>Game has a puzzle>the given answer is actually wrong
achads... I don't get it... why would the goat be more likely if we don't swap doors...
>game changes the rules>pretends it didn't so it can act smug and bazinga you
>>72580124850/50
Don't care what kind of explanation this is. The goat door doesn't matter and it's a 50/50.
>>725801248Math isn't real. It's 50/50.
>switch door>still 1/3 chance of getting it wrongIn the end it's just luck
>>725801407Because you're missing out on the context of the game. Whatever you chose, the host will reveal ALL goat doors first.Suppose you scale this to 1000 doors. You pick a door, and the host reveals 998 doors containing goats. Remember that the host must reveal all doors except one and your chosen door. Do you really think that out of all 998 doors they opened, they just happened not to pick *your* door specifically, and you just happened to hit the 1/1000 chance of picking the prize door? Of course not. 999/1000 chance you picked a goat door before, and if you don't switch, 999/1000 times it IS a goat.
>50/50Wouldn't switching give you chances greater than 50/50?
>>725802191 not when it's 3 doors
>>725802053But he only reveals one, not all of them. If he revealed all it would be 2 doors opened with goats
>>725802053I hate this logic because it doesnt account for the idea that he is just trying to psyche you out which would make sense when they pull such a grand gesture out of fucking nowhere.
Oh good. Another thread that's going to be full of people getting filtered by the Monty Hall problem. The solution is incredibly fucking simple. Instead of three doors, picture an infinite number of doors. If you switch doors, five people will die instead of just one. But if you push the goat off the bridge, it'll go back in time and kill Hitler. If the two remaining doors have a cat instead of a goat, one cat will be alive and the other cat will be dead, but you won't know which is which until you open the door. However, it's possible that the door with the car behind it doesn't actually have a car, it has a piece of cardboard in the shape of a car, and the host didn't know about it before letting you choose. One of the two goats always lies, and the other goat only ever tells the truth, but you don't know which is which. You can try asking the goats questions by slipping them notes you write in Chinese using the translation dictionary in the corner. If you pick one of the guards doors with a goat, the goat will fly across the room, but if you pick the other door with a goat, it'll just plop onto the floor. So if you tell the host, "I don't know which door it is," the host will say, "I didn't know before, but now I know," to which you'll reply, "Actually, I know now too." All of this becomes moot if the producers of the show replace each part of the car one by one because then they won't know if it's still the same car anymore.
>>725801248This puzzle is mathematical rage bait.For anyone not smart enough for it.
>>725802258The scale is to help you understand it but it seems even that is not enough.The key to this problem is that if, and only IF you chose the correct door in your first try, the host will tempt you with the wrong door. On the other hand, if you chose the wrong door, the host will tempt you with the correct door.So just do the math. 3 doors. 2 are wrong, 1 is correct. The odds of the host offering you the correct door during the bait-and-switch are 2/3.>>725802272That is not a variable of the monty hall problem.
>>725801248>Don't switch: You win by picking the correct door at the beginning (1/3 chance)>Switch: You win by picking a wrong door at the beginning (2/3 chance)
>>725801248goat door lol
>>725802554>anime reaction imagechecks out
Fuck the monty hall problem everyone knows the solution.Solve this one instead.
>>725802235I think it's true for any number of doors. When you choose if you want to switch there's only 2 doors left but you made your choice when there were more than 2. So switching isn't 50/50 because the circumstances of your first choice are relevant to your odds.
>muh theoretical probabilitygaaaaaaaay
>Algebra math puzzle to get code digits to lock>Game maker put the digits in the wrong order making me think I'm retarded
>>725802790>theoretical
>>725802641wasn't this supposed to be impossible? I did it easily
ENTER
>>725802892Sorry to inform you anon, you may have autism.
>>725802641never said "each"
>>725802979was that it?
>>725802272>it doesnt account for the idea that he is just trying to psyche you outFortunately the host will never reveal a prize door before he makes you choose to keep or switch, so this is not possible at all.
>>725803195You're not wrong doe
>>725801248>Friend uses save states to pick the right door>I tell him he didn't win the goat>He has his goat headbutt meAm I in the wrong here?
>>725803195Anon, I...
>>725803195you forgot the door in the middle
>>725802846oh I'm sorry>muh conditional probabilitygaaaaaaaaywe good now, gayboy?
