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[scriver]

@Monty Haul Problem - For reference, this was the way of putting it that helped me understand it (this time, because I know we have been through this here on the forums before, but apparently I had forgotten and gone back to 50%):

Your original door had 33% odds of being wrong. AKA there's a 66% chance that the prize is behind one of the dealer's doors. By clearing an empty door, for practical purposes you're choosing between opening two doors OR only one door (Again: the dealer KNOWS which doors are empty), because there is a 66% chance that the prize is behind one of the other doors, and if it is, the dealer has already told you behind which door it is not.

This is a great way on making sure whoever you are trying to explain it to definitely is in no mood at all to listen to you, though, Chairman:

I will keep trying to teach you because I want to see what you post once you reach enlightement.

I promise I'm not angry or annoyed. Its a difficult concept and clearly noone has taken the time to explain it to you. I'm going to educate you.

[Doomblade187]

-snip-

Oh, I remember Galleons! That game was the best!

There's a new game called "Whatever Floats Your Boat" that has decent boat building, but it's a floating fort arena deal instead of ships. Lots of boarding action.

[Reelya]

@Monty Haul Problem

That's the Monty Hall Problem.

The Monty Haul problem (also named after Monty Hall) refers to D&D campaigns when the DM gives the players too many magical items, which causes a feedback loop of having to hand out ever more powerful items just to keep the players motivated.

~~~

As for the three-doors problem, a good way to understand the general issue is to understand that the "odds" only reflect knowledge.

e.g. Monty knows that a certain door is worth 100% and the others are worth 0%. Without additional knowledge you can only assign a value of 33% to each door, and if you can narrow it down to two doors, then those doors are worth 50% and the last door is worth 0%. e.g. the true winning door is worth 100%, 50% or 33% to different people. The Monty Hall problem just sets up a situation where you know that a certain door (the player's original blind pick) must be right 33% of the time, and there's only one other choice, which logically must be correct whenever the 33% one isn't, e.g. 67% of the time. Basically, odds can be transferred from one door to another.

Some people get caught up in "how can a door be worth 67%, all the doors are worth 33%". But that misses the point: a certain door is actually worth 100% and the others are really worth 0%. Any chance on a door between 0 and 100 is just an estimate based on the different information you have about them. e.g. if someone walks in late and must choose one of the remaining two doors they can only choose the right one 50% of the time: two doors, one correct choice, a 50% chance of being correct. However, think of the analogy of horse racing. If asked to pick one of two horses with no other information, you will pick the winning horse 50% of the time. However, that in no way reflects the actual odds of each horse winning: even if one option is overwhelmingly more likely than the other you only pick right 50% of the time with no other knowledge: someone who knows something about the horses abilities will be able to pick the winner between two horse more often than 50% of the time. Similarly, with the Monty Hall problem, someone who knows which door was originally picked can do better than 50/50 chance when choosing which door is the correct one.

Switching must also win more than sticking because of logic. e.g. say you have a strategy of "Always choose Door A" then "always stick" then how could you possibly win 50% of the time? That would imply Door A was the right door 50% of the time, which is contradictory (if you had always chosen Door B or Door C then that one would be right 50% of the time as well). So Door A can only be right 1 in 3 games. However, switching always wins when sticking loses and vice-versa, so switching must win 2 out of 3 games.

[bloop_bleep]

There's a 67% chance that the car is behind one of the two doors that you didn't pick. In that case, the unopened door that you didn't pick (the door you can switch to) has the car.

Then there's a 33% chance that the car is NOT behind one of the two doors that you didn't pick. In that case, the door you picked has the car.

Therefore, in 67% of cases, completely regardless of which door Monty Hall opens, you will win if you switch.

It's pretty obvious this way, and frankly, there's absolutely no point in you arguing, pikachu, since this has been demonstrated many, many times over by many people pretty much everywhere. It's also ridiculously easy to write a program to test this. Try using this.

Code: [Select]

import random

num_runs = int(input("How many runs? "))

count = 0 # count of how many times the player would win if he switched
for i in range(num_runs):
    car_door = random.randint(1, 3)
    #print("Car is behind door", car_door)
    picked_door = random.randint(1, 3)
    #print("Door", picked_door, "is picked")
    allowed_doors = {1, 2, 3} - {car_door, picked_door}
    opened_door = random.choice(list(allowed_doors))
    #print("Monty Hall opened door", opened_door)
    if car_door != picked_door:
        count += 1

print()
print("Switching was preferable in", count, "out of", num_runs, "cases.")


[redwallzyl]

The effect also gets larger if you add more doors.

[Reelya]

Or a slightly less mathy way to express it, only because some people do seem to really not get it:

When you pick your first door, you're twice as likely to have a goat than a car. "Switching" swaps what you had to the opposite outcome, so you're now twice as likely to have a car than a goat.

e.g. if you had a 1/3 chance of having the winning prize and the guy says "do you want to swap your prize to the opposite prize?" then obviously swapping is a good idea. When you phrase it like this I don't think anyone could argue with the decision to swap. But it's mathematically the same deal Monty is giving you.

~~~

Another analogy is a deck of cards. Say the winning card is the Ace of Spades.

e.g. you pick a card from a deck of 52 completely at random and place it face down on the table, unseen.

Then, the dealer goes through the deck and discards 50 cards which aren't the Ace of Spades. He places the final card on the face down on the table, unseen.

Would you "stick" with your original card or "switch" to the dealers card? Effectively, the "door(s) you didn't pick" in Monty Hall are the same as the "cards you didn't pick" in this example. Monty takes the "unselected" options and removes all but one, which is guaranteed to be the Grand Prize unless you just happened to pick it already. But since there are more booby prizes than Grand Prizes than that's not likely.

[hector13]

Right, children, we’ve gone over it a thousand times already (hyperbole, pedant. Yes, you) we don’t need to go over it again, or in a different way. If someone wants to know how it works, Google is their friend and will likely be able to explain it in as many different ways as y’all can, but significantly quicker.

[Teneb]

So, to make an attempt to change the subject from Monty Hall 2: Electric Bogaloo...

Apparently I was selected for the closed beta of Magic the Gathering: Arena. Wasn't expecting this.

[KittyTac]

Snip

Last time I checked, almost all of the games were like "surviv palne crash!111!!!" Or "WHO MRUUDERED SPANGBAWB??". Times have changed.

[TD1]

-snip-

Oh, I remember Galleons! That game was the best!

Yea!

[Tack]

Now I kind of want to try Sea of Thieves.

[Kagus]

Now I kind of want to try Sea of Thieves.

Presumably then, you haven't been keeping up with their "anti-toxicity" development campaign which has thus far completely backfired and resulted in a salty mire of griefing, abuse and venomous echo-chambering.

[JoshuaFH]

So, to make an attempt to change the subject from Monty Hall 2: Electric Bogaloo...

Apparently I was selected for the closed beta of Magic the Gathering: Arena. Wasn't expecting this.

Isn't that almost over though? I thought it was releasing soon.

[Steelmagic]

Dear Jesus. This is Action Park level. Right off the bat the designer dropped out of high school with no engineering experience.

[TamerVirus]

IIRC when the kid was decapitated,  his head became a projectile and broke the jaw of the woman sitting behind him.

Traumatizing shit