[HN Gopher] 40k coin tosses yield ambiguous evidence for dynamic... ___________________________________________________________________ 40k coin tosses yield ambiguous evidence for dynamical bias Author : geocrasher Score : 153 points Date : 2022-06-03 14:57 UTC (8 hours ago) (HTM) web link (www.stat.berkeley.edu) (TXT) w3m dump (www.stat.berkeley.edu) | wly_cdgr wrote: | I guess to be more fair we better flip a coin to determine which | way the coin should initially face when we flip it | Imnimo wrote: | I 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 wrote: | 30/60 maybe? | | EDIT: probably not after reading the comments. I thought I was | smart ;) | feoren wrote: | 40/50 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. | finnh wrote: | Our Catan set has noticeably nonuniform dice. They roll | high numbers much more frequently than low numbers; | presumably bc the high-numbered sides weigh less (?). We | haven't buckled down and done the science but it definitely | tilts the game play, to the extent that we're considering | swapping them out for new dice. | | (or this could just be Catan Crankiness (TM), but we've all | noticed it quite a bit...) | sshine wrote: | On the subject of Catan and dice: | | https://www.chiark.greenend.org.uk/~sgtatham/dice/ | infinityio wrote: | Either 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 wrote: | Yeah, 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/#Commen | t... | | (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) | dekhn wrote: | Huh. I once wrote a MUD client that didn't have an obviously | documented way to quit and got email for years after | complaining that I had "made the application too addictive". | ycombinete wrote: | Which MUD was this? | Imnimo wrote: | Achaea | 0des wrote: | What are the odds wow | strbean wrote: | My favorite baffling RNG bias was in the game Maplestory. It | always seemed like RNG was extremely "clumpy". For example, | critical hits would frequently come in bursts - you might get | around 5 seconds of non-stop crits. | | The crafting system was heavily chance based. You'd get say 7 | attempts to augment a piece of gear, using 'scrolls' that had a | certain percentage chance of succeeding. The lower the chance, | the bigger the improvement to your gear. So a pair of gloves | that had 7 successfully applied +attack 10% scrolls would be | incredibly valuable. The superstitious method to crafting | (which, anecdotally, worked incredibly well) was to get a ton | of gloves and a ton of scrolls, and apply one scroll to one | pair of gloves and throw them away if it failed. Once you had a | single success, you would apply the scrolls as quickly as | possible to try and ride the RNG wave. In my experience, this | would very frequently result in getting 3+ successes in a row. | mertd wrote: | I'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. | btilly wrote: | They wanted to test the dynamics on long tosses (with lots of | flipping). It is easier for a toss to be long if the coin is | small. | dekhn wrote: | "We adjusted the methods of the experiment for the | convenience of the experimenter" is a common detail most | papers leave out. | frogger8 wrote: | From 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] | gus_massa wrote: | From | 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 wrote: | p isnt 0.5, which is the point of the article | | cf. https://www.wolframalpha.com/input?i=binomial+distributio | n+n... | mjburgess wrote: | If 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 wrote: | The 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 wrote: | Coin tosses are not stochastic. | https://www.npr.org/2004/02/24/1697475/the-not-so-random-coi... | semi-extrinsic wrote: | I think you're trying to say that they are not perfectly fair, | which is entirely unrelated to being stochastic. | fumeux_fume wrote: | Thank you! | t_mann wrote: | No, the article actually says that sufficiently precise | machine tosses can be considered deterministic. The | randomness comes from humans. | DeathArrow wrote: | I 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 wrote: | There'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 wrote: | Discussed here: https://news.ycombinator.com/item?id=30489022 | 29athrowaway wrote: | If you do a movement 40,000 times, you will be memorizing the | movement. | dieselgate wrote: | I 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? | benibela wrote: | That 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 wrote: | And 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-o... | closeparen wrote: | > 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. | t_mann wrote: | Interesting 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). | dekhn wrote: | I 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. | 2b3a51 wrote: | As in the paper referenced in the OA? | | https://statweb.stanford.edu/~cgates/PERSI/papers/dyn_coin_0... | | Wasn't the idea to test the difference between human and | machine tosses? | dekhn wrote: | The 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. | gus_massa wrote: | Take a look at " _Dice-O-Matic hopper and elevator_ " | http://gamesbyemail.com/News/DiceOMatic HN discussions | https://news.ycombinator.com/item?id=14806986 (246 points | | July 19, 2017 | 57 comments) and | https://news.ycombinator.com/item?id=626092 (81 points | May | 26, 2009 | 4 comments) | dekhn wrote: | yes, 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. | williamkuszmaul wrote: | If 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] | UberFly wrote: | Bring on the robot baseball umpires and the NFL robot coin | flippers. | 1970-01-01 wrote: | >>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" | TheDesolate0 wrote: | 40k seems a tad on the low side, by several orders of magnitude. | | Seems like a hastily done spring projects | eklitzke