22 ms·
How to pick a random number from 1-10
- deleted 7y ago[deleted]
- jnordwick 7y agoThis looks to be the discrete random variable problem with the alias method: https://en.wikipedia.org/wiki/Alias_method https://en.wikipedia.org/wiki/Alias_method but they don't seem to reduce each choice (1-10) to just two options.
- umvi 7y agoOr just use digits of pi; most people have at least 10 digits memorized, some have 20+ memorized. There's also a formula you can memorize for calculating the nth digit of pi, so you have infinite random numbers without memorizing an esoteric algorithm with a bazillion corner cases. That said, I still thought this was an interesting article and I loved the animated bar graphs.
- arkadiyt 7y agoIt's still an unsolved problem whether or not the digits of pi are uniformly distributed.
- umvi 7y agoJust try it out for yourself. Analyze the distribution of the first billion digits and I think you'll find they will produce a more uniform distribution than this algorithm in the article given 1 billion human responses...
- andrewbarba 7y agoMost people have at least 10 digits memorized? That is one bold claim
- umvi 7y agoI meant here on Hacker News. I would guess most of us here played with our TI-83s enough to know the first 10
- moksly 7y agoI wonder how many people on HN have even seen a TI-83, I don’t think I’ve seen one since I sold mine when I finished the Danish equivalent of high school in 99. I mean, they were apparently discontinued in 2004, that’s 15 years ago.
- woodruffw 7y agoI'm from the US and graduated high school in 2014; TI-83s were ubiquitous. I'm not sure if they were the original model or the "plus," though.
- joks 7y agoProbably the plus. The TI-84 Plus was the calculator my high school (and maybe middle school) offered - I graduated in 2016.
- corysama 7y agoIn the US TI has established a multi-decade monopoly in schools. Basically, the teachers are only familiar with specifically them, so they require student only use them, so new teachers are only familiar with them. As a result, a new TI-85 equivalent is only trivially upgraded from what I used 25 years ago and costs exactly as much minus inflation.
- moksly 7y agoWow, why aren’t students using laptops?
- celticninja 7y agoI'm not sure that most people have memorized the first 10 digits of Pi. I know 3 for certain, any more than that and I can look them up.
- stOneskull 7y agoI think most would know the first 5 because it's pretty accurate making 3.14159 into 3.1416 and you forget what's after the 9
- joks 7y ago3.14159 might even be a stretch though. I'm pretty sure the average person (or american at least) would only know 3.14
- spookthesunset 7y agoThat is pretty arrogant to think that just because somebody posts here they have 10 digits of pi memorized. This is a public forum. Anybody can post. You and everybody else posting here are in all likelihood just average intelligence. There is nothing exclusive about using this forum. You aren’t the first or the last random person to exist here. Don’t let your own supposition of your intelligence get to your head. There is even a theory for that.... Dunning Kruger.
- umvi 7y agoMemorizing digits of pi is easier than memorizing the algorithm in the article. 3.14159265, come on, stop making such a big deal of this.
- davidddavidson 7y agoI count only nine digits so it looks like you gatekept yourself out.
- PointersAreFun 7y agoI have found that 3.2 is a good enough approximation, with the added benefit of being perfectly representable as an integer (32) when scaled by 10, simplifying the math and optimizing the performance since floats are not necessary, just integer divide the result by 10
- RandomBacon 7y ago0-9: Look at the second hand on your watch, what is the last digit? odd/even or heads/tails: is the seconds odd or even?
- peteretep 7y agoI bet that has sample bias as there’s a small amount of choice in when they reply
- the_pwner224 7y agoOnly if they know the time. For binary selection, keep the watch and tell them to make an indication (say something) in a few seconds. Note down whether the seconds were even or odd, then hand them the clock and swap roles. Keep the watch hidden until the moment you need to inspect it; record the time as soon as you can see the watch. Merge the two notepads to get the final stream of randoms. For last digit of seconds, wait a few minutes between each query (making sure they can't see the clock during the rest period). "A few minutes" is imprecisely measured by you, who does not have access to a clock. They delay would foil any attempts at them keeping track of the time in their head. Bonus for distracting them to help with that. And instead of asking them for the last digit, have them flip the watch and then record the time that you [both] first saw.
