Impeccable logic
- Thread starter Kes
- Start date
- Status
Sponsored Links
My theory is that the banker's basic rule with just two boxes left is most probably
Offer = Min + 1/3 ( Max - Min )
as that will put the greatest pressure on the contestant's decision.
Min and Max being the two amounts in the boxes.
The offer will be adjusted to avoid an obvious rule being seen and depending on the contestant's attitude it will be set above or below the calculated amount.
Offer = Min + 1/3 ( Max - Min )
as that will put the greatest pressure on the contestant's decision.
Min and Max being the two amounts in the boxes.
The offer will be adjusted to avoid an obvious rule being seen and depending on the contestant's attitude it will be set above or below the calculated amount.
In my case, because of that annoying Monty Hall.
I agree now that DonD swap odds are 50/50. After all there is 20/1 chance that the contestant chose £1, and 20/1 that he chose £250k. So 50/50.
But why in Monty Hall's case, or DonD with three boxes, why is it 3/2 to swap? It doesn't matter who opens the 'spare' door, there wouldn't be a swap offerred unless the empty/£1/goat had been shown, so it should be 50/50, shouldn't it?
- Joined
- 10 Jul 2004
- Messages
- 14,983
- Reaction score
- 4,682
- Country
For f**ks sake will someone open the so**in box
Sponsored Links
P
pna
It is 50-50 in Monty Hall as well. The website is wrong. You originally had a 33% chance of guessing the door with the car behind, and when he shows an incorrect (goat) door, he does improve your odds for the choice you are about to make, but only to 50% - two doors - one with a goat, one with a car. Probabilities are not cummulative - each decision is separate. It doesn't matter how long your winning streak has been, when it comes to choosing between two boxes, the choice is 50-50.
To answer the OP, I think the only logical way to improve one's chances is to bribe someone at DonD...
trouble is its not 50-50 when there is an offer aswell trying to influence the decision. you have the dilemma of whether to accept an offer of hard cash to take home with you or the choice of possibly losing so the odds have increased, do i take the offer or open one of two boxes?
So the whole of academia, after many years of wrangling, is wrong? It's not only the one website concerned, every website gives the MH choice between two boxes as 1/3 to 2/3, so swap. (In our case we are ignoring any banker offer.)
I wish someone would come up with an answer soon. Mind you, I'm beginning to get quite fond of the goat.
this entire topic should be devoted to bankers.
an entire 'wunch' of them.
cheers for that one Nige F.
Ok game 1. The contestant has 1 in 20 chance of picking any of the figures available. In this case 250K. There is also a 19 in 20 chance that someone else has the box with 250k in it.
On this instance i would gamble that the contestant doe not have the 250k.
One box is now eliminated, but not the 250k box. So now the contestant has a 1 in 19 chance that he has the box and also 18 in 19 chance that he does not.. Still odds are stacked against him and you would bet he didnt have it.
This continues and 10 boxes are left, the contestant has a 1 in 10 chance he has it and a 9 in 10 he does not. The odds a now shortenting but they are still against him.
Important bit - Some where in those other 9 boxes is a £1. Now the person standing behind this box does not know whats in it. So he also has a 1 in 10 chance of having the 250k and a 9 in 10 of not having.
Right, we are down to three boxes.
Each person now has a 1 in 3 chance of having it and a 2 in 3 of not having it.
My point - Each person including the contestant in the middle with his box on the table are and have always been equal having the same odds as each other on whether they have the 250k box through out the game.
Someone mentioned at the beginning of the game the contestant had a 19 in 20 chance of not having it so swapping is always better. But 18 contestants have been eliminated therefore the person who has got the £1 (Unknowingly) at the beginning of the game still started with a 1 in 20 chance, exactly the same as the contestant. Therfore also having a 19 in 20 chance that they will not have the box. Again the same as the contestant.
So 2 boxes left, each person has a 1 in 2 of having it and a 1 in 2 chance of not. 50:50 chance
On this instance i would gamble that the contestant doe not have the 250k.
One box is now eliminated, but not the 250k box. So now the contestant has a 1 in 19 chance that he has the box and also 18 in 19 chance that he does not.. Still odds are stacked against him and you would bet he didnt have it.
This continues and 10 boxes are left, the contestant has a 1 in 10 chance he has it and a 9 in 10 he does not. The odds a now shortenting but they are still against him.
Important bit - Some where in those other 9 boxes is a £1. Now the person standing behind this box does not know whats in it. So he also has a 1 in 10 chance of having the 250k and a 9 in 10 of not having.
Right, we are down to three boxes.
Each person now has a 1 in 3 chance of having it and a 2 in 3 of not having it.
My point - Each person including the contestant in the middle with his box on the table are and have always been equal having the same odds as each other on whether they have the 250k box through out the game.
Someone mentioned at the beginning of the game the contestant had a 19 in 20 chance of not having it so swapping is always better. But 18 contestants have been eliminated therefore the person who has got the £1 (Unknowingly) at the beginning of the game still started with a 1 in 20 chance, exactly the same as the contestant. Therfore also having a 19 in 20 chance that they will not have the box. Again the same as the contestant.
So 2 boxes left, each person has a 1 in 2 of having it and a 1 in 2 chance of not. 50:50 chance
this entire topic should be devoted to bankers.
an entire 'wunch' of them.
cheers for that one Nige F.
I'm with you noseall
Can you believe there are 8 pages about a gameshow.
Wait.... here's a post telling me it's about mathematics and probable chance
Whatever
Jackpot has it covered in my opinion.
