most people will think of when you ask them for a "hard word" — is better than playing technically-legal-but-irritating words like "qi" or "syzygy" or "crwd."
Odds are if you're playing hangman you're bored off your ass and trying not to doze off or stab anyone with a ballpoint pen out of sheer frustration. Winning is sort of beside the point.
posted by nebulawindphone at 12:00 AM on April 8, 2012 [3 favorites]
Odds are if you're playing hangman you're bored off your ass and trying not to doze off or stab anyone with a ballpoint pen out of sheer frustration. Winning is sort of beside the point.
posted by nebulawindphone at 12:00 AM on April 8, 2012 [3 favorites]
Hmm. On reflection, that comment sounded a little more geeky-middle-schooler-with-Stockholm-Syndrome than I meant it to....
posted by nebulawindphone at 12:01 AM on April 8, 2012 [1 favorite]
posted by nebulawindphone at 12:01 AM on April 8, 2012 [1 favorite]
ESIARN TOLCDU PMGHBY FVKWZX QJ
R S T L N and E still works.
posted by XhaustedProphet at 12:05 AM on April 8, 2012
R S T L N and E still works.
posted by XhaustedProphet at 12:05 AM on April 8, 2012
He missed the relative value of consonants vs vowels. It is easier to guess vowels given definite consonants, than to guess consonants given definite vowels.
posted by aeschenkarnos at 12:41 AM on April 8, 2012 [1 favorite]
posted by aeschenkarnos at 12:41 AM on April 8, 2012 [1 favorite]
Hangman anecdote: The 8th grade French teacher (who was nasty to me for years) asked us to play hangman. She picked me to come to the blackboard, secretly choose a French word and draw the hangman parts, when students didn't guess a letter correctly. Finally, the hangman was finished and nobody guessed the word. The teacher asked me to whisper the word in her ear. I leaned over and said the French word for seal, phoque (pronounced "fuck"). Ordered outside, the rest of the hour I spent out in the hall soaking in the deep smug.
posted by nickyskye at 12:42 AM on April 8, 2012 [20 favorites]
posted by nickyskye at 12:42 AM on April 8, 2012 [20 favorites]
nebulawindphone: technically-legal-but-irritating words like "qi" or "syzygy" or "crwd."
WUT
posted by syzygy at 3:23 AM on April 8, 2012 [3 favorites]
WUT
posted by syzygy at 3:23 AM on April 8, 2012 [3 favorites]
Nick Berry's earlier work on the analysis of games was much better, in which he concluded that "Every Loser Wins".
posted by gene_machine at 4:08 AM on April 8, 2012
posted by gene_machine at 4:08 AM on April 8, 2012
ETAOIN SHRDLU?
posted by Faint of Butt at 6:35 AM on April 8, 2012 [1 favorite]
posted by Faint of Butt at 6:35 AM on April 8, 2012 [1 favorite]
(Looking back at this post, I wish I had put a bit more thought into it. The pattern of missing letters in the links doesn’t make sense).
Anyhow, the non-Hangman links have some great stuff too. For example, regarding Chutes & Ladders:
posted by Jasper Friendly Bear at 6:59 AM on April 8, 2012
Anyhow, the non-Hangman links have some great stuff too. For example, regarding Chutes & Ladders:
In England, where I grew up, it goes by the name Snakes and Ladders. According to the internet, it is possible to trace the origins of the game back to the 2nd Century B.C. as the Indian game of Paramapada Sopanam — "The Ladder to Salvation."His analysis of Battleship is a great example of mathematical modelling. He starts off with a really simple strategy—randomly shoot anywhere on the board. He then starts iterating through it, making refinements.
It was invented by Hindu spiritual leaders to teach children about the rewards of good deeds and the negative consequences of bad ones. The snakes represent vices and poor decisions, and the ladders represent virtues and sound morality. The game first made its way to England in 1892, and was commercially sold in the United States in 1943 by Milton Bradley under the name Chutes and Ladders. It has been speculated that Square 100 represents the Hindu idea of Nirvana (and you thought it was just a kids’ game!)
posted by Jasper Friendly Bear at 6:59 AM on April 8, 2012
The Hangman results seem skewed by word endings (such as -s, -ed, and especially -ing) that are equally weighted in the dictionary but less likely to appear in an actual game.
posted by Casuistry at 7:02 AM on April 8, 2012
posted by Casuistry at 7:02 AM on April 8, 2012
phoque (pronounced "fuck")
Actually it's closer to "fock." Perhaps she was punishing you for poor pronunciation?
posted by yoink at 7:09 AM on April 8, 2012 [1 favorite]
Actually it's closer to "fock." Perhaps she was punishing you for poor pronunciation?
posted by yoink at 7:09 AM on April 8, 2012 [1 favorite]
I put up pneumonoultramicroscopicsilicovolcanoconiosis as the word in 6th grade. My teacher never let me put up the word again.
posted by Splunge at 7:50 AM on April 8, 2012 [3 favorites]
posted by Splunge at 7:50 AM on April 8, 2012 [3 favorites]
Does this mean I have 6 or 7 more Transformer movie clones to look forward to? Someone explain the Battleship tie-in for me.
posted by yerfatma at 8:29 AM on April 8, 2012
posted by yerfatma at 8:29 AM on April 8, 2012
Thanks for posting this, it's nifty!