- gizmo686 7y agoThere is a simpler solution if you do not mind leaving entropy on the table. Break the people up into groups of two without regard for their selection. If two people provide the same number, ignore them. Otherwise, output "0" if the first person's number is smaller then the second, and output "1" if the first person's number is larger. From this, you have a sequence of uniformly random bits, from which you can construct a uniformly random number between 1 and 10. A simple way (although, again, likely leaving entropy on the table) is to break these bits into groups of 4; interperate them as 4 bit unsigned integers, and discard any result that is not in the range 1-10.
- FabHK 7y agoThat works and is perfectly uniform (if the people are i.i.d.), but requires quizzing around 20, 40, 60 or more people for a number before you can deliver one, while the algorithm described only requires one or two. EDIT: Not quite that many, more like around 9, 18, 27 or so, see below.
- rbmktechik 7y agoParents algorithm always works, the one described has a massive failure mode - people slowly learn that they are likely to say 7 and self-censor by picking another number. Or maybe in a different culture the distribution changes (say China and the numbers 4, 8).
- FabHK 7y agoExcellent point. The algorithm in the article is predicated on a specific distribution and iid, GP algorithm is predicated only on iid.
- OscarCunningham 7y agoI would guess that in China the probabilities of 4 and 8 goes down. Asking people to pick randomly drives them away from special numbers.
- 7y ago
- kevmo314 7y ago> Ideally we want to preserve as much of the initial distribution (i.e. do as little chopping and changing) as possible. I was thinking through the post that this sounds like a straightforward problem and it is: https://stackoverflow.com/a/5953133/86433 https://stackoverflow.com/a/5953133/86433 Except the introduction of an "ideally" optimization condition turns it from a straightforward transform into something requiring a linear programming solver. I wonder if the resultant algorithm is actually any simpler though...
- alexandercrohde 7y agoMaybe an easier solution would be to append all the answers, take a hash (e.g. sha1), then convert the last 2 digits from hex to decimal, and mod 10. 1 liner. -- EDIT: I lied, this doesn't work, it biases towards 1-5. I guess you could convert to decimal, and divide by (FFFFFFFFFFFFF / 10)
- vzaliva 7y agoI would call this "PHP hacker solution" :)
- alexandercrohde 7y agoYeah, there's a few types of "great solutions" in engineering. There are those that run really fast (big O) and those that can be written really fast. 99% of the time the job calls for engineers who can come up with the second type of solution.
- LeoPanthera 7y ago"But, let’s say you have to do this without access to coins, computers, radioactive material, or other such access to traditional (pseudo) random number generators. All you have is a room of people." Can you do a SHA1 in your head?
- guan 7y agoNot quite in his head, but Ken Shirriff did SHA-256 with pencil and paper: http://www.righto.com/2014/09/mining-bitcoin-with-pencil-and-paper.html http://www.righto.com/2014/09/mining-bitcoin-with-pencil-and...
- FabHK 7y agoWould be slightly biased, though (256 is not divisible by 10, you'd have to reject if >=250, say). EDIT: and don't forget to add 1.
- deleted 7y ago[deleted]
- justinpombrio 7y ago...or just add up the answers mod 10. This has the property that if even a single person answers uniformly at random, then the final number you compute will be uniformly random, regardless of how everyone else answers.
- moultano 7y agoI'd love to see something written up about how quickly this converges, assuming the variables are i.i.d and distributed according to the distribution in the article.
- samscully 7y agoEmpirically, from running a quick script on the data in the article, it seems like you only need to sample 5 numbers to get a distribution that looks uniform using this "sum mod 10" method.
- pishpash 7y agoIf you're going for empirical, why not ask for between 1 and a very large number? May as well extract as much entropy per person as possible for post-processing.
- jameshart 7y agoMod10, no matter how large the number you’re only keeping the last digit (assuming they choose base 10 numbers), which... is probably no more random than asking them for a single digit in the first place.
- lonelappde 7y agoDon't do mod 10, sum the digits.
- throwaway287391 7y ago> This has the property that if even a single person answers uniformly at random Has any human ever proven they're capable of this? Generating truly random sequences is more or less impossible for humans AFAIK. (E.g., see https://news.ycombinator.com/item?id=19336754 https://news.ycombinator.com/item?id=19336754 which challenges you to do just that. Spoiler: you will probably fail miserably.) It's an interesting idea, but in practice I think relying on the assumption that "even" one person is truly answering randomly (let alone uniformly at random) is a non-starter. But perhaps if there are enough people, the resulting sequence blends enough entropy together to get something that looks almost like a uniform random variable anyway? It would be interesting to test empirically.
