10 ms·
40k coin tosses yield ambiguous evidence for dynamical bias
- h2odragon 4y agoThis field of study obviously needs a much larger number of tossers.
- lumost 4y agoFrom a physics stand point, coin tossing is similar to knife throwing or axe throwing. It's completely within human capability to intentionally or unintentionally time the toss with some degree of accuracy. I doubt anyone can be "good" at this (otherwise it would be a great grifting trick), but surely this creates at least a marginal bias in the data at a high enough scale.
- TimesOldRoman 4y agoEven that poses a fun test. What flipping method is needed to ensure some level of randomness. I love that idea of a grifter being able to flip a coin as they choose.
- MisterBastahrd 4y agoProbably a device that would uniformly toss the coin with regards to force applied at X number of different strengths.
- ChadNauseam 4y agoOr have both people flip a coin secretly, then reveal the coins and XOR the results :D
- faheel 4y agoMaybe letting the coin fall on a hard surface, so that it has a chance to bounce/spin randomly before falling flat (or staying on its side!)
- bitcurious 4y agoWhen I was around 15 I tried to master the controlled coin flip, having been exposed to the idea in one of the Stainless Steel Rat books by Harry Harrison. I reached around 80% success flipping for heads, so long as I used the catch-and-show method. It was easier with heavier and bigger coins, tougher with lighter and smaller ones. Letting the coin drop the the ground and bounce took me back to 50%. Satisfied that it could be done, I moved on - never used the skill, except as a party trick.
- gfodor 4y agoThis is why the casino people get upset when you roll the dice at a craps table and continually avoid hitting the back wall. The rubber pyramids lining the wall are critical to ensuring they maintain their edge :)
- raegis 4y agoSame here. Long ago I tried to generate an encryption key by flipping a coin. After getting a rhythm and flipping heads 20 consecutive times I gave up.
- titzer 4y agoYou could still XOR longer runs together, reducing the bitrate but mostly eliminating the bias.
- inimino 4y agoThere is a protocol for this... you flip the coin twice. HH or TT you ignore, HT or TH you keep (and treat as H or T). This eliminates any bias towards H or T that the coin or flipping procedure may have.
- Jaepa 4y agoAntidotally I can confirm that it is possible toss a coin like that. It helps have a larger coin and to impart it with relatively little rotation.
- TedDoesntTalk 4y agoI can consistently flip a US quarter and get the desired outcome. I have not measured accuracy but is definitely 80% or more. This can be with a quarter I just picked up at a store… no special wear.
- williamkuszmaul 4y agoFrom what I've heard, Perci Diaconis (one of the authors of the original paper) actually could do this. He was a magician before he became a mathematician, and a lot of his early mathematics work focused on math relating to the magic tricks he used to do
- dhosek 4y agoArt Benjamin at Harvey Mudd College is another magician/mathematician. The two skills line up pretty well, it seems. When I got my math teaching credential there were two people in my cohort who did magic tricks as well as at least one teacher at the school where I did my student teaching.
- deleted 4y ago[deleted]
- kloch 4y agoIn roulette this is known as the "dealers signature" where a bored zoned out dealer can sometimes hit the same region/sector of the wheel on consecutive spins. I've seen this happen (or at least appear to happen) in real life where an obviously bored dealer was consistently hitting the same 1/3'd of the wheel and players were taking advantage of it. After a while a suit shows up and starts giving heat not to the players but to the dealer. Chatting them up with nonsense conversation to distract them out of their zone. This wasn't a pit boss/supervisor but casino security - guys that emerge from back rooms to give heat to card counters in blackjack. The distraction worked: the now very awake and nervous dealer was no longer hitting similar areas and the players moved on to other tables.
- paxys 4y agoPeople can definitely get "good" at coin tossing. It isn't even too difficult a trick to master. It's not really possible to use it in any kind of grift scenario though, because there aren't any real world cases where you can win money (or gain any advantage) just by tossing a coin a certain way. Rolling dice has a lot more potential, but those are in turn heavily monitored, e.g. in casino settings.
- JulianWasTaken 4y ago> there aren't any real world cases where you can win money (or gain any advantage) just by tossing a coin a certain way. Paying off a referee to have the coin turn up heads in overtime in a football game seems like it may net you some profit.
- paxys 4y agoIf you can pay off a referee then the coin toss would be the least effective way to do it. A single bad call would gain you a much bigger advantage.
- dTal 4y agoIt has far more plausible deniability, however.
- bluGill 4y agoMaybe. It only takes one bad call at the right time to throw a game. If the ref is consistently bad and missing call for both sides what is one more bad call? I don't care much about bad refs so long as they are consistently bad. However a perfect ref who missing one critical call is a lot more suspicious. Of course I prefer a great ref, but I can work with a fairly bad ref.
