M54
The people vs probability
June 26 2015
Comments
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Andremmo
11 years ago
It is complicated to explain but you should change to the box number 2 to improve your chance of winning from 33% to 66%.
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RHP User
11 years ago
box 1.... - Posted from rhpmobile
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RHP User
11 years ago
I'm fond of sticking with what I got.
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RHP User
11 years ago
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RHP User
11 years ago
Would've chosen that from the start. Besides... I got a peanut!! Yeeeeeahhhhhh!!
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RHP User
11 years ago
1957 to 1971 there was a popular game show on Australian TV called Pick A Box...Barry Jones the former politiciian was its most famous and successful contestant...I choose box number two because KiwiBred is smart and good at puzzles 😊xxFreya
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RHP User
11 years ago
The choice is dependent on whether or not the host knows where the cash is, also the problem must state that the host must open a box. Sorry Simon you have not specified if the host knows where the cash is, thus there is ambiguity in the determination of probability. Nor does the type of situation have any certainty. The player has only one go, reducing the odds from 1/3 to 2/3 are still not anywhere near a certainty. So assuming the host knows where the cash is.C is cash P is nutsCPP you have prize host shows nutsPCP you don't have prize host shows us nutsPPC this is eliminated as host would not have shown us box 3 At this stage the odds of cash have improved but are still even at 1/2 so the would be no good reason to changeC is cash P is nuts X openedCPXPCX The important bit is that the host must open a box. We must rewind back to the 3 boxes and consider the situation of picking box one. Each box has a 1/3 chance of having the cash. So box one has 1/3 and the remaining boxes have 2/3 if considered as together1/3..|-2/3--|.. Sum = 1/1 [X]__[X]__[X] Now opening box three moves the odds of box three to 0 (no chance) but your odds still remain at 1/3. But the mathematics says that the total odds must sum to 1 to 1. That means that box two will now have the 2/3 odds 1/3..2/3..Zero sum = 1/1[X]__[X]__[P] _odds of box 3 having cash = 0 Sticking with box 1 gives you lower odds than with box 2 which now has 2/3 odds. You should always switch, so I go for box 2 because I am not a big fan of peanuts. This problem is counter intuitive and belongs to a special class of problems that are paradoxical in nature and has similar logical argument to Hilbert's Infinite Hotel and Schrödinger's cat paradoxes, both of which rely on pure faith of mathematical proof rather than the human capacity to understand (knowing, see "Chinese Room" as an example of knowledge without understanding). Most people will insist the odds are 1/2 even when shown the proof. It is not until simulations of the problem are created that the nature of the true odds 2/3 are seen. The problem then becomes common sense not because of understanding, but because experience says so. To cross threads. Regarding a couple sleeping together with one cheating, and using condoms or not. The odd thing is that when the testing rate rises for the couple and the cheating is at a high level the use of condoms in the home bedroom actually increase the chance of getting an STI from the cheating partner if the couple gets tested regularly. The software constantly shows a 5% safer outcome for couples that do not use the condoms. I did not list this result as I do not understand why. It seems counter intuitive, but the simulation is consistent and may be another veridical paradox
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RHP User
11 years ago
I will select now the Right hand side box please. Number 2 - Posted from rhpmobile
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RHP User
11 years ago
When I chose box one, my odds were 1 in 3, the other two boxes together 2 in 3. When one of those was removed (and contained a peanut), my odds shifted to 1 in 2. I don't see a need to change my mind. My odds of winning are now 50-50. It's like the question: "A woman already has two boys, what are the odds her next one will be a girl?" Same answer.
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RHP User
11 years ago
Blindmans arse......oh, sorry, got distracted....... Im a "safe" person so Ill stick with number one.