- AlphaWeaver 7y agoA few years ago I was stumped by a similar question about generating uniformly random numbers with less than ideal constraints. The helpful minds at MathOverflow solved it [0] but it wasn't something that you could guarantee would always work. (The question explains in more detail... Due to the miniscule probability of a never ending sequence of less than ideal random integers.) I'm curious whether this technique could be applied to my original problem! [0]: https://math.stackexchange.com/q/1273214/196899 https://math.stackexchange.com/q/1273214/196899
- deleted 7y ago[deleted]
- yarg 7y agoYou could use the biased distribution to build a lookup table for a less biased distribution. Build a 10^n lookup table with an entry for each of the possible (ordered) n-tuples of values, give each entry a weight of the product of the probabilities of each of the n values making the entry. Create a set of probabilities for each output and initialise to zero, run through each of the generated tuples in descending order of weight, set the lookup value to the output with the current lowest probability (or the first, or feed in another PRNG - but you have to stop somewhere) and increase the probability according to the weight associated with the tuple. At the end of this process you'll have a PRNG that's at least as good as the input (and generally better) - although you'll need to query the seed PRNG n times per result. The higher the value of n the better the output (Although the lookup table will become quite large).
- yarg 7y agoThis solution gives no consideration to security only the distribution of outputs.
- rland 7y agoI actually laughed out loud when I saw the image of the human RNG distributions. 7 is a random number. Who knew?
- seba_dos1 7y ago7 was what came into my mind right after reading the title. Seeing it later in the text felt like a magic trick.
- jldugger 7y agoI feel like you could probably 'fix' it by the following protocol: 1. Ask your participant to write down a random number. 2. After they've written that number down, inform them you will guess at their number, and give them a dollar if you guess wrong. 3. Ask if they'd like to change their random number. 4. Allow them to write down their new number. The before/after would probably change the distribution, and pretty much demonstrate that people can be more random when motivated.
- gmac 7y agoI'm sure the distribution would change, but not sure it would be closer to uniform. It's now a completely different problem: choose a number most resistant to guessing. For example, if the participant hypothesises that your guess will be a "random" number chosen by you, she should always pick 10.
- Tagbert 7y agoI usually just look at my watch and use the last digit of the seconds value. 0=10 reasonably random
- lerax 7y agoVery easy to predict.
- Tagbert 7y agohow so? if you ask me for a number from 1-10 and I use my watch, how do you have any predictive information? Even if you looked at your watch there is no reason it should have the same seconds value as mine. Obviously this is not really something you could automate and if you were to use a clock on an ongoing basis you might be able to predict likely numbers, but that was not in the original scenario.
- mrpdaemon 7y agoAh but there is a reason for my watch to have the same seconds value as yours, and that is if our watches are kept synchronized to an accurate time source, for ex. via NTP. By assuming otherwise you're sidestepping the problem by claiming you already have a reliable RNG. Heck, even granted you have an unsynchronized watch, your "random" numbers are easy to predict, I'll ask you for a random number once per second and after a few answers I don't need to ask any more to know your answer.
- lonelappde 7y agoThis is an example of a precise analysis that is unhelpful because it is irrelevant in the contexts in which the algorithm would be used. It's like saying "all algorithms are constant time-complexity in practice because computers are finite". True but useless.
- dwild 7y ago> I'll ask you for a random number once per second and after a few answers I don't need to ask any more to know your answer. You know that we aren't computers right? We don't need any fancy software to detect that kind of attack.
- ngoel36 7y agoThis assumes independent events. If someone picks 7 and you ask them for another random number, it is highly unlikely (certainly not 28.1%) that they will pick 7 again.
- harryh 7y ago"Ask another person for a random number"
- kstenerud 7y agoOr have them give the last digit of the age of their oldest living family member.
- roberto 7y agoWhat about Benford's Law?
- harryh 7y agoBenford's concerns the first digit, not the last digit.
- ComputerGuru 7y agoExcept in a distribution that doesn’t go past one digit, of course (no, really, it isn’t that rare to be able to apply Benford’s irl to sequences that don’t go past ten). But, yeah, not applicable in this case.
- ridaj 7y agoDue to the distribution of people's age towards the "old" end of the scale, I'd guess that this is more likely to be 0 than 9?
- roberto 7y agoYeah, I'm curious to look at data, but I think this will be skewed towards lower digits.