wrote: | It was an undergraduate research project. | h2odragon wrote: | This field of study obviously needs a much larger number of | tossers. | [deleted] | [deleted] | [deleted] | a9h74j wrote: | Next crypto class: Proof of coin tosses. | _jal wrote: | Too bad ibankers make too much to want to be study subjects. | whoomp12342 wrote: | If we are looking that granular of detail, does the shape and | weight distribution of the coin matter? | [deleted] | sbf501 wrote: | Referees need to start rolling a d20. | jonhohle wrote: | Isn't that why you "call it in the air"? | segfaultbuserr wrote: | Or 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 wrote: | > 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. | modernerd wrote: | Please send us further down this rabbit hole, it sounds | fascinating! | | What sort of flourishes/fidgets do you find yourself | gravitating to most? | | What does great sleight of hand coin magic look like? Who do | you admire most? | | Where should someone get started if they want to explore this? | mrandish wrote: | > What sort of flourishes/fidgets do you find yourself | gravitating to most? | | There are a huge variety and it's mostly down to personal | preference. Popular flourishes include coin rolls and coin | stars. Popular slights include dozens of different palms with | single and then multiple coins. | | > What does great sleight of hand coin magic look like? | | Done right it can be absolutely mind-blowing. For an example | take a look at some of Danny Goldsmith's videos | (https://www.dannygoldsmithmagic.com/). Danny is very, very | good but like a lot of specialized skills, those who aren't | deeply into it won't be able to notice a meaningful | difference between the top 20% of coin workers. | | > Who do you admire most? | | That's really down to personal taste and style. One unusual | thing about magic is that the "best magicians" in the eyes of | other experienced magicians are generally people you've never | heard of. Fame doesn't really correlate with the pinnacle of | skill. While most famous magicians like a David Copperfield | are skilled, they would be the first to tell you they can't | hold a candle to the most skilled coin workers or card | mechanics. | | > Where should someone get started if they want to explore | this? | | For _serious_ coin work, Danny 's teaching videos would be a | good start. Look for ones he flags as being appropriate for | novices. For learning the art of magic in general, I'd | suggest not wasting money buying individual "tricks" unless | you just want a few easy party tricks to amaze (or annoy) | friends with. Most people who get deep into magic discover | that the most valuable and broadly applicable knowledge comes | from books, videos and live learning (called "sessioning" by | close-up workers). I don't buy much magic in recent years | because I'm at the point of just perfecting skills, so it's | hard to recommend an online store but a safe bet for | beginners would be Vanishing Inc. | https://www.vanishingincmagic.com/. The guys that run VI are | deeply experienced and they seem to avoid selling a lot of | the 'crap magic' that looks amazing to novices but isn't | actually all that useful. I was at a lecture by the co- | founder a few weeks ago and the guy not only has deep | knowledge and mad skills, he clearly loves magic and is good | at teaching. | | If you just want to watch some higher-quality magical | performances, I'd suggest Penn & Teller's "Fool Us" show | (lots of clips on YouTube). The technical coordinator on that | show, Michael Weber, is a long-time magical inventor and | author who is well-regarded by other magicians. He and Teller | work together to curate the acts that get on the show and | you're basically getting to see some top notch talent hand | selected by guys who know the difference. | tash9 wrote: | Well it's not like we're gonna run out of undergraduates, just | do the experiment again. | tetris11 wrote: | Unrelated question: how do your hands look after handling coins | so constantly as you do? Is there a slight sheen to them? Do | you have less hair on your hands than you normally would, or | more? | mrandish wrote: | No, there's no noticeable difference in the skin surface of | my hands. Over years of practice, serious coin workers do | develop substantial hand muscle strength and joint | flexibility but that's not visually noticeable. It's also | just a byproduct of practice and not needed for most of what | we do. The key physical ability isn't applying force, it's | actually enhanced sensitivity. I can feel precisely where the | coins are and feel how the weight is shifting as they move. | This sensitivity enables precise control which is really the | key thing. | spdionis wrote: | Funnily enough, but also not surprising, it's the same for | drummers and their preferred type of sticks. | raincom wrote: | It is called "kinesthesia", which is important in playing | musical instruments, sports, flying aircraft, etc. With | respect to flying, pilots trained by Army (navy, airforce) | develop these skills far better than those directly | recruited by carriers from colleges. We can see those | results in some fatal crashes (Air France 447, Asiana 214). | I am not blaming the pilots. When one flies with the aid of | machines (fly by wire, simulators), one doesn't develop the | kinesthesia required to get out of tricky situations(when | instruments don't work or when instruments misread, etc). | AndyNemmity wrote: | The same is true for card magicians, and card handling. I | have a lot of things I can do with my hands and joints that | aren't something you can see. | | Same with enhanced sensitivity. I can fairly accurately | tell you how many cards I pick up from a group. It's just | practice, once you can do 2, you do 3, all the way up to | 10, to 15 to 20. | posterboy wrote: | Is that a kind of