>>725803451don't call me gayboy
>>725803509don't be gay
>>725803196Yes it is. If someone chose the right door and its in YOUR INTEREST(even if its a whim) for them to not win thats exactly the action someone would take.In this scenario though the host is practically doin an extremely generous favor like its a fuckin charity event.
>>725803385What did I forget this time?
>>725803612the circle to summon the demon
>>725802979>trough
>>725803557you're supposed to bring reality into the monty hall problem
>>725802554You have the same chance of picking the right door no matter how big the scale is.
Okay but imagine you switch and you get the wrong door when you had the right door originally. You gonna stand there and mumble about statistics to the host? I'd rather fail of my own volition than fail because I mathcucked myself.
>>725801747Well it's more that schools fail to actually teach practical application of probability.
This one is perfection
Its kind of insane how many low iq retards this question always filters. https://www.youtube.com/watch?v=4Lb-6rxZxx0
>>725803557>the host is practically doin an extremely generous favor like its a fuckin charity event.The show accountants already took into account the fact that switching is always optimal. It's not charity at all.
>>725803649and now?
>>725803612that is not one line and you missed that one door on the right
Yeah, no. I'm gonna go with my gut.
>>725804013Then they would also take into account that most people would not accept that switching is optimal.
>>725802053>>725802554retarded tranny jeet, you aren't even man enough to post on nu/a/ get the FUCK out
>>725804098Plz look at mine I think I actually got it once and for all >>725803985
>>725804212That guy wasn't me by the way
>>725804212You want to see me naked?
>>725802979didn't say anything about not being able to turn the doors into walls
>>725804235>that one cross at the left side making it obvious that it isn't one lineare you even trying?
>>725804304not a single person on Earth wants to see your gross brown body
>"puzzle game">it just uses chess or someshit that takes 10000 hours to understand
>>725803740That is reality. A situation like that would not occur if you didnt already choose properly or the host is very good natured. You go on a gameshow and at best if you chose the wrong door theyll let you see you were wrong and then let you choose again if not let you lose on the spot.
>>725803167>>725804364
>>725804603chess is not a puzzle game
>>725802272It's assumed that the host was always going to do it. But yeah if 2 people played before me and both chose a goat, then I played and suddenly the host did this shit I would not switch.
Easy
>>725804820Artifical difficulty
Why can't people just do this IRL to test it?
>>725802641
>>725801407Because if you decide to swap, picking the car means getting the goat, and picking the goat means getting the car. You are more likely to get a goat since there are two of them, so swapping means you are now more likely to get a car. That's why you swap. You also may choose to be a retard and pick randomly when you're left with just two doors, this way you have 50/50.
>>725802641The test is that an autist will try to solve it while a non autist will go back to having sex. There I solved it. I'm a genius.
>>725805037redraw this without the lines passing through the other supply circles and you win forever
>>725804603Chess is actually very easy to understand. You can get really far with just tactics and calculation which don't require any memorization or learning beyond the basic rules.
>>725805191
>>725805024people have done it with bots and confirmed
You can easily get 100% odds of winning by picking door number 3 on purpose. Get fucked Monty, I want the goat.
>>725805332NTA, good job but the real autism test is doing this shit at all
>game has strategies that only the highest level players understand
>>725805518>I want the goat.why though
>>725805659Because I am the GOAT
>>725805617your probably right, i fall into the category of "not diagnosed but I'm pretty sure"but I'm married and have a son so i can't be doing too badly for myself.
>>725801248>>725801407It's easier to figure out if instead of doors you think of them as playing cards and hands. One card wins, other two cards are bust.1. At the start of the game you pick one random card.2. The host picks ALL the leftover cards (two in this case).Q: Is it more likely that you or the host holds the sole winning card?A: Your hand has 1/3 chance of containing the winning card (you picked 1 out of 3), while the host's hand has 2/3 chance (as he holds all the other cards).After that the game continues. The host showing his cards save one mystery card actually does nothing for the chances. It's the simple fact that his hand contains more cards, therefore it's more likely to also contain the winning card. Then you're given a choice of either sticking with your own initial hand (1/3 chance of containing the winning card) or the host's hand (2/3 chance of containing the winning card). Doors-goats-cars bullshit works basically the same way: you only pick one door, while the host holds all the other doors.
>>725801407Kek fpbp underrated af
>logically proven>mathematically proven>experimentally proven>half of /v/: "nuh uh, that's wrong"Remember this the next time you're tempted to argue with someone here.