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RHP User
11 years ago
so would stay with Box 2. Things are always better with 2s ... twice the fun! LG
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Tall74nHard9
11 years ago
Did you still remember what you were getting up to at the end of your explanation ? I can't remember precisely where I have heard it from, but an old conventional wisdom says that your first choice in any situation is usually the best one to stick with. Freya you might be able to enlighten us in regard to that. Tall
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MsJonesy
11 years ago
And if I win the peanuts... well I do like nibbling on nuts so I would still be happy ;)
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RHP User
11 years ago
Stick with box 1. Once I've made I decision, I tend to stick with it unless I'm shown evidence that my original choice is incorrect. In this case, I don't think I've been shown that evidence. I could have been shown that evidence in Blindman's post, but it was too long and looked overly complicated. My eyes glazed over as soon as I saw it. Sorry.
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RHP User
11 years ago
Ordinarily, presuming the host knew which is the correct box, his subsequent actions would be the deciding factor as to wether I switched or held. Whilst there was nothing indicating that the host was aware of the correct box, the OP is very strongly geared towards 'standard assumption', which, as you know, is the fatal flaw of any veridical type paradox.
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RHP User
11 years ago
I'm not a nut nibbler. More of a licker/sucker ;)
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RHP User
11 years ago
Should never be ignored.
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Seachange73
11 years ago
Box 2. Chances are 50% as the probability changed and is not static when Box 3 is a known component. Calculating probability is based on predicting the outcomes occuring given a finite set of unknowns In this case. Meander us spot on. And the oOP testing our beliefs that we are irrational and stubborn. Lol. Red flag. At the end of the day, peanuts or cash, all good. I get to go TV. Am immortalized On celluloid. ;-)
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RHP User
11 years ago
What "the big pile of cash" is? It could be 10.000 Indonesian Rupiah, worth about a dollar.
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Seachange73
11 years ago
SOLD! !!@ Lol
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madotara69
11 years ago
"Should" is a powerful thing. Should picking the right box matter enough when at the very best it only ever could be something that should not matter? I say "throw the arms up into the air, wave them all about, put the left foot in and ask the universe, for what shall be shall be". Mado Mado Tara xx
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RHP User
11 years ago
Humanity worked out how to track the motion of celestial bodies to an accuracy of minutes before we worked out how to workout how to predict the chance of rolling double six with a set of dice. It is still very poorly understood by the general population. Given that the cash can be won with a 2/3 chance, I wonder if anyone knows how many games you would need to play before to be sure you won the cash?
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Seachange73
11 years ago
all good stuff buddy. Still havent told us which box did the universe say you should pick? I hope It is right. Lol
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RHP User
11 years ago
Box 2. I always pick even numbers.
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RHP User
11 years ago
Stay with your first choice - Posted from rhpmobile
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RHP User
11 years ago
LOL @ being on a game show. The odds are higher in RHP...lol
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RHP User
11 years ago
Quoting 'madotara69' "Should" is a powerful thing. Should picking the right box matter enough when at the very best it only ever could be something that should not matter? You're right! It doesn't matter. The puzzle is not so much about the box itself, it's more to do with information challenging previous decisions.
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RHP User
11 years ago
Quoting 'Meander' When I chose box one, my odds were 1 in 3, the other two boxes together 2 in 3. When one of those was removed (and contained a peanut), my odds shifted to 1 in 2. I don't see a need to change my mind. My odds of winning are now 50-50. It's like the question: "A woman already has two boys, what are the odds her next one will be a girl?" Same answer. But I don't get second question, please explain?
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RHP User
11 years ago
Quoting 'JackMacker' Quoting 'Meander' When I chose box one, my odds were 1 in 3, the other two boxes together 2 in 3. When one of those was removed (and contained a peanut), my odds shifted to 1 in 2. I don't see a need to change my mind. My odds of winning are now 50-50. It's like the question: "A woman already has two boys, what are the odds her next one will be a girl?" Same answer. But I don't get second question, please explain? Like the box question, it all depends on WHEN the question is asked. If you ask before a woman has children what the odds are of her having two boys and a girl: The possibilities: boy+boy+boyboy+boy+girlboy+girl+girlgirl+girl+girl Possibility of two boys and a girl= One in four If you ask when a woman has already had one boy: boy+boy+boyboy+boy+girlboy+girl+girl Possibility = One in three If you ask when a woman has already had two boys: boy+boy+boy boy+boy+girl Possibility = One in two = 50/50 Hope that makes sense.
