Ignore Bait: Highest IQ, Many Questions, Odds makers invited...
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When young (and dumb) I made a ton of money one afternoon in Vegas expermenting with Martingale.
Thought I found the holy grail.
Colored up an swore they shorted me a few chips. No problem, I'll win that back right quick.
Lost the whole roll in a couple of minutes.
First and last time for that.
Here's what makes the problem both interesting and confusing. The choices are not "always switch" or "always keep". There is a third choice that makes your chances of winning 50/50. Let your choice be determined by a flip of a coin. If you initially chose right (1/3) half of that time you will give away a winner while half of the rest of the time you will keep a loser. That's 1/6 + 1/3 = 1/2 of the time you will lose. That's why people who assume the decision to keep/switch is 50/50 say there's a 50/50 chance of winning, and if they choose to make that decision 50/50 or close to it (by listening to the audience, for example) they're right. They make it 50/50 by assuming it's 50/50 and introducing a 50/50 event into their decision.
She’s Baaack
You know where the car is 100% of the time
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The contestant can never know where it is 100% of the time.
You lost me on this logic - you are overthinking this.
It’s actually a fairly interesting observation if we think about it.
Let’s say we have 3 contestants. A, B, C.
A: always swaps
B: flips a coin
C: always stays
They each play 100 games. And we assume the 1/3 and 2/3 stats hold up perfectly for ease of illustration.
A: wins 67 games
B: (see analysis below)
C: wins 33 games
Player B, decides in his opinion it’s 50/50 and flips a coin to decide every time. For ease of analysis we will say the 50% choice holds up.
So Player B will hold 50 games and switch 50 games.
Hold = 1/3 of 50 = 17 games
Stay = 2/3 of 50 = 33 games
So, now Player B wins 50 games.
So, what he’s saying is that if a player decides incorrectly in their mind that it’s 50/50 and truly does pick a different strategy 50% of the time, we now introduce a win rate of 50% over the long haul.
That doesn’t mean the odds are 50%. Just that it’s a better strategy than always staying and a worse strategy than always switching.
Math is fun.
Basically, if a person takes a completely random approach they effectively killed part of the information that Monty provided them.
They just exclude a door that was opened and turn the odds into a true 50/50 via bad (but less terrible than just staying) decision making.
They just exclude a door that was opened and turn the odds into a true 50/50 via bad (but less terrible than just staying) decision making.
Instead of doors imagine it a dating scenario. Your potential spouse is behind one door and the other two are short term relationships.
If you pick right the first try there is no need for switching. Picking the spouse in a group of three vs picking the spouse in a group of two what difference does it make? Its exactly the dating to wedding scenario.
How often do you hear about people being left at the marital ceremony?
The argument about math and modeling only works academically or for standardized tests. This thread feels worthy for technical job interviews.
If you pick right the first try there is no need for switching. Picking the spouse in a group of three vs picking the spouse in a group of two what difference does it make? Its exactly the dating to wedding scenario.
How often do you hear about people being left at the marital ceremony?
The argument about math and modeling only works academically or for standardized tests. This thread feels worthy for technical job interviews.
I'm little surprised by this response. My response (and all of vapoolplayer's responses) was to the following scenario:
1. There are three doors. One has a car and two have a goat.
2. You you pick a door.
3. After you pick, Monty opens one of the two doors that you didn't pick. Monty knows which door has the car and will only reveal a door that has a goat. If the car is behind one of the two doors you didn't choose, Monty will open the other one. If both doors have a goat, then Monty picks one at random.
4. Monty offers you a choice. Stick with your original selection or switch to the door that Monty didn't reveal.
As has been stated here many times, you should switch because the car will be behind the door that Monty didn't open with 2/3 probability. My only point is that, given that Monty will never open the door with the car, seeing a goat behind the door he opens does not tell you anything new.
Suppose you pick door #1.
If door #2 has the car, Monty will open door #3.
If door #3 has the car, Monty will open door #2.
if door #1 has the car, Monty pick one at random.
So if Monty opens door #2, you should switch to door #3. If he opens door #3, you should switch to door #2. The point of my post is that regardless of which door Monty opens, you should switch from your initial choice.
vapoolplayer's post makes my point. He said: "If you knew going in that he was going to open the door and show a goat, you should have already made the decision to switch." In other words, when Monty opens a door with a goat behind it, the only thing you "learn" is that one of the two doors had a goat behind it. But you already knew that. Monty opens one of the two doors you didn't pick, but only one can have a car behind it and he will never reveal the car. So when Monty opens a door with a goat, there is no new relevant information.
I agree with vapoolplayer that a different game would require a different decision rule. I was just surprised that he started talking about a different game than the one he had posted on multiple times.
I agree. See my post on page 15 (#289) and my most recent post.
I literally said “what the fuck” out loud.
I wish this was a troll post. It would be amazing.
True, but you said you know where the car is 66% of the time when it's actually 100%
Now I'm pissed... Your comment made unblock him. There goes a few more brain cells....
When I say me, I’m speaking from the contestant POV. I might have not been clear on that.
If we are saying the contestant knows 100%, then I’ll have to hear explanation to see what I’m missing.
I only read the first 10 pages or so. Did Major Miscue ever come around?
He finally admitted that he did in another thread, to counter somebody who mentioned his lack of understanding as it related to another topic.
He never admitted it here.
When people finally come to understand that they were wrong about something, why is it so hard for them to just man up and say so?
How refreshing would that be?