Tim Ellis is the founder of Seattle Bubble. His background in engineering and computer / internet technology, a fondness of data-based analysis of problems, and an addiction to spreadsheets all influence his perspective on the Seattle-area real estate market.

The selection starts at 4%. Unless rates are below 4%, you will always guess correctly by picking 4%. I think providing a range would be better. Also, where is the selection for less than 4%? Boy, I’m picky today. :) Does “by 2014” mean by Jan 1 or Dec 31? I’m thinking by Jan 1, 2014.

RE:Jonness @ 1 & jrc @ 2 – Yes, you’re both correct, if your goal is just to maximize your chances of being right then you would choose the lowest option. But since there’s no prize on the line here and responses are anonymous there’s really no point in maximizing your odds. The point of the poll is to respond based on how high you think rates will go.

RE:The Tim @ 3 – I picked 4% anyways in order to maximize my chances of being right. I accept that others could turn out to be more right than me. But at least I won’t have to admit to ever having been wrong about anything. :)

If you ever watched the Showcase Showdown on “Let’s Make a Deal,” then you know the strategy. You get nothing if you bid over the limit, but you still have a chance if you bid under.

Speaking of Let’s Make a Deal. You have 3 doors to choose from, and one of them has a grand prize behind it. You pick one of them hoping the grand prize is behind the door. Monty Hall then opens one of the doors you didn’t pick, revealing the prize is not behind it. He then offers for you to either keep the door you originally selected, or choose the other unopened door.

1) What is the probability of winning the grand prize if you keep with your original selection?

2) What is the probability of winning the grand prize if you decided to switch doors?

You can reveal the answer, but don’t reveal the methodology just yet. Leave it open for others to reason this one out before revealing the solution.

RE: I guess they could be lower than right now, but what are the odds of that happening?

IMO, the odds of >= 3.5% to < 4% and >= 4% to < 4.5% are the same.

To Blurtman: I only have 2 posts left, so I'm maximizing my real estate by combining two in this post. I think the answers to the question I posed could generate an interesting debate, but we shall see. Maybe this isn't interesting to anyone who didn't watch Let's Make a Deal. :)

RE:Jonness @ 6 –
A) The “Showcase Showdown” and closest without going over are features of “The Price is Right,” not “Let’s Make a Deal.”

B) If you switch your choice you have a 2/3 chance of winning. Conversely if you don’t switch your chances are only 1/3 (the original odds before he revealed a door).

RE:Jonness @ 6 – Let’s try this a different way. After the first door is revealed to not have the prize, Monty takes you to the sound proof room in the back, where you can snack on bratwurst and Cheezwhiz doughnuts, from Kraft, America’s fine food company.

A new contestant is ushered out, and Monty instructs the new contestant to pick one of two doors, with the grand prize being behind one. The new contestant is oblivious to what has previously transpired, but is a bit thrown off by the EMT’s rushing to the back room. Nonetheless, what is the new contestant’s chance of wining the grand prize?

Pfffft. Rates will be right back down to where they were 6 months ago by the end of the year. General long term (10+ years) rates over 4.5% throw the FED into a negative cash flow situation given the current mix of their holdings. Would also add $500B a year to federal deficits. And would further chill an economy that is already slowing down. 2014 is a big election year. Add it all up and although “they” might like to try and pull back there will be additional QE in some form or another. The short term mentality always wins in national politics.

2015 would be a great time to sell though if you want to hold onto your gains.

RE:Jonness @ 6 – This question always irritated me, because the question assumed that the game show host was acting in the contestant’s best interest. Your version of the question may be different from the one I learned; in my version the host only optionally asked the question, not every time you made a guess.

That assumption, though, was never explicitly stated. If you modify the game show host to act in a hostile fashion, the probability changes.

OK. I have one post left here. Apparently Tim watched a lot of game shows as a kid, because he’s correct. Then again, he probably took a discrete math or a statistics class or two along the way, which I suspect is how he knows the answer.

So let’s look at it another way. At the start, you pick one of three doors. At that point you have a 1/3 chance of winning. The other two doors represent a 2/3 chance of winning. If you had a chance to switch sides up front, what would you do? I would take the two doors instead of one, because I know the probability of winning is twice as good when having two doors.

And I wouldn’t care if the game show host offered to reveal that one of my two doors did not have the grand prize. I already knew that, so why would I think simply demonstrating this to me by lifting one of my doors that doesn’t have the grand prize would change my odds of winning?