>>725805745you better be raising your kid right, good parenting is the only way to unfuck future generations
>>725805870he is a good kid and gets good grades, dunno how much of it is my doing but i try at least.he is 11 now and reading at a college level and tests within the top 5% for mathematics and reading for his age, though i wouldn't be surprised if he has a bit of the 'tism like i believe i do.
>>725802053I never got why this explanation makes it more apparent to some people. I understand the probability just fine and have used this example when people had a hard time understanding it and they often get it but I never understood why.
>>725805846Most of /v/ understands the solution. It's just fun to bait with and pretend to be baited with.
Would you keep your case or switch here? The actual solution is, of course, to just take the deal instead of gambling like a greedy retard, but ignore that part https://www.youtube.com/watch?v=p4qMWef8wJw
>>725805846A significant portion of people people not being able to recognize a rigged game where the result is altered by the person presenting it even when it's carefully explained to them exactly how it works sounds about right.
A door is always opened, the initial choice is an illusion.It is always 50/50, it never was anything else.
>>725806187I think people get confused by the original problem because the numbers are pretty small and close to each other.>I pick one door out of three.>Then I just pick one out of two, right?>It's 50/50, right? There's only two doors!Increasing the number emphasizes the difference between the actual chances involved. Instead it's>I pick one door out of one thousand.>Then I just pick one out of two, right?>But wait, what are the chances I lucked out on picking the correct door the first time out of one thousand? It can't be 50/50!
>>725806553why do you think gambling exists?
>>725801537>>725801618It takes courage to speak the truth in a world full of Jewish lies. This.
>>725806184just keep him on the path of proper education, he could easily be working a fantastic paying job by 25godspeed you retard
>>725806638>A door is always openedthe person opening the door knows the correct answer and is obligated to eliminate an incorrect answer. so it was 33% when you picked the first time
>>725806187When there's 3 doors>I picked originally from 3 doors>One of the bad options got removed. I guess it's a 1/2 now>Kinda want to stick to what I know, so I won't switch1/100>I picked originally from 100 doors>Wait wtf, he removed 98 bad doors?>Either I somehow got extremely lucky with my pick, or that suspiciously untouched door is actually the right one>I'm switching, no way I actually got the right door out of 100 doorsIn other words, it's designed to be a logic trap, and adding more doors makes it clear that there was a leap of logic in the 3 door scenario.
>>725806719Because most casino games have a 90%+ rtp so instead of losing all your money in one go you lose small percents day after day. The pace being slow enough that you never realize you've lost 1000s,10,000s,1x10^6s. Until you've been at it for years.
>>725807061And every game has some for of a tie. Which makes up the bulk of your game results and dds downtime between losses without actually giving the players their money back.
>>725806719gambling is entirely based off psychological manipulation
>>725801248You know you can just code your own version in Python and look at the results if you run it 10000 times, right?Wait, people like you can't actually use logic.
>>725802053Yes I do think I picked a good door.Counterpoints?
>>725807368>4th dimension beings using 3 dimensional paper for autism test
>>725807368>>725807462that's just how the electric is wired IRL, it literally goes over and past your house
>>725807447Sure. You can't argue against preferences. And if you like the door at least twice as much as the other one, you can definitely keep it. It's just that the other door is twice more likely no matter what you like.
>>725806719Because it's scamming that benefits the government. If they actually cared about the populace, they'd ban it like other scams.
>>725807368>hot air riseskino
>>725807372
>>725807328>>725807683that was a rhetorical question you autists
>>725808717Who says we can't answer rhetorical questions?
>>725808717gambling is no laughing matter
>>725806184I firmly believe high functioning 'tism and big smarts go hand in hand and might not necessarily even be 'tism for all its symptoms but being on a whole different level from your monkey peers that can barely communicate, let alone with someone who understands things much better, double empathy problem and all.
>>725801248I would pick door number 3 because 3 is the best number.
>>725808530DELETE THIS RIGHT NOW
>>725801248Once a door is removed it becomes an entirely new question and all previous answers no longer matter. It's 50/50.