- aidenn0 4y agoI believe NFL coin tosses let the coin hit the ground. All methods I know of biasing a coin toss involve catching the coin. As long as the coin hits the ground and bounces at least once, a lot of randomness is re-introduced.
- samatman 4y agoForcing a coin toss of the sort described in the article is well within reach of the interested stage magician. Forcing a coin toss of the kind used in sport, where the coin hits the ground, is more difficult.
- feynmanalgo 4y agoYou don’t have to be a magician. I was impressing other kids doing exactly this, you just toss so the coin goes high but turns slowly and catch it in your hand rather than let if fall to the ground. After not so many tries you get a pretty good intuition on how you have to throw to get the desired result.
- samatman 4y agoIt works the other way around, this kind of trick is (stage) magic so if you're doing it, hey presto, you're a magician.
- kadoban 4y agoThere's also a particular method to get the coin in a tilted spin that looks (and sounds) _remarkably_ like a real flip, and is I think going to be more repeatable than what you're describing.
- posterboy 4y agoIt wouldn't be. People who fall for shell games have to accept that it's fishy and just want to show they are better.
- frogger8 4y agoFrom the article The experiment Over the Spring 2009 semester two Berkeley undergraduates, Priscilla Ku and Janet Larwood, undertook to do the required 40,000 tosses. After preliminary experimentation with practical issues, there was formulated a specific protocol, described in detail below. Cutting to the chase, here is the complete data-set as a .xlsx spreadsheet (see sheet 2). This constitutes a potentially interesting data-set in many ways -- one could compare numerous theoretical predictions about pure randomness (lengths of runs, for instance) with this empirical data. For the specific question of dynamical bias, the relevant data can be stated very concisely of 20,000 Heads-up tosses (tossed by Janet) 10231 landed Heads of 20,000 Tails-up tosses (tossed by Priscilla) 10014 landed Tails
- deleted 4y ago[deleted]
- gus_massa 4y agoFrom https://www.wolframalpha.com/input/?i=binomial+distribution+n%3D20000%2C+p%3D0.5 https://www.wolframalpha.com/input/?i=binomial+distribution+... the standard deviation is almost 71, so it's a 3.3 sigma for Janet and .2 sigma for Priscilla. Since this is not particle physics, we can conclude that Janet (or her coin) is doing something wrong.
- mjburgess 4y agop isnt 0.5, which is the point of the article cf. https://www.wolframalpha.com/input?i=binomial+distribution+n%3D40000%2C+p%3D0.508 https://www.wolframalpha.com/input?i=binomial+distribution+n...
- mjburgess 4y agoIf there is the theoretical 50.8% we would expect 20,230 same-face-up in 40,000 flips. We find here 20,245. Pretty compelling.
- zeroonetwothree 4y agoThe data is consistent with a hypothesis that there is some smaller bias in favor of the side you started with (say 50.4%) and an additional bias in favor of heads (say 50.4%).
- GartzenDeHaes 4y agoCoin tosses are not stochastic. https://www.npr.org/2004/02/24/1697475/the-not-so-random-coin-toss https://www.npr.org/2004/02/24/1697475/the-not-so-random-coi...
- semi-extrinsic 4y agoI think you're trying to say that they are not perfectly fair, which is entirely unrelated to being stochastic.
- fumeux_fume 4y agoThank you!
- t_mann 4y agoNo, the article actually says that sufficiently precise machine tosses can be considered deterministic. The randomness comes from humans.
- DeathArrow 4y agoI think that every physical system is a little biased. That's what they change the balls at lottery for every game. I've read an article about a guy who was observing frequencies at roulette long time ago and, based on that, he made some wins. The casino learned that and switched the tables each day, so he wasn't able to win any more.
- bombcar 4y agoThere's someone who built a craps table and perfected exactly how to throw the dice. If you control the inputs, you control the output. I could see someone learning exactly how to flip a coin to control how it lands, or at least greatly influencing the outcome.
- macintux 4y agoDiscussed here: https://news.ycombinator.com/item?id=30489022 https://news.ycombinator.com/item?id=30489022
- wly_cdgr 4y agoI guess to be more fair we better flip a coin to determine which way the coin should initially face when we flip it
- 29athrowaway 4y agoIf you do a movement 40,000 times, you will be memorizing the movement.
- dekhn 4y agoI think my approach would be to build a coin-flip machine (well, several) that could operate independently, then use computer vision to get the final readout (the result of the flip). Then, if it deviates from expected, use a high speed camera to watch the coins. Oh, and randomize everything about the trials.