Poking at the idea a bit further, Casuistry makes an interesting point about word choice in hangman. I'd guess that whole classes of words are more likely than others, in addition to various cases and tenses. (As an aside, I used to love a game we called "abstract twenty questions," where the only rule was that your choice couldn't be a physical object or action. Way more fun than the usual version, especially in the role of the answerer.)
Surely there exist online word guessing games with detailed logging; I wonder what it would take to convince one of them to let us access their data. It'd be pretty cool to see what words are actually chosen.
For that matter, I'll bet battleship position choices are pretty far from either random or optimal most of the time. If you ask a human to put 100 random dots on a piece of paper, the result looks nothing at all like an actual random distribution. (Can't recall where I first read that. I definitely didn't invent it.)
posted by eotvos at 11:28 AM on April 8, 2012
Poking at the idea a bit further, Casuistry makes an interesting point about word choice in hangman. I'd guess that whole classes of words are more likely than others, in addition to various cases and tenses. (As an aside, I used to love a game we called "abstract twenty questions," where the only rule was that your choice couldn't be a physical object or action. Way more fun than the usual version, especially in the role of the answerer.)
Surely there exist online word guessing games with detailed logging; I wonder what it would take to convince one of them to let us access their data. It'd be pretty cool to see what words are actually chosen.
For that matter, I'll bet battleship position choices are pretty far from either random or optimal most of the time. If you ask a human to put 100 random dots on a piece of paper, the result looks nothing at all like an actual random distribution. (Can't recall where I first read that. I definitely didn't invent it.)
posted by eotvos at 11:28 AM on April 8, 2012
The secret to Battleship? Draw a big X starting in the middle of the board. It works great until the other guy figures out that you do it every time.
posted by Splunge at 11:48 AM on April 8, 2012
posted by Splunge at 11:48 AM on April 8, 2012
Actually it's closer to "fock."
Of course it is. That's exactly why the juiciness of the smug was so satisfying, I got to whisper "fuck" with a French accent into the ear of a chronically mean teacher.
posted by nickyskye at 11:49 AM on April 8, 2012
Of course it is. That's exactly why the juiciness of the smug was so satisfying, I got to whisper "fuck" with a French accent into the ear of a chronically mean teacher.
posted by nickyskye at 11:49 AM on April 8, 2012
For that matter, I'll bet battleship position choices are pretty far from either random or optimal most of the time. If you ask a human to put 100 random dots on a piece of paper, the result looks nothing at all like an actual random distribution. (Can't recall where I first read that. I definitely didn't invent it.)
Well, and in any case, it's not clear that random distribution of ships would actually be optimal. If you know your opponent's guessing strategy, you can come up with a non-random arrangement of ships that will do better against it than a random arrangement would.
Of course, the smart thing to do at that point is for your opponent to rotate between guessing strategies. Which means you need to be able to predict when they're going to rotate....
What I'm trying to say is, Battleship is totally gonna be the new iterated prisoner's dilemma.
posted by nebulawindphone at 12:14 PM on April 8, 2012 [1 favorite]
Well, and in any case, it's not clear that random distribution of ships would actually be optimal. If you know your opponent's guessing strategy, you can come up with a non-random arrangement of ships that will do better against it than a random arrangement would.
Of course, the smart thing to do at that point is for your opponent to rotate between guessing strategies. Which means you need to be able to predict when they're going to rotate....
What I'm trying to say is, Battleship is totally gonna be the new iterated prisoner's dilemma.
posted by nebulawindphone at 12:14 PM on April 8, 2012 [1 favorite]
"Rhythm" is a great Hangman word unless the person happens to pick an "h".
Also "myrrh."
posted by Sidhedevil at 6:30 PM on April 8, 2012
Also "myrrh."
posted by Sidhedevil at 6:30 PM on April 8, 2012
Myrrh has the additional advantage that it's a fucking blast to say out loud.
posted by nebulawindphone at 6:34 PM on April 8, 2012
posted by nebulawindphone at 6:34 PM on April 8, 2012
The rest of that blog is all pretty interesting stuff (so far). If you've not come across Benford's Law, for example, do read this post on it.
posted by motty at 8:01 AM on April 9, 2012
posted by motty at 8:01 AM on April 9, 2012
I haven't played professionally or anything, but I've got a near 100% success rate with ETAOIN SHRDLU. The best part is that my kids still haven't noticed I guess the same letters in the same order every time.
posted by DU at 5:44 AM on April 11, 2012
posted by DU at 5:44 AM on April 11, 2012
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posted by Kid Charlemagne at 10:38 PM on April 7, 2012 [7 favorites]