Comments by "possumverde" (@possumverde) on "Numberphile" channel.

  1. Voitcu I can somewhat agree with you on the tuning...they could have tuned up to make "Eb" 314Htz. However with the tempo, there's no version of 314 that would really work. 3.14 and 31.4 would have been dreadfully slow while 314 would be approaching thrash metal territory...and you don't even want to hear something in 22/7 time...It's doable but would sound far too alien to most listeners to even be listenable...They did what they could and still have a listenable end product...
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  2. For practical purposes, it's wrong... Simple simulation will show you that regardless of which door you initially choose and/or whether you switch choices later, you will always win the desired prize 50% of the time you play the game. Period. This is because the guaranteed removal of one of the goat doors by rule means that one of the goat doors is never actually a legitimate choice (as a chosen door cannot be removed) and thus should not be included when calculating the probabilities. It's essentially an illusion and could be removed before or after your first choice with no effect on the end result. Which of the two goats is removed doesn't matter. All that matters is that one is guaranteed to be removed (and thus could never have been chosen.) That's the whole beauty of the problem. It's essentially just a clever way of making a coin flip more interesting than... a coin flip. The producers of the show could easily estimate their costs (50% win rate) while viewers/contestants with either poor or exceptional maths skills would actually think their choices mattered. The former due to having no clue and the latter due to overthinking it. You could add more doors and the odds of winning regardless of your choices would be equal to the initial number of doors minus one (1/3 for 4 doors, 1/4 for 5 etc.) Again simulation bears this out. You could even add more stages with more guaranteed removal of doors and your odds would ultimately be equal to those for the initial number of doors minus the total number of removed doors. Simulation backs that up as well. All because any doors that get removed, regardless of when, could never have been chosen to begin with (as chosen doors can't be removed) and thus might as well have never existed for purposes of determining probabilities. Edit: Technically, if more stages are added then it could be possible to drop a previously chosen door if you were to switch choices. I was assuming you stick to the original choice. For gameshow purposes though they wouldn't drop a previous choice like that because it would mean that choice was definitely not the prize. As such you wouldn't have tension of the possibility that you switched from the winning door.
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  3. Actually that makes me wonder if it is even possible to physically construct a perfect circle out of anything in reality. A string (or even a drawn line etc), is made up of finite points (atoms etc) so even if the string / line was only one atom thick you'd end up with a bunch of angles (formed by imaginary lines from one nucleus to the next) which only appear to be a circle when you "zoom out"...though that's probably over thinking it...
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  4. +vuvuzelaelaela You're right. While pile shuffling can mix things up quite well, it is not a truly random method. It's been a long time since I played any of the trading card games but I remember that, due to pile shuffling lacking true randomization, the tournament rules usually allowed it as part of the shuffling process but not as the final method employed.
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  5. I usually just play a song back in my head that I know is either 60 or 120 beats per minute (there's a ton of them) and use that as a kind of metronome when counting out seconds...120 comes in real handy on the rare occasion that half seconds are needed...
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  6. For practical purposes, the explanation really is wrong. The guaranteed removal of one of the goat doors essentially means that there are only two legitimate doors to choose from initially. The removed goat door (which of the two doesn't matter) could never have been chosen as a chosen door could never have been removed. As a result, you will win the grand prize 50% of the time regardless of which door you choose first and/or whether you change your choice later. Simple simulation bears this out. There's a reason why you never see this particular explanation of the Monty Hall problem that includes simulation results to back it up... it's because when one's calculations do not match real results, it's generally a safe bet that it's not reality that's getting it wrong.
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  7. Their explanation is incorrect so don't worry about understanding it. Regardless of which door you choose first and/or whether you change your choice later, you will always win the grand prize 50% of the time. Period. This is because you only ever had two legitimate choices to begin with. The guaranteed removal of one of the goat doors means that door could never have been chosen since a chosen door could never have been removed. It's essentially a two door problem from the start. Were you to add more doors, then the odds of winning regardless of your choices will always match the probabilities for the number of initial doors minus one (1/3 for 4 doors, 1/4 for 5 etc.)
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  8. It's wrong. Simple simulation refutes it. Regardless of which door you pick first and/or whether you change your choice later, you will always win the grand prize 50% of the time. This is because the guaranteed removal of one of the goat doors means you only ever had two legitimate doors to choose from at the start as the removed door could never have been chosen since a chosen door could never have been removed.
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  9. Another way to look at it. If one or both objects are in motion, they will remain in motion until some force stops them. The actual distance being "halved" would be set at the point their inertia could carry them to under current conditions were they not in each others way. This way, at some point in the new "halving" process the objects will indeed collide. But that involves tossing physics into the mix and math has no need to include something as messy as reality in it's workings...
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  10. Don't bother trying to understand it because it's wrong. The game was structured so that Monty would always remove one of the goat doors regardless of which door you picked initially. As a result, sticking to the original pick would win 50% of the time. This is easily proven via simple simulation. There was no real trick to it. He would always reveal and remove one of the goats whether your initial pick was the other goat or the car didn't matter. Since one of the goats was always going to be removed, you really only had two legitimate doors to choose from at the start which is why contestants won 50% of the time on average. Changing their choice had no effect whatsoever. Think about it. If there really were some statistical advantage to be had on the part of the contestant, do you really think the producers would have used such a game? They knew that contestants would win 50% of the time and based their estimated cost of prizes on it.
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