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RHP User
11 years ago
Quoting 😝 umm oh Gday Mado6 and hello Tara9 Quoting 😜 mmm xxKiwiBredxx Firstly your foot is looking fantastic We must fit the slipper asap 😘 Quotingly agree : Your right it does not matter . Where the fuck is Simon ? Hey Simon keep ya money keep ya Box !! Who gives a fuck , can we fuck it or what?? - Posted from rhpmobile
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RHP User
11 years ago
Just Sniff the nuts out.... 😂
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RHP User
11 years ago
my first thought was stick with box 1, by introducing a further condition in this case making a second choice in fact decreases the probability of success as compared to the original condition.
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RHP User
11 years ago
Quoting 'Meander' When I chose box one, my odds were 1 in 3, the other two boxes together 2 in 3. When one of those was removed (and contained a peanut), my odds shifted to 1 in 2. I don't see a need to change my mind. My odds of winning are now 50-50. It's like the question: "A woman already has two boys, what are the odds her next one will be a girl?" Same answer. Revealing the peanuts in No.3 makes no change to the initial probability, it simply removes No.3 as being an option. No.2 remains 2 in 3, sticking with No.1 remains 1 in 3, therefore, switching theoretically increases the odds from 1 in 3 to 2 in 3.
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RHP User
11 years ago
Quoting 'xKiwiBredx' Revealing the peanuts in No.3 makes no change to the initial probability, it simply removes No.3 as being an option. Why? The initial probability is 1/3 and you're saying that doesn't change? So removing no. 3 as an option would be 1/(three boxes- box 3= two boxes), so 1/2. C'mon, Simon do tell.
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RHP User
11 years ago
with Box number 1, based on the theory they are most likely trying to change your mind by showing you there is a peanut in box 1, as they have a vested interest for you to doubt yourself and choose the wrong box. I suspect if you had chosen the box with the peanut to start with they may not have shown you what was is box 3. But who knows, still 50/50 choice.
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RHP User
11 years ago
with Box number 1, based on the theory they are most likely trying to change your mind by showing you there is a peanut in box 1, as they have a vested interest for you to doubt yourself and choose the wrong box. I suspect if you had chosen the box with the peanut to start with they may not have shown you what was is box 3. But who knows, still 50/50 choice.
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RHP User
11 years ago
Maybe it is a sign it is Box 2 ?
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RHP User
11 years ago
Thanks for bringing that to my attention. What I meant to say was that revealing the peanuts does not shift your odds to 1 in 2. The 2 in 3 has not changed as Box.No.2 and Box No.3 still remains part of the set. The only change is the knowledge that the money is not in Box No.3.
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RHP User
11 years ago
Assuming the cash was in 3 then the host would have revealed 2. There are 2 boxes, you know one has a peanut the other has the cash. How sure do you want to be Blindman because if it 100% there is no amount of attempts to be 100% sure
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RHP User
11 years ago
Paintme sneaks into the room, swipes everyones boxes and all the nuts into her knickers and slinks out again. I'm an all or nothing kinda gal. Love to all xxx
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madotara69
11 years ago
A 50\50 chance you are wearing any knickers at all paintme
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RHP User
11 years ago
I now agree you should switch. Good riddle, it's really hard to rationalize why that is the case
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RHP User
11 years ago
I would choose to box that didn't smell like peanuts. - Posted from rhpmobile
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RHP User
11 years ago
Quoting 'PaintMeHappy' Paintme sneaks into the room, swipes everyones boxes and all the nuts into her knickers and slinks out again. I'm an all or nothing kinda gal. Love to all xxx I already have box number 3! I already bagged that ages ago! I have already eaten my peanut, and am leaving the rest of you to fight over the other boxes to see if indeed there is any cash... By the way, my peanut was delicious. Never look a gift horse in the mouth...