- codetrotter 7y ago> The easy thing to do is to ask someone “Hey, pick a random number from 1 to 10!”. The person replies “7!”. Seven factorial is way bigger than 10. Just kidding, sorry. But what I was actually going to say was, when I read the title of the post, before clicking through, I decided to think of a number myself and I chose the number seven. So it was fun to see that same number in the article. 10% chance in theory and in reality it’s about 25% likely for someone to pick the specific number I did. If only the odds in the lottery were this good. Why, by the way, is it that seven is so popular?
- sophiebits 7y agoIt's large and prime, so it feels less "round".
- hackerbabz 7y agoI think 7s feel more random because they are so uncommon in normal life. We want to avoid multiplying or dividing by 7 whenever possible. Imagine if "a dozen" were 7 instead of 12.
- earenndil 7y agoWe see 7 all the time, though, in a week.
- iambateman 7y agoI was going to pick seven as well. Personal guess for why it’s a favorite... 1. I want to signal that I’m creative. If you say “random, between 1-10” picking 5 feels amateur. 2. You said “between 1-10”, which is inclusive of 1 and 10, but you positioned me to not choose the poles with the word “between.” 3. It feels random to iterate through options and settle on one. I iterate by counting up. Since 5 is out, that leaves 6,7,8,9 in my big pile’o’random. From there, for whatever reason 7 tends to stand out. Crazy how predictable we are.
- kovrik 7y agoMy guess: it is all about culture. I guess asian people are more likely to choose 8 (lucky number) and avoid 4 (unlucky number).
- firebatpi 7y agoThere's no need to solve the distribution balancing problem with linear programming. You can just use a greedy algorithm where you repeatedly give probability mass from numbers with more than 10% to numbers with less.
- yyhhsj0521 7y agoThis can be generalized to having any distribution, simulating a die: http://www.keithschwarz.com/darts-dice-coins/ http://www.keithschwarz.com/darts-dice-coins/
- oarabbus_ 7y agoAm I missing something, or is this a textbook case of overfitting? It's a neat project, but at the bottom he prescribes what to do if the person says 1-3, or if they say 4 or 5, etc. Therefore, it's completely overfit to the Reddit data at the top.
- foota 7y agoI think the situation given is that you know the skewed input distribution.
- duchenne 7y agoOverfitting typically happens when the number of training samples is small compared to the number of parameters of the model. It especially happens when the input space is high-dimensional. Here the input space has a only one dimension. The model has 10 parameters. There are 8500 samples. So, the author safely assumes that no over-fitting occurs.
- tfha 7y agoWrong. You are assuming a good selection over the whole search space of humans. If you took HN I bet you would get a different distribution. The Reddit data only applies to sampling Redditors sampled using similar strategies, the generalization is limited by how general the collection strategy was
- duchenne 7y agoYes, there is a possibility that the sample is biased. But that does not matter for this experiment. The OP says that the model should be built with people in the same room than him, and then the human RNG should be executed with the same people. As a consequence, OP has to capture the bias of the people in his room to make his RNG work. The model would break only if the people in the sample change their strategy to pick random numbers after some time. The data from Reddit is just used as an example of how to make a human RNG from redditer random picks. As long as the training and testing are done from the same group of people, there is no issue, even if this group is biased. Moreover, I don't see any prior reason to believe that redditors and HN readers would have different biases. That would be an interesting experiment, though. However, the predominance of the number 7 in article's data might be a western culture thing.
- stOneskull 7y agoHow about 1 person labels 10 people 1 thru 10 and another person not knowing how they're labeled chooses 1 of those people edit: the first person labels the 10 in a jumbled up way, then the 10 people not knowing how they are labeled then jumble themselves up
- testplzignore 7y agoThis seems like it could work pretty well. It would be interesting to try it out. I see two possible sources of bias: 1. The way in which a person labels the others won't be random. And multiple people may exhibit the same pattern. For example, let's say that people are biased towards trying to label an "average" person as #1. This might be based on height, weight, attractiveness, etc. Then a given person may have an uneven distribution of labels attached to them. Further compounding this could be that the most "average" person is the one most likely to be chosen by the second person. 2. You would need to come up with a random way to pair up the first and second person. The worst case might be that the same two people are always paired with each other, and each person always chooses the same person in the room. Then you would end up with a series of 10 digits repeating themselves.
