settle a bet

MrPillowTalk

Ok its been here before but there is some argument on the symantics.

you are on a game show where you have to choose between boxes 1, 2 and 3 in one of the boxes is a million quid in the other two is nothing. choose a box.

having chosen a box, the show host removes one of the other two boxes as it does not contain the prize, now he offers you the option of either choosing to stay with the box you originally chose or change to the remaining box.

What do you do and why?

SilverFox261

You take the swap.

When you were offered the original choice you had a 33.3% chance of getting it right, and 66.6% of getting it wrong. The game show host must remove one empty box. If you picked right the first time aka: picked the money, then both boxes that are left are empty and therefore it does not matter which box he picks. This will happen 33.3% of the time.

But, if you picked wrong the first time, which will happen 66.6% of the time, then the game show host will only have one possible box to throw away, leaving the box containing the money.

Therefore you're chance of winning goes from 33.3% to 66.6% if you take the swap.

Theres a good explaination in this vid:

http://www.youtube.com/watch?v=mhlc7peGlGg

hotspur

And it makes it easier to see if instead of 3 boxes you imagine it's 1 million boxes. Box you pick is 1 in a million shot, box remaining...not so much.

bohsman

Imagine there are 10 boxes, host removes 8 and offers the swap, easy decision, same reasons but odds are obv even more in your favour.

pistolpeter

SilverFox261 wrote: »

You take the swap.

When you were offered the original choice you had a 33.3% chance of getting it right, and 66.6% of getting it wrong. The game show host must remove one empty box. If you picked right the first time aka: picked the money, then both boxes that are left are empty and therefore it does not matter which box he picks. This will happen 33.3% of the time.

But, if you picked wrong the first time, which will happen 66.6% of the time, then the game show host will only have one possible box to throw away, leaving the box containing the money.

Therefore you're chance of winning goes from 33.3% to 66.6% if you take the swap.

Theres a good explaination in this vid:

http://www.youtube.com/watch?v=mhlc7peGlGg

well said

ianmc38

The Monty Hall Problem

RichieLawlor

Watch '21' the film, Kevin Spacey and the Nerdy guy explain it. It's called variable change

BobSloane

In before someone says it's 50/50, retardo debate and inevitable lock

strewelpeter

The Monty Hall problem came up as an analogy for explaining some commercial option in a company I worked for once. No matter how many ways or how many times I explained it (You'd think that Hotspurs 'imagine you start with a million boxes' should be idiot proof) the accountant in the company just refused to get it. He eventually accepted that he was wrong and from then on he'd come up to me every couple of weeks and have me explain it to him again.

Company went El Busto. Obv.

YULETIRED

Does anyone have a link to that one hotspur mentioned a few weeks ago, the one in the University where the correct decision oddswise was to guess the answer , I'd like to send it on email to some folk.


I remember explaining the MH problem to a copper friend of mine and he got it straight away, I'm shocked an accountant didn't get it, Could it be the fact my mates is a betfair degenerate

bops

obv bluff, take the box that they took away imo

Jesus Wept

Or throw Monty a box to the face and hotwire the car.

Anyhow, I'd prefer the 'joke prize' - the elephant goat.

Icarus152

A goat.

Davey Devil

I didn't realise MPT owned Louie's Bistro. I was in there for lunch a while back and it was top quality. Keep up the good work Eoin.

hotspur

YULETIRED wrote: »

Does anyone have a link to that one hotspur mentioned a few weeks ago, the one in the University where the correct decision oddswise was to guess the answer , I'd like to send it on email to some folk.

http://www.youtube.com/watch?v=icGaDA0hLMk 12mins in.

I'm sure it's in print if you google, but there are a lot of hat puzzle variants out there.

Whyno

Change your mind = change your luck imo.... whats the third option
Ah sh1t i`m confused...Whats the bankers offer :pac:

HeeHawsCantona

x

carfax

Mr PT & Gholi; is it possible for you two to have a few beers together without an argument over nothing?

MrPillowTalk

well played lads booked me the 1200 win.

lol at those that refuse to believe in variable change.

MrPillowTalk

Davey Devil wrote: »

I didn't realise MPT owned Louie's Bistro. I was in there for lunch a while back and it was top quality. Keep up the good work Eoin.

thanks we do our best.

pok3rplaya

€1200!!?? Damn I need to start hanging around with Gholi

Gholimoli

i cant pay up so ive decided to leave ireland for good.

the_cat_is_back

Interesting. So on the show 'Deal or No Deal' (Not that i watch that muck ) the contestant should always take the swap when offered it at the end (when there are two boxes left)?

the_cat_is_back

the_cat_is_back wrote: »

Interesting. So on the show 'Deal or No Deal' (Not that i watch that muck ) the contestant should always take the swap when offered it at the end (when there are two boxes left)?

Monty Hall is a zero sum game, while Deal or No Deal isn't really. You are going to win something, no matter what. The size of the reward is all that is in dispute. While you should always swap in Deal or No Deal the concept isn't wholly analogous for 3 reasons:

1. In the Monty Hall problem, no matter how many doors you expand it to, there is only 1 car and x number of goats. If we accept that the goats have no inherent value to the player then there is only one beneficial outcome. In Deal or No Deal there are a number of beneficial outcomes for the player.

2. When you initially select your box you have a 1 in 22 (I think that's the right number of boxes, not sure) chance of selecting the quarter million. However, when you are offered the swap at the end you may have only a 1p and a 10,000 box remaining. This alters the maths somewhat in a way that the Monty Hall problem does not have to deal with.