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RHP User
11 years ago
Quoting 'Blindman67'Given that the cash can be won with a 2/3 chance, I wonder if anyone knows how many games you would need to play before to be sure you won the cash? how certain do you mean? the probability of winning should approach 1 asymptotically as number of games increases
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RHP User
11 years ago
This is easy to prove by playing the game with a dice, paper, and pencil. Roll the dice. Get the number and divide by 2 using the remainder to select the box to put the cash in. Then pick box one, or use a dice to pick a random box. Then if it is not the cash eliminate the box without the cash. Then record the two results if you stick to the box you picked or if you switch. It wont take long, maybe 12 or so games for the result to come in that switching has the clear advantage. The maths tells it how it is, We must always rely on maths as intuition is unreliable and flawed. This is the beauty of science. Anyone can do the experiment to see if the facts are true or not. The odds of switching 2/3 playing the game will show this as true. This work for any number of boxes. If the game has 4 boxes then switching will improve the odds to 1/4+(1/4*1/2) for 5 the switch will give new odds to 1/5+(1/5*1/3)
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RHP User
11 years ago
Any time this comes up the result is the same. First thoughts are that it doesn't matter, that choosing between the two remaining boxes is 50/50. But it's not correct. The answer is you should always change to the other box - it has a 2/3 probability of being correct. There are a couple of good explanations above. I tried to explain this to a few friends years ago and in the end had to actually play the game to prove it. It is very easy to prove. The point is that people make assumptions that are sometimes hard to shake - even with hard evidence. I let this run for a bit to see it in action and the result was predictable. People who haven't heard the problem before assume it is 50/50. Nothing wrong with that - it's a tricky question. What's interesting is the number of people who continue to insist it's 50/50 after being given the answer and explanation. It was prompted by Blindman's condom analysis. I don't have time to check the math there but given what I've seen from him I'd assume it's correct (at least for the scenarios given - there will be many others where it doesn't hold). Almost everyone dismissed it outright because it simply does not fit with both intuition and many years of conditioning. It's also safer to drive home drunk than to walk. Doesn't mean I'm going to do it, because there are other issues like the safety of others to consider. The math doesn't lie, whether you choose to use it or not is up to you.
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RHP User
11 years ago
I do know what I am talking about when it comes to probability. Condoms Consider herpes. Its a game of Russian roulette. With out condoms you play with 3 bullets in 5 chambers, with a condom on you play 1 bullet in 25 chambers. If I play one game I play with condoms, but play 15 times you are at the same odds. I have been asked why then are we all not infected, we have all played many times with many strangers, if condoms did not work I should have an STI. It all comes down to how many people have STI. A good lot of you (around 1 in 4 for our demographic) have herpes, in this thread there are 25 posters so statistically 6 of you have herpes and if you always use condoms you are not less likely to have it, you caught it while having safe sex. Only those that have had sex less than 15 times in your life can claim any chance of being less likely to have it. If posters were even male female numbers I could reliably say there would be 4 women and 2 men with it. Include HPV and around 8 of you have an STI. Its about the same for HPV (warts) and again having safe sex always makes no difference to the chance of having it, it only take one bullet to kill, one cross infection to get an STI Who here know with certainty that they don't have herpes (HIV2) or HPV. Its not part of the standard STI test. I am clean I have been recently tested. If I have sex I know that the only person I put at risk is my self. The 8 or so of you that do have HIV2 or HPV put not only your self at risk of catching another STI, but you put at risk the person you sleep with and all the people that have sex with that person and so on, condom or not. All those that have not checked for HPV or HIV2 potentially do the same, you just don't know so why are you having sex with out checking. Get tested. Ask for HIV2 and HPV (guys HPV requires a visual inspection) I know you are not getting tested because so many of you are claiming to be clean, its statistically improbable you are all clean because the rates are so high. The sad fact is that people that always use condoms are more likely to have a STI because they are less likely to get tested and tend to do more risky sex, Always for sex (condoms) for me means, high risk individual. Unless you can prove you have been tested I will not play.