What trips most people up with this problem is, they assume lifting a door without the prize is a random act, and that any of the 3 doors could be randomly lifted. Thus, each of the remaining two doors represents 1/2 odds. But this is not how the game works. The only door that will be lifted is one of the 2/3 odds doors that the game show crew knows does not have the grand prize. Thus, the act of lifting the door does not change the odds of winning.

RE:Jonness @ 18 – How does intent change the odds? Wether Monty knew that the door he lifted was empty or not, the fact remains, that when there are only two doors left, the prize is behind one, Are you implying that the odds of the new contestant (in post 15), oblivious to what had transpired with the previously lifted door, is also 2/3 or 1/3?

I would like to make a $1 bet with you. I am thinking of a number between 1 and 1,001. When you have published your number, I will reveal 999 numbers which are not correct. You may then choose to keep your number or switch to all the other numbers. (You already knew that 999 of them must be wrong) Since this would make your odds 1,000:1 in favor, you will surely do so. All I ask is that for giving you a 1,000:1 advantage in odds that you will give me a 100:1 advantage in payout. I can’t be more fair than that. Maybe we could do it 100 times as a test of probability.

RE:Jonness @ 18 – It’s a pretty well-known stats problem. There’s even a whole page on Wikipedia dedicated to it. Here’s a handy visual from that page for those who still aren’t convinced that switching is the right strategy.

Fun Monty Hall trivia – decades ago there was an episode where one of the goat prizes was an oil rig – they had rented it for the episode. IIRC (which is doubtful) there was a tussle when the contestant opted for that as the prize, since it was worth significantly more than the “real” prize.

Scenario A: never switch doors.
1/3 chance of choosing the right door.

Scenario B: always switch doors.
if you chose the right door initially(1/3 probability), 0% chance of winning.
if you chose one of the two wrong doors (2/3 probability), 100% chance of winning.

So, Tim’s answer is right — if you choose to switch, so long as you picked one of the wrong doors at the outset, you will win. And it’s twice as likely that you chose a wrong door at the start!

The selection starts at 4%. Unless rates are below 4%, you will always guess correctly by picking 4%. I think providing a range would be better. Also, where is the selection for less than 4%? Boy, I’m picky today. :) Does “by 2014” mean by Jan 1 or Dec 31? I’m thinking by Jan 1, 2014.

If any answer is correct, 4% is.

RE:Jonness @ 1 & jrc @ 2 – Yes, you’re both correct, if your goal is just to maximize your chances of being right then you would choose the lowest option. But since there’s no prize on the line here and responses are anonymous there’s really no point in maximizing your odds. The point of the poll is to respond based on how high you think rates will go.“The point of the poll is to respond based on how high you think rates will go. ‘

Why not just say that then ?

RE:The Tim @ 3 –But doesn’t the word “high” suggest higher than right now? I guess they could be lower than right now, but what are the odds of that happening?

RE:The Tim @ 3 – I picked 4% anyways in order to maximize my chances of being right. I accept that others could turn out to be more right than me. But at least I won’t have to admit to ever having been wrong about anything. :)If you ever watched the Showcase Showdown on “Let’s Make a Deal,” then you know the strategy. You get nothing if you bid over the limit, but you still have a chance if you bid under.

Speaking of Let’s Make a Deal. You have 3 doors to choose from, and one of them has a grand prize behind it. You pick one of them hoping the grand prize is behind the door. Monty Hall then opens one of the doors you didn’t pick, revealing the prize is not behind it. He then offers for you to either keep the door you originally selected, or choose the other unopened door.

1) What is the probability of winning the grand prize if you keep with your original selection?

2) What is the probability of winning the grand prize if you decided to switch doors?

You can reveal the answer, but don’t reveal the methodology just yet. Leave it open for others to reason this one out before revealing the solution.

RE:Jonness @ 6 – Will this be on the final?By ARDELL @ 5:

IMO, the odds of >= 3.5% to < 4% and >= 4% to < 4.5% are the same.

To Blurtman: I only have 2 posts left, so I'm maximizing my real estate by combining two in this post. I think the answers to the question I posed could generate an interesting debate, but we shall see. Maybe this isn't interesting to anyone who didn't watch Let's Make a Deal. :)

RE:The Tim @ 3 –I didn’t know what to do, so I freaked out, powered my computer down and rocked myself in the corner. This has severely upset me. ;)

Come on Erik! You are the math guy around here. What’s the answer?

RE:Jonness @ 10 –No idea.

RE:Jonness @ 6 –If I remember correctly the person who stays with the original pick has a higher probability of winning.

I forget the reasoning. I think it’s because your odds of winning at the beginning, with three choices, are better than those of a choice of two.

RE:Jonness @ 8 –I will gladly sell you my comments on this thread.