3. You don't HAVE to open your box. In the Monty Hall problem you must select a door and good luck to you; but the addition of the Banker's Offer means that you do not have to open the box you began with, or any box at all for that matter. While the Banker almost never offers a +EV for the player it is another factor to consider and one which further distinguishes the Monty Hall problem from any application to Deal or No Deal

Small Change

Deleted User wrote: »

While you should always swap in Deal or No Deal the concept isn't wholly analogous for 3 reasons:

I always felt that the option to swap was 0EV in Deal or No Deal.

At the start of the game, each box has a 1/22 chance of having each of the amounts.
Unlike the MH problem, nothing occurs in the course of the game that changes the odds for one box relative to the other remaining boxes.

For example, in a game where the two remaining boxes contain 250K and 1p respectively, each box should have a 50% chance of having the 1p.

the_cat_is_back

Deleted User wrote: »

Monty Hall is a zero sum game, while Deal or No Deal isn't really. You are going to win something, no matter what. The size of the reward is all that is in dispute. While you should always swap in Deal or No Deal the concept isn't wholly analogous for 3 reasons:

1. In the Monty Hall problem, no matter how many doors you expand it to, there is only 1 car and x number of goats. If we accept that the goats have no inherent value to the player then there is only one beneficial outcome. In Deal or No Deal there are a number of beneficial outcomes for the player.

2. When you initially select your box you have a 1 in 22 (I think that's the right number of boxes, not sure) chance of selecting the quarter million. However, when you are offered the swap at the end you may have only a 1p and a 10,000 box remaining. This alters the maths somewhat in a way that the Monty Hall problem does not have to deal with.

3. You don't HAVE to open your box. In the Monty Hall problem you must select a door and good luck to you; but the addition of the Banker's Offer means that you do not have to open the box you began with, or any box at all for that matter. While the Banker almost never offers a +EV for the player it is another factor to consider and one which further distinguishes the Monty Hall problem from any application to Deal or No Deal

Small Change wrote: »

I always felt that the option to swap was 0EV in Deal or No Deal.

At the start of the game, each box has a 1/22 chance of having each of the amounts.
Unlike the MH problem, nothing occurs in the course of the game that changes the odds for one box relative to the other remaining boxes.

For example, in a game where the two remaining boxes contain 250K and 1p respectively, each box should have a 50% chance of having the 1p.

Well let's say our only goal in Deal or No Deal was to get the 250k. We have 22 boxes, i.e a 1/22 chance of having the 250k. If we get down to the last two boxes and the two remaining amounts are 1p and 250k. We turn down the banker's deal as 250k is our only goal.

Originally we had a 1/22 (roughly 4%) chance of picking the 250k and 21/22 (roughly 96%) of not getting it. We are offered the swap. By sticking with the box nothing has changed. However, by swapping it we know that if we picked incorrectly the first time around (96% probable) the box left over is the 250k.

ArmaniJeanss

the_cat_is_back wrote: »

Well let's say our only goal in Deal or No Deal was to get the 250k. We have 22 boxes, i.e a 1/22 chance of having the 250k. If we get down to the last two boxes and the two remaining amounts are 1p and 250k. We turn down the banker's deal as 250k is our only goal.

Originally we had a 1/22 (roughly 4%) chance of picking the 250k and 21/22 (roughly 96%) of not getting it. We are offered the swap. By sticking with the box nothing has changed. However, by swapping it we know that if we picked incorrectly the first time around (96% probable) the box left over is the 250k.

No, above is different situation. Deal or No Deal is 50/50 under your example.

However If Noel Edmonds stopped the game with 3 boxes left, and told you which one of the 2 you hadn't originally picked contained 1p and asked you do you want to swap, now a swap becomes 66%.

Its the extra information which changes the probabilities.

doke

Mrs. Doke suggests jiggling the box you originally chose before you decide.

Then again, a pre-emptive jiggle is her approach to most of the big decisions.

Goodluck2me

the_cat_is_back wrote: »

Well let's say our only goal in Deal or No Deal was to get the 250k. We have 22 boxes, i.e a 1/22 chance of having the 250k. If we get down to the last two boxes and the two remaining amounts are 1p and 250k. We turn down the banker's deal as 250k is our only goal.

Originally we had a 1/22 (roughly 4%) chance of picking the 250k and 21/22 (roughly 96%) of not getting it. We are offered the swap. By sticking with the box nothing has changed. However, by swapping it we know that if we picked incorrectly the first time around (96% probable) the box left over is the 250k.

this is completely different to the MH problem as there is no change in information.

the_cat_is_back

ArmaniJeanss wrote: »

No, above is different situation. Deal or No Deal is 50/50 under your example.

However If Noel Edmonds stopped the game with 3 boxes left, and told you which one of the 2 you hadn't originally picked contained 1p and asked you do you want to swap, now a swap becomes 66%.

Its the extra information which changes the probabilities.

Goodluck2me wrote: »

this is completely different to the MH problem as there is no change in information.

I'm probably just looking at it wrongly. I thought that if in the original example where you had three options and one incorrect is eliminated you could apply the same logic to having 22 boxes with 20 eliminated. As in both cases you're left with two options, one wrong and one right. Brain working a bit slow today but I'll get it eventually

ArmaniJeanss

the_cat_is_back wrote: »

I'm probably just looking at it wrongly. I thought that if in the original example where you had three options and one incorrect is eliminated you could apply the same logic to having 22 boxes with 20 eliminated. As in both cases you're left with two options, one wrong and one right. Brain working a bit slow today but I'll get it eventually

In the Monty Hall problem you are not left with 2 boxes, you are left with 3 boxes one of which is known. In your DOND example you are left with 2 boxes neither of which are known.
In the MH problem you are obviously never going to pick the known 'bad' box, but its presence influences the overall maths. The situation at the end of DOND is never a comparable situation.