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RHP User
11 years ago
Quoting 'S_OnTheLoose' Quoting 'Blindman67'Given that the cash can be won with a 2/3 chance, I wonder if anyone knows how many games you would need to play before to be sure you won the cash? how certain do you mean? the probability of winning should approach 1 asymptotically as number of games increases Good answer, in fact perfect, the number of games played approaches infinity as you approach 1. There can never be 100% certain, but in my book 99.999% is good odds and would only need 12 games
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RHP User
11 years ago
How does that explain those of us who went against the trend and picked Box 2 instead of the stipulated Box 1 and then stayed with their choice? From Wikipedia, the free encyclopediaChaos theory is the field of study in mathematics that studies the behaviour of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems aredeterministic, meaning that their future behaviour is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behaviour is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz LG
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RHP User
11 years ago
Your mathematics and probability here, is just incorrect. Lets put it this way. The money goes into either box 1, 2 or 3 at random. it could be in any box...right?The money never moves. So there is NO variable.Whichever box you choose is irrelevant. So we'll stick with the story and say box number 1.You show box number 3 is empty. Great. Now here is where your theory falls. The money never moves. It could be in box number 1 all along. Or number 2 equally. All you have done is revealed that it isn't in box number 3. Tell me how changing your choice right here changes the forces of physics to make the money now end up in your box more often than not? By this logic, you should always choose box number 2, as it is going to end up a winner more times than not...right? Wrong.By this logic, what happens if you had've chosen box number 2 for a start, and then you change to number 1. Does this mean that the money now ends up in box number 1 magically more often now than box number 2? Wrong. I'm sorry, but chance and probability doesn't change because you change your mind. It is a standard constant. Next you will be telling me you can bend spoons with your mind too.....
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RHP User
11 years ago
Anyone want to play the game with me at the next Meet and Greet? ;-)
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madotara69
11 years ago
box is the remote egg in.. bahahahahaha
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RHP User
11 years ago
That's very fucking funny.
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RHP User
11 years ago
The puzzle is a veridical paradox. The logical thing to do would be to take Box. No.3 out of the equation - not doing so is considered counterintuitive, if not absurd - hence the paradox.
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RHP User
11 years ago
You people are too smart for me, I'm going back to Mensa.
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RHP User
11 years ago
Blindman posted a way to test the theory above, but here's a fun way to do it with a friend. First, don't tell them what you are testing - get someone to play by challenging them to a guessing contest. Grab 3 cups and a coin. Let your friend guess first. You put the coin under one of the cups and then ask them to guess where the coin is. After they guess, show them one of the remaining cups - one that doesn't have the coin under it. Ask them to stay with the original guess or change their mind. Most people will stay with their original guess most of the time (due to a wonderfully irrational thing called loss aversion - another topic entirely). They will change their minds some of the time, and some will do it more than others. Do it 20 times. 12 is probably enough, but I like to make sure and the more games the better. Your friend will get it right somewhere between 5 and 10 times, depending on luck and how often they change cups. Then repeat with you doing the guessing. Change your mind every time. You will get it right somewhere between 12 and 16 times depending on some luck. Be prepared to be called a cheat, because unless your friend knows the game you will win* Post the results here when you are done. Last time I tried it the result was 10-15 in my favour with 20 games each. For additional fun, maybe play with DoctorPercival and put a bet on it while you are at it *it is of course possible to be really unlucky with this game, just like it's possible to spin 10 heads in a row. Don't bet the farm.
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RHP User
11 years ago
People are predictable in aggregate, but it's pretty hard to know what any one individual will do. Most people will stay with their first choice most of the time, but there's no chance that everyone will behave the same way. That's a different topic though. The interesting part about this is the number of people that prefer to believe their intuition over the math even when presented with clear explanations. Not sure I'd like to think that all our actions are deterministic, but that really is another discussion.
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RHP User
11 years ago
Quoting 'SimonDoes'Not sure I'd like to think that all our actions are deterministic, but that really is another discussion. yeah, but since we don't know the entire system's state, it's unpredictable by us - even if deterministic - so detach a part of your brain and enjoy the ride :)
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