>>725807372https://montyhall.io/you can use the website too. also knowing the real context and adding doors really helped me understand this problem
>>725809413>Once a door is removed it becomes an entirely new question and all previous answers no longer matter.False
>>725801248Increasing the amount of doors and applying the same logic helped me statistically understand why this makes sense. If you had 50 doors with 49 goats, it's a shot in the dark. You pick a door and it's objectively a 1/50 chance to get it right. Then Monty goes ahead and opens 48 doors with goats. Two doors left. You really think you were lucky enough to get the right door on your first random 1/50 try? Or did Monty not open that door because he literally had no choice. You're pitting your 1/50 against his 49/50. This question is only difficult to figure out because of the scarcity of the doors, but in the end you're pitting your 1/3 against his 2/3.
>>725809668You are free to think that if you want.
>>725810029He literally has to leave one door left for there to be a choice at all. It's just as likely that your door is right as it is his.
>>725810204>Once a door is removed it becomes an entirely new questionThe question is does switching improve your chancesWhat question do you think is being asked
>>725810335so whats the probability that, of the 50 doors, yours is the hit? and he just HAPPENED to knock out all the other doors EXCEPT the one thats yours? the odds are 49/50 if you switch
>>725801407>why would the goat be more likely if we don't swap doors...it's not though?
>>725807368
>>725810335Okay, let me make it even more obvious for you. There are a MILLION doors. The prize is behind one and you're told to pick. You go "fuck this stupid challenge it's literally one in a million" and pick a door at random. Then, all the rest of the doors are opened except for one. What's more likely, that the right door was just shown to you by process of elimination or that your random one-in-a-million choice was actually correct? With these kinds of odds, the right door is literally shown to you. The very rules of the game have statistically guaranteed to you that there is a 999,999/1,000,000 chance that the other door is the correct one. The statistically advantage of 2/3 vs 1/3 is not nearly as great as this so it's less obvious, but the logic is all entirely the same.
Is Who wants to be a millionaire just a game of luck?I mean, there's 33.34% chance of being right unless the person happen to know the answer, and lifelines can only get you so far into the game
>>725810381Same as it is for the remaining door to be the hit. It didn't swap places or anything it stayed where it was. It's just as likely before the reveal as after.
>>725810650i know you're just trolling, but there are people out there who genuinely think like this, and they are allowed to vote or drive on the same roads as me. sad world
>>725810629i had a friend that looked like your pic but he was not a good person
>>725810681Not trolling. 100% genuine. It would be like believing it's not raining outside as long as you don't look out there to check yourself. It'll be where it is regardless.
>>725801248*Ahem*What’s more embarrassing? Picking the right door, then swapping and getting it wrong OR picking the wrong door but staying true to your conviction?Remember you’re on a TV show. The host wants to humiliate you. He knows the probabilities, everyone does. The game show has been running for at least five years, so around 2,000 doors have been opened. Your math can’t help you with the exception. Don't you trust your guts and luck? Do you have no autonomy? Also OP is a faggot
>>725804005But once you open one door, it's no longer 1/3 vs 2/3, it's now 1/2 vs 1/2Opening the door changes the situation.
>>725810712Let's say there are 15 questions with 4 choices each. Let's also say there are 3 lifelines: call-a-friend, 50-50, and ask-the-audience.For each of the 15 questions, there is only 1 correct answer, and 3 incorrect answers, so immediately your chances are 1/3 = 33.34%. You can use each lifeline once. Using phone-a-friend, let's say gives you a 95% chance the person you call is correct. So 1 question is 95%. Similarly, we can say ask-the-audience gives you a 95% chance. Finally, 50-50 will remove 2 wrong answers, so you have 1 right answer and 1 wrong answer, so you basically know the answer. To recap:Question 1: 33.34%Question 2: 33.34%Question 3: 33.34%Question 4: 95% <--- ask-the-audienceQuestion 5: 33.34%Question 6: 33.34%Question 7: 33.34%Question 8: 33.34%Question 9: 95% <--- phone-a-friendQuestion 10: 33.34%Question 11: 33.34%Question 12: 33.34%Question 13: 33.34%Question 14: 33.34%Question 15: 100% <--- 50-50Total: 690.08%Divided by 15 questions = 46.00%So basically, it's more a less a game of chance, but more than half the people on the show will lose, so it's not very fair. That show is making tons of money off of people
>>725807368>workers & resources: soviet republic utilities in a nutshell
>>725806187it drives home the most important part of the riddle in that the host removes incorrect choices. which is what the entire thing rests upon and the entire reason changing your choice makes sense.