subdigitizing? | gfodor wrote: | Imagine being in the room when they realized that, after forty | thousand coin tosses, they screwed up the experiment. Oops. | ihattendorf wrote: | Then it becomes an 80k coin toss experiment :) | sillysaurusx wrote: | This is how ML training goes. My longest run was 2 months | before it collapsed. | the__alchemist wrote: | That's super interesting! Of note, the book Quicksilver (First | book in the Baroque Cycle) goes into a few diatribes about | subtle differences in coins in Europe a few hundred years ago; | eg coins being valued by metrics other than their face value. | | Eg: > "I say, Daniel, is it true what they say, that those | coins are perfectly circular?" | | > "They are, Isaac--not like the good old English hammered | coins that you and I carry in such abundance in our pockets and | purses." ... >"if someone clips or files a bit of metal off the | edge of a round coin with a milled edge, it is immediately | obvious." | | > "That must be why everyone is melting those new coins down as | fast as they are minted, and shipping the metal to the | Orient...?" Daniel began, | | > "...making it impossible for the likes of me and my friend to | obtain them," Isaac finished. | | > "Now there is a good idea--if you can show me coins of a | bright silver color--not that black stuff--I'll weigh them and | accept them as bullion." | | > "Bullion! Sir!" | | > "Yes." | | > "I have heard that this is the practice in China," Isaac said | sagely. "But here in England, a shilling is a shilling." | | > "No matter how little it weighs!?" | | > "Yes. In principle, yes." | | > "So when a lump of metal is coined in the Mint, it takes on a | magical power of shillingness, and even after it has been filed | and clipped and worn down to a mere featureless nodule, it is | still worth a full shilling?" | | > You exaggerate," Daniel said. "I have here a fine Queen | Elizabeth shilling, for example--which I carry around, mind | you, as a souvenir of Gloriana's reign, since it is far too | fine a specimen to actually spend. But as you can see, it is | just as bright and shiny as the day it was minted--" | | > "Especially where it's recently been clipped there along the | side," the lens-grinder said. | | > "Normal, pleasing irregularity of the hand-hammered currency, | nothing more." | 0des wrote: | Are we all in the same book club or something? | gibspaulding wrote: | A substantial chunk of the books I read are based on HN | recommendations, so... yes? | robwwilliams wrote: | Egghead book club. Neal Stephenson, Greg Bear, Greg Egan... | User23 wrote: | > BTW, there are coin magicians who have mastered the ability | to flip a normal coin and control the outcome to >95%. | | I managed 11 heads in a row with a quarter when I was in high | school. I was intentionally going for heads so it was either | beginner's luck or an absurd statistical fluke. | onphonenow wrote: | Even when not trained if you are basically looking to | "repeat" a motion, you can get a reasonably consistent flip. | A lot of folks think these far out results are just | statistics, but statistics actually tells us how incredibly | rare this would be. | | 11 in a row is perhaps still part fluke without training, but | as long as you were trying to do the same thing again not | unreasonable. | [deleted] | kadoban wrote: | If you're not using a specific technique, that was just a | fluke. | | I'm not a magician, I just learned this one trick/set-of- | tricks (and I'm not 95% success at it either). | [deleted] | swayvil wrote: | Would 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)? | zuminator wrote: | They 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. | deweller wrote: | > 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 wrote: | > > _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)_ | lumost wrote: | From 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. | paxys wrote: | People 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 wrote: | > 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 wrote: | If 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 wrote: | It has far more plausible deniability, however. | bluGill wrote: | Maybe. 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 wrote: | I 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 wrote: | Forcing 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 wrote: | You 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 wrote: | It 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 wrote: | There'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 wrote: | It wouldn't be. People who fall for shell games have to accept | that it's fishy and just want to show they are better. | bitcurious wrote: | When 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 wrote: | This 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 wrote: | Same 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 wrote: | You could still XOR longer runs together, reducing the | bitrate but mostly eliminating the bias. | TimesOldRoman wrote: | Even 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 wrote: | Probably a device that would uniformly toss the coin with | regards to force applied at X number of different strengths. | ChadNauseam wrote: | Or have both people flip a coin secretly, then reveal the | coins and XOR the results :D | faheel wrote: | Maybe 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!) | Jaepa wrote: | Antidotally 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 wrote: | I 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 wrote: | From 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 wrote: | Art 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] | kloch wrote: | In 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. ___________________________________________________________________ (page generated 2022-06-03 23:00 UTC)