- stOneskull 7y agoi don't know how strict it is with having no props. i think a blindfold could be acceptable because it can be used from the materials of the people in the room but i don't know about actual labels (maybe post-it notes) or a marker pen. so the first person can't see the people and can only like touch their back to put the label on. edit: but then it gets to where you may as well just put the numbers in a hat :P
- quickthrower2 7y agoIf I had to generate a random number I would do this: As I ask each person I cycle a secret number through 0-9 in my head. (I increment mod 10 after I ask each person) When I ask I get their answer, I secretly add my secret number modulo 10 (and consider 0 === 10) and record this in secret. Then record a tally for each number, the one with the most wins. This assumes the asked people will not know or guess my internal number. So I seed based on the first person's number (OK they know!) but everyone else wont. Edit: someone came up with a simpler solution: https://news.ycombinator.com/item?id=20315835 https://news.ycombinator.com/item?id=20315835
- solotronics 7y agoSo you need access to a uniform RNG to implement this as it takes the human bias and multiplies by a factor and the RNG... so why not just use the uniform RNG?
- shhsshs 7y agoYou do not need access to a uniform RNG for this - he uses more humans to get the redistribution chance.
- deleted 7y ago[deleted]
- foota 7y agoIf you can widen the answers the people can give you could first determine the distribution of a larger width (i.e., pick a number from 1 to 100) then map those to the 1-10 distribution based on their frequency. This is effectively the same as the person proposing sampling tuples.
- philshem 7y agoTop poker players have mental models for generating random numbers at the table, to avoid predictable play. I can’t find any link, but it doesn’t require a room full of people (or a wristwatch).
- rajacombinator 7y agoOr just carry a coin-like flippable object. (Cell phone?)
- testplzignore 7y agoAnd if no objects are allowed in the room at all, then pick the lightest person and flip them :) Though flipping a person multiple times is difficult, so it could be biased towards 1 flip.
- gkfasdfasdf 7y agoThere is a simple way to generate random numbers in your head: https://groups.google.com/forum/#!msg/sci.math/6BIYd0cafQo/Ucipn_5T_TMJ https://groups.google.com/forum/#!msg/sci.math/6BIYd0cafQo/U...
- quietbritishjim 7y agoFor ease of reference, here is the text at that link verbatim: Choose a 2-digit number, say 23, your "seed". Form a new 2-digit number: the 10's digit plus 6 times the units digit. The example sequence is 23 --> 20 --> 02 --> 12 --> 13 --> 19 --> 55 --> 35 --> ... and its period is the order of the multiplier, 6, in the group of residues relatively prime to the modulus, 10. (59 in this case). The "random digits" are the units digits of the 2-digit numbers, ie, 3,0,2,2,3,9,5,... the sequence mod 10. The arithmetic is simple enough to carry out in your head. This is an example of my "multiply-with-carry" random number generator, and it seems to provide quite satisfactory sequences mod 2^32 or 2^64 , particularly well suited to the way that modern CPU's do integer arithmetic. You may choose various multipliers and moduli for examples of random selection of the types you ask about. A description of the multiply-with-carry method is in the postscript file mwc1.ps, included in The Marsaglia Random Number CDROM with The DIEHARD Battery of Tests of Randomness, available at http://stat.fsu.edu/pub/diehard/ http://stat.fsu.edu/pub/diehard/ George Marsaglia
- jhanschoo 7y agoThe general method illustrated here (rearranging a sufficiently uniformly distribution over 100 into a very-close-to-uniform distribution over 10) is a special case of a topic in information theory called randomness extraction: https://cs.haifa.ac.il/~ronen/online_papers/ICALPinvited.pdf https://cs.haifa.ac.il/~ronen/online_papers/ICALPinvited.pdf https://people.seas.harvard.edu/~salil/pseudorandomness/extractors.pdf https://people.seas.harvard.edu/~salil/pseudorandomness/extr... The problem being solved is trying to obtain a distribution arbitrarily close to uniform from sampling a known random distribution.
- deleted 7y ago[deleted]
- bubblewrap 7y agoWhat number are people most likely to pick the second time if you ask them twice?
- pishpash 7y agoMaybe the most likely number of the ones they haven't picked? So 5 if you picked 7 and 7 if you picked anything else. This should be tested.
- deleted 7y ago[deleted]
- ajuc 7y agoIn similar situation (we were playing RPG while on a trip, and we needed to "throw dice") - we simply had the DM count silently and the player that was "throwing" say "STOP". It was pretty much uniform.