>>725810827how do you explain >>725810608 then? whats more likely? that you picked the 1/1,000,000 choice from the get go? or that the host eliminated 999,998 other options, and there is one door that suspiciously was left out?
>>725810629Yes, the question themselves are mostly there so that the audience tunnel visions on the ones they know and start believing they could do better than the contestant. In other words, it's great entertainement due to how it hides its very unfair nature.
>>725801248Persona 5>people only started dreaming in colour when colour TVs were invented>the total amount of gold in entire human history is only 3 swimming pools
>>725810965It's not suspicious. He has to leave one to give the choice at all. If yours is the winning door he is forced to pick one at random. You can think of it like before you make any choice at all what are the odds that the door he ends up leaving is the winner? Same as it is for the one you pick because it stayed put.
>>725810898Your math is wrong, why is the final % higher than the % of getting a single question right?
>>725801248Its 50/50 regardless what you doEither you win or you dont
>>725810898I dont think you add up chance in series like that, I remember having an argument with a D&D DM about a monk rolling more natural 1'salso with 4 answers why is your chance to get the correct 33% and not 25%?
>>725811220>If yours is the winning door he is forced to pick one at random.IFyours is the winning door, which is a 1/1,000,000 chance. if you cant understand that part, then just make the number bigger. what if you need to pick 1 door out of 1e100 doors? you will never, EVER pick that door in your entire lifetime. it just wont happen. there are more doors in that hypothetical situation than there are atoms in the universe. now lets say every single door except your pick, and 1 random fucking door was eliminated. is it still 50/50?>>725811237>>725811325that pasta is older than both of your ages combined
I don't know what game it is but I specifically remember a puzzle that's a series of seemingly random numbers with zero relation, you are tasked with finding one in the middle of the series. The answer to the puzzle is they're all the winning scores of the superbowl throughout the years
>>725811382>that pasta is older than both of your ages combinedim 33 and have never seen it in my life, the more you know.
>>725801248>pick 1>host reveals 3>ok so it's a 50/50 between 1 and 2>UHHHHHHHHHHHH NO??????>YOU DUMB IDIOT, WHAT ABOUT THE THIRD REALITY WHERE HE REVEALED 2>What about it? We know for a fact we're not in that reality. It's one of the few concrete things we know>UHHHHHHHHHHHHHHHHHHHHHHHHH JUST COUNT IT>PLEASE, PLEASE JUST COUNT IT>I NEED TO JUSTIFY MY DEGREE AND JOB PLEEEEEEEEEEEEEEEEEEEEASE"No"
>>725802272>host is trying to psych you outin that case, isn't it better to use an objective method rather than depend on your feelings?
What if I thought goats are pretty cool and I already have a car?
what would the odds look like if there were 5 doors but host still only revealed one before letting you switch?
>>725811647why stop at 5? just keep adding doors until the odds are obvious. look at >>725811382
>>725801248The original choose 1 of 3 game...
>>725811382Number of doors eliminated doesn't matter it becomes a question of is it in this door or that one. Before the game starts you had the option to pick that random door he left open it has the same chance of being the winner as the one you end up picking. The prize didn't move. As long as the chance of your door being the winning one remains the final question will always be 50/50.
>>725811683read nigga, that's not what I asked about
>>725811647You pick between a 1/5 by staying or a 26.67% by switching. Switching literally always benefits you, even if barely.
>>725811758sorry anon, i think you might be retarded
>>725810897Was about to argue with ChatGPT about it, but the 100 door example in the video actually make sense now.1 of 3 doors = 1/3 chance, but if you switch your chances goes up to 1/21 of 100 doors = 1/100 chance, but if you switch your chances goes up to 1/2
>>725811382Yes, because you either win or you don'tCheckmate, atheist
>>725811830>1 of 100 doors = 1/100 chance, but if you switch your chances goes up to 1/299/100*
>>725811830YESYou finally get it. Glad we all could learn something today.
>>725811758low iq unironically
>>725811220>It's not suspicious.
>>725802450>Another thread that's going to be full of people getting filtered by the Monty Hall problem.Your problem is that you believe /v/ is still full of genuine people posting their genuine opinions.
>>725811830woulln't it be 99 out of 100 because youre picking a hundred doors?
>>725802450It's very obvious some people are baiting but it's entertaining watching autists try to reason with them.
