   Random Numbers and Humans
  So a friend of mine was talking about how rock, paper, scissors takes quite a bit of skill. How they have tournaments and "master" players. I mean, I can see increasing your chances a little bit by knowing rock is used most often, and that players may tend to avoid using the same move more than 2 times in a row in order to seem unpredictable (which obviously has the opposite effect). But these are things I'm sure a "skilled" player would know and avoid.Then I brought up the point of how would a skilled player use tactics if their opponent didn't try to play psychological games and just chose random moves. The conversation then veered off into how humans are predictable and the idea of psychological suggestion. I thought he was overstating the effectiveness of suggestion and the number of situations where it could be used. He's probably been watching too much Derren Brown.Anyway, the point is that I was thinking about humans and their ability to generate good "random" numbers. I was reading how humans are incredibly bad at choosing random numbers. Such as the tendency to think odd numbers are somehow more random than even numbers. How they will avoid picking numbers that end in 0 or 5. And that prime numbers are a very common choice.I thought it would be kind of cool (and probably incredibly useless) to be able to generate pretty good random numbers using only the brain. It sounded like it would be fun to see how good of an algorithm that could be developed while still be simple enough to calculate in the mind. It's not like I'm expecting to pass the diehard tests, but an algorithm that's good enough that no other human would be able to reasonably guess your next choice.I was thinking of something language based. Since humans aren't good at memorizing a large sequence of numbers, but can easily memorize a sentence.Let's just worry about generating a random yes/no bit (with that we can generate larger numbers using binary numbers... though that gets more difficult as the numbers get larger). Such as assigning a 1 or 0 to each letter in the alphabet in such a way that the distribution is close to 50/50 when taking account that letters like 'e' come up more often. Then simply walk through the sentence and generate the bits.The problem is that words/sentences have too many patterns. So I was thinking of ways to decrease that a bit. Such as combining every 2 letters, or something like that.Anybody else have any ideas/algorithms?Sorry, I know this is probably a weird post and not very practical, but I thought it was interesting and wanted to see if I'm the only one who thinks so...   
  An idea: try thinking of a movie or a story, then think of a short, 1 sentence summary of it. For each word in the summary, if there's an odd number of letters you get a 1 and if it's even you get a 0.Remembering the summary as you try to count letters might be a bit hard and time consuming though. Also, I don't know if there's a significant bias for words used in a sentence.   ;  How about you get 22-23 people together in a room and see if any two of them share a birthday?  Make sure to get new people each time!   ;Quote:Original post by vrageThen I brought up the point of how would a skilled player use tactics if their opponent didn't try to play psychological games and just chose random moves. The conversation then veered off into how humans are predictable and the idea of psychological suggestion. I thought he was overstating the effectiveness of suggestion and the number of situations where it could be used.The problem with using completely random numbers in ro sham bo is that it guarantees a 50% win / loss rate.  People who are really good at ro sham bo can hit an 85% win rate with ease, far beyond statistical pure luck.  The fact that some people are consistently good proves there's something there besides luck.In the two Red Bull Tournaments of about 80 people, Mark Thomas won 2nd place twice and Frances Anne Ricketts won 3rd place and 1st place.  That would be extremely rare if the outcome was decided entirely by chance.A completely random strategy would be useful if we were facing a "pro", since it would guarantee a 50% success rate where as the conventional strategy would give you a 15% success rate.   The only catch is that it cannot be something that is calculated right before the throw, or else you risk leading your hand and making it non-random.  It has to be something non-obvious, outside of your control and quickly calculable.  What that could be, I don't know.   ;  If I decided to choose the same number over and over for all the eternity, could you prove mathematically that the process I'm using for picking it, at it's very root, isn't truly random?   ;  If you only want to generate a single bit, something very simple should suffice - like determining whether a person was born on an odd or an even date. If you want something a bit more repeatable then keeping running track of the median of blinking intervals and using deviation from it to decide whether the bit should be set or not might be good idea. You'd need some equipment for that though.Generally speaking, if you want to use a human being as a RNG then you'll simply have to factor in the psychological element. There's no way around that - our bodies are linked to the brain and the best theory we have about the brain is psychology.Speaking of Derren Brown and rock-paper-scissors. There's an explanation that the secret to DB's winning/losing streaks has got very little to do with skill so much as sheer psychology. I've tested this myself and I've managed to lose 9 times consecutively. Only problem was - I was trying to win.SPOILER (the explanation coming up): the method described goes something like this: for the first round you cheat. Nothing more nothing less - you lower your hand half a second later and you catch what the opponent is going to do. Depending on whether you want to lose, win or draw, you then choose the appropriate figure. For the next rounds, with the majority of people, it will suffice to adapt a round robin system, eg: if your want to win and your first hand was rock (opponent threw scissors) then you continue with the assuption that the opponent's next hand will be rock, which makes yours paper, next yours becomes scissors, then rock and so forth. Like I said - I've had moderate success failing at this (eg getting the opposite result to what I intended) and cannot verify that this in fact is how Derren Brown does it on screen. But I do believe there's some incredibly simple and transparent psychological solution to this; I also believe there's a good reason why he never promises to win, lose or draw more than five times in a row.   ;  You could just learn to run something like a Linear congruential generator in your head. They're obviously not random, but in a situation where you want to avoid the psychological problems of trying to create random numbers, they probably work better than trying to generate randomness in an ad hoc way.   ;Quote:Original post by PrefectYou could just learn to run something like a Linear congruential generator in your head. They're obviously not random, but in a situation where you want to avoid the psychological problems of trying to create random numbers, they probably work better than trying to generate randomness in an ad hoc way.Agreed.First, there is the open debate of the existence of random numbers.  The question of universal determinism has been proven to be unprovable.  So we don't even know if there is such a thing.Next, you need to define what a random number really is.  You can have statistical randomness that passes many tests, yet still has detectable patterns found by other tests.Most of us interpret "random numbers" as a well-distributed unpredictable sequence generator, considering only a very small window of observation.  But that isn't necessarily random.Imagine a random number generator. When you look at it you observe the same value appear a billion times in a row.  That can still be random.  It could be exactly equal probability as any other billion-selection pattern, you just happened to observe it over a uniform -- but still random -- section.Your RPS example is misleading, because in the pure form there are no 'reveals' or 'tells'.  In the pure statistical form of RPS there can be no strategy.Playing RPS in real life there are reveals and tells.  There is psychology, and there strong patterns of 'attacking', 'defending'.  Much like in poker, RPS is not about your hand (either cards or your literal hand), instead it is about reading your opponent, learning their tells, figuring out what they are most likely to do next, and reacting accordingly.If all you care about is generating a few less-predictable numbers, memorize a simple algorithm.  Anything less and you might as well just pick rock every time.  ("Good old rock. Nothing beats that!")   ;Quote:Original post by frobIf all you care about is generating a few less-predictable numbers, memorize a simple algorithm.  Anything less and you might as well just pick rock every time.  ("Good old rock. Nothing beats that!")Well, I don't know.  Memorizing a lengthy string (say 100) of random numbers numbers generated from quantum phenomena works pretty well for most cases, too.  Most people won't notice if you sometimes repeat your whole sequence unless they're looking for it.   ;Quote:Original post by cowsarenotevilQuote:Original post by frobIf all you care about is generating a few less-predictable numbers, memorize a simple algorithm.  Anything less and you might as well just pick rock every time.  ("Good old rock. Nothing beats that!")Well, I don't know.  Memorizing a lengthy string (say 100) of random numbers numbers generated from quantum phenomena works pretty well for most cases, too.  Most people won't notice if you sometimes repeat your whole sequence unless they're looking for it.Exactly my point.You might have your "random numbers" being the first 10 digits of pi, or something similar, but that is no different than always choosing "rock". It is not random, and those who know it could see your obvious pattern.With training and thought people can get pretty good at making statistically random numbers, especially if they know the statistics that will be run.We had a competition at work a while back to who could make a list of 100 digits.  The results were run through a chi-squared, gap, and overlapping orderings (poker) tests.  It's obviously a very small sample, but it was a fun competition.  Knowing the tests in advance made it easier to think about the numbers, and I was one of the better-scoring random number generators.  Not great, but still pretty good.  With practice I could probably do better.  The funny thing was that we found one obvious cheater. :-)   