- testplzignore 7y agoIf you have a pair of scissors or are willing to ask people to take a brief bit of pain... Hair. Cut (or pull) off a chunk of hair from everyone in the room. Put in a big pile. You'll have hundreds of thousands of hairs. It will be a glorious mess :) Now ask people in the room to grab a handful of the hairs and count them. Take the last digit of the each count - there's your random number. You could maybe get multiple digits from a single handful - just be aware of Benford's law.
- benj111 7y agoSo this relies on that being a somewhat normal distribution (7 being the most common number). What if the people were primed by the first person saying 7? What if the first person had said 3? So really you'd need to get your 'random' numbers, check the distribution, than redistribute your 'random' numbers. Which doesn't seem random or 'random' to me.
- simonh 7y agoPut everyone in a numbered sequence unknown to them. Add their chosen number to their sequence number, mod 10. This re-maps everyone’s choices so they actually have no idea what number they are actually choosing and efficiently redistributes the bias in their choices without massively complicated functions. It is also robust to changes in the distribution pattern. However it would only work well if you had at least 10 people and the number of people is divisible by 10.
- bifel 7y agoWouldn't putting "everyone in a numbered sequence unknown to them" require a random number, which we don't have?
- Fronzie 7y agoAssuming you would put them in 10 buckets, that order wouldn't have to be random, as long as people have similar biases.
- simonh 7y agoActually the proposal in the article requires that the group's biases be stable and uniform, where mine doesn't.
- hk__2 7y ago> Wouldn't putting "everyone in a numbered sequence unknown to them" require a random number, which we don't have? No, because that ordering can be chosen by someone not in the sequence.
- hanoz 7y ago> Wouldn't putting "everyone in a numbered sequence unknown to them" require a random number, which we don't have? Yes. The above answer just obfuscates the issue. Consider ten people overwhelmingly biased towards 7. The suggested approach in all likelihood gets you 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then what? You're clearly not much closer to getting a single random number without a random way of picking one of them.
- disconnected 7y agoUse the middle square method: https://en.wikipedia.org/wiki/Middle-square_method https://en.wikipedia.org/wiki/Middle-square_method It can be trivially calculated with pencil and a paper and will be random enough. You just need to pick a seed and off you go. If it was good enough for Von Neumann it is good enough for you.
- clwk 7y agoHow about not using 'pick a random number from 1-10' as the source of entropy? For example, have everyone (from a group of some size) select a natural language sentence of 5 words or more, sum the ASCII values of the upcased alphabetical characters of everyone's sentences, and take the last digit (then add one).
- billysielu 7y agoIt's not random if you're forcing it to be uniform. May as well skip the math and do this instead: Divide all the people into groups of 10. Have the members of a group play each other at whatever, e.g. arm wrestling, to produce a rank from best to worst. Their rank becomes their answer. Now everyone will reply with a number as close to uniform as the total number of people is divisible by the number of choices.
- jjgomo33 7y agoDidn't the world agreed already that the new Pseudocode Language was Python?
- sokoloff 7y agoSurvey for analysis on this thread: https://www.surveymonkey.com/r/XWML9JM https://www.surveymonkey.com/r/XWML9JM
- sokoloff 7y agoData (including a batch I paid for on Mechanical Turk): https://docs.google.com/spreadsheets/d/1Dh0wiTCRkBhckWGXtjZgI_7CX1ZEbqbw4d1KACt8CdU/edit?usp=sharing https://docs.google.com/spreadsheets/d/1Dh0wiTCRkBhckWGXtjZg... (Amusingly, "69" is an over-represented response...)
- lurquer 7y agoThe 8500 students are numbered off (assigned id's) from 1 to 10. Then you wait. Your first random number is the ID of the first person who dies. Second random is the ID of second person to die. Etc. Fairly slow algorithm. And only good for 8500 random numbers. But I think it would give a good distribution.
- wbirthy 7y agoYou could use the month of birthday as random source，if it is bigger than 10，then ignore.
- jeromebaek 7y agoThe interesting part is the recursive application of the algorithm. I'm wondering why it isn't applied fully recursively but only up to one step. Surely, if the algorithm can generate a uniform probability distribution, it can also generate an arbitrary probability distribution, so why not use that arbitrary probability distribution in order to generate the uniform probability distribution?