- gus_massa 4y agoTake a look at "Dice-O-Matic hopper and elevator" http://gamesbyemail.com/News/DiceOMatic http://gamesbyemail.com/News/DiceOMatic HN discussions https://news.ycombinator.com/item?id=14806986 https://news.ycombinator.com/item?id=14806986 (246 points | July 19, 2017 | 57 comments) and https://news.ycombinator.com/item?id=626092 https://news.ycombinator.com/item?id=626092 (81 points | May 26, 2009 | 4 comments)
- dekhn 4y agoyes, that's a design. It's hard to see the details because the video is poor and the explanation is a bit rambling. It looks much more complicated than necessary and from what I can tell, the rolls themselves aren't truly independent because dice can interact with each other.
- 2b3a51 4y agoAs in the paper referenced in the OA? https://statweb.stanford.edu/~cgates/PERSI/papers/dyn_coin_07.pdf https://statweb.stanford.edu/~cgates/PERSI/papers/dyn_coin_0... Wasn't the idea to test the difference between human and machine tosses?
- dekhn 4y agoThe link on that page doesn't resolve, nor is that what the short writeup about the undergraduate work is about. Most of what the statisticians conclude about the physics seems to be based on poor experimental design. measuring human biases in coin flips seems to be a bit off the point-- you'd do better building a machine that emulates humans better, than to take two people and collect a large number of samples between them. Put another way: when somebody builds a robot and collections the results of thousands of coin tosses, picking two undergrads at stanford and using their physical mechanisms does not advance any useful scientific argument about bias in coin flipping. It just muddles reality with advanced stats on heavily biased data.
- sbf501 4y agoReferees need to start rolling a d20.
- jonhohle 4y agoIsn’t that why you “call it in the air”?
- segfaultbuserr 4y agoOr just use von Neumann's debiasing algorithm - toss twice, and see if it's head-tail or tail-head, retoss when you get repeated heads or tails. It doesn't prevent dishonest tosses (if you can manipulate the bias in each toss), but should work to eliminate a consistent dynamic bias by an honest tosser.
- mrandish 4y ago> A first comment is that it would have been better for each individual to have done both "Heads up"and "Tails up" tosses (which was part of the intended protocol, but on this aspect of the protocol there was a miscommunication) That was a pretty unfortunate error in the experiment. Maybe it doesn't matter but now we don't know. It would also have been nice to have them swap coins halfway to expose any individual per coin biasing. It may seem like an irrelevant thing but I've been a lifelong magician specializing in advanced slight of hand coin magic. I carry a set of coins with me all day, every day and handle them constantly. It started out as practice but evolved into both practice and a kind of fidget toy. I have sets of coins I've probably handled for thousands of hours over decades. Most people think of coins as immutable but they actually change quite a bit after hundreds of hours of handling. Most advanced coin magicians don't tend to use "trick" coins from a magic shop because they are actually too limiting. The coins I use are completely normal circulated coins but they are very specific because there are subtle differences in how coins handle which, at the most advanced levels, can matter. I have year-matched sets of coins I've carefully assembled because they have the degree of surface wear (sometimes called 'softness') and edge-milling which works best for the style of slights I do. Coins also vary in shape and many aren't quite round. I've actually hired a specialized machinist (aka coin-smith) to 'true-up' the shape and then re-mill the edges of certain coins. Based on my admittedly unusual experience in handling coins, I suspect that weight, edge and surface variations in individual coins could have a material aerodynamic impact at this statistical level (sub-half a percent). BTW, there are coin magicians who have mastered the ability to flip a normal coin and control the outcome to >95%. While the coin is normal in every way, it does need to be a coin they've specifically trained with. Otherwise the hit rate falls considerably.
- gfodor 4y agoImagine being in the room when they realized that, after forty thousand coin tosses, they screwed up the experiment. Oops.
- ihattendorf 4y agoThen it becomes an 80k coin toss experiment :)
- deweller 4y ago> of 20,000 Heads-up tosses (tossed by Janet) 10231 landed Heads > of 20,000 Tails-up tosses (tossed by Priscilla) 10014 landed Tails Why not do 10,000 Heads-up and 10,000 Tails-up tosses for each person?
- pc86 4y ago> > A first comment is that it would have been better for each individual to have done both "Heads up"and "Tails up" tosses (which was part of the intended protocol, but on this aspect of the protocol there was a miscommunication)
- williamkuszmaul 4y agoIf the coin were unbiased, we could compute the exact probability of getting 10231 or more heads with 20000 flips as: "sum (20000 choose x)/2^20000 for x from 10231 to 20000", which Wolfram Alpha evaluates to 0.00056. The probability of getting a number of flips that differs from 10000 by at least 231 is twice that, so about 0.001. So, in fact, the probability of this happening by dumb luck is about 1/1000. That's pretty strong evidence.