RE:Jonness @ 6 –A) The “Showcase Showdown” and closest without going over are features of “The Price is Right,” not “Let’s Make a Deal.”

B) If you switch your choice you have a 2/3 chance of winning. Conversely if you don’t switch your chances are only 1/3 (the original odds before he revealed a door).

Added an additional response to the Open Thread.

RE:Jonness @ 6 – Let’s try this a different way. After the first door is revealed to not have the prize, Monty takes you to the sound proof room in the back, where you can snack on bratwurst and Cheezwhiz doughnuts, from Kraft, America’s fine food company.A new contestant is ushered out, and Monty instructs the new contestant to pick one of two doors, with the grand prize being behind one. The new contestant is oblivious to what has previously transpired, but is a bit thrown off by the EMT’s rushing to the back room. Nonetheless, what is the new contestant’s chance of wining the grand prize?

Pfffft. Rates will be right back down to where they were 6 months ago by the end of the year. General long term (10+ years) rates over 4.5% throw the FED into a negative cash flow situation given the current mix of their holdings. Would also add $500B a year to federal deficits. And would further chill an economy that is already slowing down. 2014 is a big election year. Add it all up and although “they” might like to try and pull back there will be additional QE in some form or another. The short term mentality always wins in national politics.

2015 would be a great time to sell though if you want to hold onto your gains.

RE:Jonness @ 6 – This question always irritated me, because the question assumed that the game show host was acting in the contestant’s best interest. Your version of the question may be different from the one I learned; in my version the host only optionally asked the question, not every time you made a guess.That assumption, though, was never explicitly stated. If you modify the game show host to act in a hostile fashion, the probability changes.

OK. I have one post left here. Apparently Tim watched a lot of game shows as a kid, because he’s correct. Then again, he probably took a discrete math or a statistics class or two along the way, which I suspect is how he knows the answer.

So let’s look at it another way. At the start, you pick one of three doors. At that point you have a 1/3 chance of winning. The other two doors represent a 2/3 chance of winning. If you had a chance to switch sides up front, what would you do? I would take the two doors instead of one, because I know the probability of winning is twice as good when having two doors.

And I wouldn’t care if the game show host offered to reveal that one of my two doors did not have the grand prize. I already knew that, so why would I think simply demonstrating this to me by lifting one of my doors that doesn’t have the grand prize would change my odds of winning?

What trips most people up with this problem is, they assume lifting a door without the prize is a random act, and that any of the 3 doors could be randomly lifted. Thus, each of the remaining two doors represents 1/2 odds. But this is not how the game works. The only door that will be lifted is one of the 2/3 odds doors that the game show crew knows does not have the grand prize. Thus, the act of lifting the door does not change the odds of winning.

RE:Jonness @ 18 – How does intent change the odds? Wether Monty knew that the door he lifted was empty or not, the fact remains, that when there are only two doors left, the prize is behind one, Are you implying that the odds of the new contestant (in post 15), oblivious to what had transpired with the previously lifted door, is also 2/3 or 1/3?RE:Jonness @ 18 –I would like to make a $1 bet with you. I am thinking of a number between 1 and 1,001. When you have published your number, I will reveal 999 numbers which are not correct. You may then choose to keep your number or switch to all the other numbers. (You already knew that 999 of them must be wrong) Since this would make your odds 1,000:1 in favor, you will surely do so. All I ask is that for giving you a 1,000:1 advantage in odds that you will give me a 100:1 advantage in payout. I can’t be more fair than that. Maybe we could do it 100 times as a test of probability.

RE:Jonness @ 18 – It’s a pretty well-known stats problem. There’s even a whole page on Wikipedia dedicated to it. Here’s a handy visual from that page for those who still aren’t convinced that switching is the right strategy.Fun Monty Hall trivia – decades ago there was an episode where one of the goat prizes was an oil rig – they had rented it for the episode. IIRC (which is doubtful) there was a tussle when the contestant opted for that as the prize, since it was worth significantly more than the “real” prize.

For the Monty Hall question:

Scenario A: never switch doors.

1/3 chance of choosing the right door.

Scenario B: always switch doors.

if you chose the right door initially(1/3 probability), 0% chance of winning.

if you chose one of the two wrong doors (2/3 probability), 100% chance of winning.

So, Tim’s answer is right — if you choose to switch, so long as you picked one of the wrong doors at the outset, you will win. And it’s twice as likely that you chose a wrong door at the start!

RE:Kilen @ 23 –Nice and concise presentation. Lucky for me that Jonness did not take me up on my bet.

Offer is hereby expired.