>game has infinite money glitch
>>725811782To elaborate on this, you can essentially split the doors into clusters>The door you picked at first, the 1/5>The other doors, which have a 4/5 chance of containing the winning doorSince the other cluster has -1 junk door, you can divide the 4/5 by 3 instead for the individual odd that the door picked by switching is the winning door, giving you a 26.67% chance of getting the winning door. If there's always only one door opened, your odds lower by adding more doors, since you spread out your odds further with each door added. They never get lower than the original pic though, since you never spread your odds thinner than the original scenario does.
>>725812026The post you're replying to is obviously genuine, though.
>>725811758>Before the game starts you had the option to pick that random door he left open it has the same chance of being the winner as the one you end up picking.>Before the game startsYes, before the game starts.
>>725813564And the prize didn't move even after the game started.
>>725809413>I don't understand how can I use the information provided in previous iteration therefore I should disregard it and treat the next iteration as a completely new question
>>725813952The info would need to be worth using to carry over.
>>725813864Yes, right again. The prize never moves.If there are 100 doors, I know you agree that after you make your choice the chance you picked the prize is 1/100.But after 98 empty doors are opened, do you think the chance you picked the prize becomes 50/50?
>>725801407You had a 1/3 chance of picking the car. That means you had a 2/3 chance of NOT picking it. The act of revealing a goat is arbitrary: there's always at least one left that you didn't pick. The real question being asked is "did you get it right the first time?" If you think your first 1/3 was right, you stay. If you don't think you got it (a 2/3 chance), it's better to switch.
>all of these retards using mathI chose the right one the first time.Why?Because I'm just better.
>>725811607You can sell the car for multiple goats.
>>725814718It's a 50/50 of getting it right if you switch once there are only 2 options. It's a 1/100 of getting it right the first time, the one you are being offered to switch to also had a 1/100 chance of being right at the start of the game before any choices were made. The prize never moves the chances of that particular one being offered being the winner are the same as the one you did end up picking, everything else is noise.
>>725801248What's wrong with getting the goat? I thought men love goats.
>>725811830So you have a 1% chance to win if you stay, and a 50% chance to win if you swap. What about the other 49% of the time?
>>725812930It's probably not, but someone who is could read my reply.
>>725812707What happens in the other 53.33% of the time?
>>725815349You lose.
>>725815349The other 49% was eliminated between the first and second choice. It no longer exists.
>>725803167yes but it says "all three" and "and"
>>725807368You can't do that!YOU JUST CAN'T OKAY!?
i understand this is all just a deltarune reference but wtf are you guys even talking about
>>725802573Holy shit. I am in college right now and you just helped it click. Sad to say I am not taking advanced mathematics but thanks anyway
>>725815321>It's a 1/100 of getting it right the first timeCorrect.>the one you are being offered to switch to also had a 1/100 chance of being right at the start of the game before any choices were made.Correct.And logically, the chance that that the prize is behind a door that you didn't pick is 99/100.
>>725801248Always switch.
>>725815664What if you have to pick between two doors and after you pick the host reveals -1 doors with a goat behind it? Should you swap?
>>725802450That was great. I felt the buttfluster of each and every one of those conundrum wash over me like gentle ocean spray
>>725815440You switch to the wrong door.
>>725802053>Suppose you scale this to 1000 doors. You pick a door, and the host reveals 998 doors containing goats.How do you know he wouldn't open 499. Or 1. You're extrapolating from a sample of 1.
>>725807368congratulations, you have autism
>>725811414Dungeon Encounters.https://en.wikipedia.org/wiki/List_of_Super_Bowl_championsOpen this page then Ctrl + F for "49–26"Scroll down, then notice the numbers for the winning teams
>>725802258>But I DID have breakfast!There's no hope for you, huh?
>>725819742The host can open any number of doors he wants. Switching is still preferable.The law of total probability means that p(win if switch) + p(win if not switch) = 1. No matter if the host opens 1 door, or if he opens 100 doors, or if he does a backflip and burns the studio down, the fact remains that when you made your first choice, the probability was 1/1000, and it will always be 1/1000 simply because the host will never reveal a door with a prize before you get a second choice.Therefore, because p(win if not switch) = 1/1000, then p(win if switch) = 1 - 1/1000 = 999/1000If the host opens 998 goat doors, then the only remaining door must be the prize door with probability 999/1000. If the host opens 997, then each remaining door has 999/2000 chance of being the prize door, and so on.