- deleted 4y ago[deleted]
- TheDesolate0 4y ago40k seems a tad on the low side, by several orders of magnitude. Seems like a hastily done spring projects
- eklitzke 4y agoIt was an undergraduate research project.
- Imnimo 4y agoI used to play a MUD (a text-based proto-MMORPG). It had a command to let you flip a coin. After many years, a player felt like they were noticing more tails than heads. They ran some experiments, and eventually an administrator checked the code - it turned out there was an off-by-one error in the coin flip logic (which inexplicably relied on generating a random number 1-10), such that coin flips had been 40/60 since the release of the game, and no one had noticed for over a decade.
- nicoco 4y ago30/60 maybe? EDIT: probably not after reading the comments. I thought I was smart ;)
- infinityio 4y agoEither could be the case - if it was generating numbers from 1-9 instead of 1-10 30/60, if it was comparing <= 5 vs <5 it could be 40/60
- Imnimo 4y agoYeah, I'm almost certain it was the latter. I remember they shared the code snippet, but that was in 2007 and the game's forums have been replaced since then. I did find a recounting of it: https://forums.achaea.com/discussion/comment/249213/#Comment_249213 https://forums.achaea.com/discussion/comment/249213/#Comment... (and the associated quest to discover the easter egg of a coin landing on its edge with 1 in a million odds that was added when the bug was fixed)
- feoren 4y ago40/50 probably. One of the 10 numbers never showed up. 1-5 tails, 6-9 (should be 10) heads. I ran into the same thing when I made a custom dice roller for Settlers of Catan. Rand(1, 6) never produced a 6, which you could tell if you inspected the comments closely, but still feels counter-intuitive to me.
- 4y ago
- benibela 4y agoThat reminds me of parapsychology They have performed lots of experiments where you do a random experiment and try to change the outcome with your mind.
- feoren 4y agoAnd this comment reminds me of one of my favorite articles I've seen linked from HN, "The Control Group Is Out of Control", relating to parapsychology as the control group for science and how that's not actually necessarily looking great for science itself: https://slatestarcodex.com/2014/04/28/the-control-group-is-out-of-control/ https://slatestarcodex.com/2014/04/28/the-control-group-is-o...
- closeparen 4y ago> It just means that the standard statistical methods of science are so weak and flawed as to permit a field of study to sustain itself in the complete absence of any subject matter.
- zuminator 4y agoThey mentioned that when A tossed the coin, B would record the result on a spreadsheet. But did A know the result of each coin toss as it happened and read it off to B, or did B whisk the coin out of A's hand without A's knowledge of the outcome? Ideally it should be without knowledge of the outcome, so that A's tossing style wouldn't be subconsciously influenced by the result in a kind of self-inflicted Clever Han(d)s effect.
- mertd 4y agoI'm fixated on the fact that they used a dime. That's a very small coin. I can't say I fully understand the dynamical bias mechanics but u had expected that they use a quarter. It's much larger and easier to toss.
- whoomp12342 4y agoIf we are looking that granular of detail, does the shape and weight distribution of the coin matter?
- UberFly 4y agoBring on the robot baseball umpires and the NFL robot coin flippers.
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- dieselgate 4y agoI didn’t read the paper with a fine toothed comb but it seems like the two undergraduate researchers were flipping the coins by hand? If anyone can confirm or deny I would very much appreciate it! Bringing this up because it seems to introduce much variability into each flip?
- t_mann 4y agoInteresting experiment! Here's a suggestion for a new protocol: set up a stand at some busy places (stadiums, train stations,...) and ask random passers-by to toss a coin a few times 'for science'. Should be easier to get to statistically meaningful orders of magnitude (if not, go to a cosplay event in 'The Witcher' costumes, that should help ;)), and arguably far more representative for the situations that we care about: the two participants will have become far more experienced at coin tossing after 20k tosses, but we care more about random people who hardly ever toss coins (we already know that people who practice a lot can control the outcome of a toss with reasonable accuracy).
- kortex 4y agoYou are still talking about dozens/hundreds of hours of work. Better way would be to embarrassingly parallelize the problem. Get large groups of people to flip coins and collimate the result.
- swayvil 4y agoWould a true rng (electron noise or whatever) be an acceptable substitute for physical coinflipping? Has anybody tried this while under the influence of "psychic power enhancers" (psychedelics, meditation, sex, etc)?
- 1970-01-01 4y ago>>separate the effect of individual tossing style from any possible effect arising from the physical difference between Heads and Tails. But it is very hard to imagine any such physical effect, so we presume the observed difference (if real rather than just chance variation) is due to some aspect of different individual tossing style. Much more boring title: "40k coin tosses reveal bad presumption and a biased coin"
- Apocryphon 4y agoWell of course; to be anything else would be Chaos.