End of!
End of!
There's a very easy way to convince all the doubters.
Take three upturned cups and a small object that each cup can conceal underneath.
Ask a family member to act the part of Monty Hall, i.e. to hide the object underneath one of the cups (without you seeing), and, after you've made your first choice, to lift a cup that doesn't conceal the object. Then you make your swap decision, and then you see which cup conceals the object.
Do this about thirty times, and see how often the object appears under each cup. Unless one of you cheats, I expect that it will be about 10 times under each one.
If you believe that the probability that we're all debating is 50:50, and if you're right, then the object will be under the cup that you first chose about 15 times, instead of about 10.
If anyone wants to send me video footage of such an experiment, proving that the odds work out to be 50:50, then I will gladly send £100 to the person to do so. This is a genuine offer.
If anyone wants to make me the same offer, then I'll gladly send a video that demonstrates that the odds are in favour of swapping, i.e. 1/3 probability of the object being under the cup I first choose.
I daresay that someone will want to claim that this experiment doesn't fairly or accurately represent the problem being discussed. To that person I make the following offer: construct any practical demonstration, of your own choosing, that shows that the alleged 50:50 odds are correct, and I'll still send you £100.
_____________
PS - this offer is not open to Kes or JohnD. Sorry guys, but that's the price of being both civilised and correct from the very beginning.
_____________
Edit: other members who can forget the idea of receiving 100 of my hard-earned spenderoonoes are megawatt and BigBurn. Not because they were right, but because they're always wrong.
Take three upturned cups and a small object that each cup can conceal underneath.
Ask a family member to act the part of Monty Hall, i.e. to hide the object underneath one of the cups (without you seeing), and, after you've made your first choice, to lift a cup that doesn't conceal the object. Then you make your swap decision, and then you see which cup conceals the object.
Do this about thirty times, and see how often the object appears under each cup. Unless one of you cheats, I expect that it will be about 10 times under each one.
If you believe that the probability that we're all debating is 50:50, and if you're right, then the object will be under the cup that you first chose about 15 times, instead of about 10.
If anyone wants to send me video footage of such an experiment, proving that the odds work out to be 50:50, then I will gladly send £100 to the person to do so. This is a genuine offer.
If anyone wants to make me the same offer, then I'll gladly send a video that demonstrates that the odds are in favour of swapping, i.e. 1/3 probability of the object being under the cup I first choose.
I daresay that someone will want to claim that this experiment doesn't fairly or accurately represent the problem being discussed. To that person I make the following offer: construct any practical demonstration, of your own choosing, that shows that the alleged 50:50 odds are correct, and I'll still send you £100.
_____________
PS - this offer is not open to Kes or JohnD. Sorry guys, but that's the price of being both civilised and correct from the very beginning.
_____________
Edit: other members who can forget the idea of receiving 100 of my hard-earned spenderoonoes are megawatt and BigBurn. Not because they were right, but because they're always wrong.
There's a very easy way to convince all the doubters.
Take three upturned cups and a small object that each cup can conceal underneath.
Ask a family member to act the part of Monty Hall, i.e. to hide the object underneath one of the cups (without you seeing), and, after you've made your first choice, to lift a cup that doesn't conceal the object. Then you make your swap decision, and then you see which cup conceals the object.
Do this about thirty times, and see how often the object appears under each cup. Unless one of you cheats, I expect that it will be about 10 times under each one.
If you believe that the probability that we're all debating is 50:50, and if you're right, then the object will be under the cup that you first chose about 15 times, instead of about 10.
If anyone wants to send me video footage of such an experiment, proving that the odds work out to be 50:50, then I will gladly send £100 to the person to do so. This is a genuine offer.
If anyone wants to make me the same offer, then I'll gladly send a video that demonstrates that the odds are in favour of swapping, i.e. 1/3 probability of the object being under the cup I first choose.
I daresay that someone will want to claim that this experiment doesn't fairly or accurately represent the problem being discussed. To that person I make the following offer: construct any practical demonstration, of your own choosing, that shows that the alleged 50:50 odds are correct, and I'll still send you £100.
_____________
PS - this offer is not open to Kes or JohnD. Sorry guys, but that's the price of being both civilised and correct from the very beginning.
This is a flawed method irrelevant to the opd post. When you pick the first cup there should be a 1 in 3 (33.3333%) chance of getting the object. However by removing a cup with it not in. You will never ever pick the right one first time giving you a 0% chance of getting it.
How can it be a 50:50 when there is three cups. Its impossible
Softus thats all well and good but i could say the same thing.
3 cups and a 1 in 3 chance of picking the correct one on my first go.
I could play that game 10000000,0000000000,00000000 times and still never get it, as there is manual intervention that prevents me. Purely an unfair and an unlogical experiment when comparing to the ops scenario.
Now if there was 3 cups and you got 3 people to stand with them not knowing which one has the object under them, there is a guarenteed 1 in 3 chance that one has it. And each person has the same 1 in 3 odds and also has 2 in 3 of not having the object. Now if one gets eliminated then the other 2 people still have a 1 in 2 chance and also a 1 in 2 chance of not having it. And on that occasion its 50:50
3 cups and a 1 in 3 chance of picking the correct one on my first go.
I could play that game 10000000,0000000000,00000000 times and still never get it, as there is manual intervention that prevents me. Purely an unfair and an unlogical experiment when comparing to the ops scenario.
Now if there was 3 cups and you got 3 people to stand with them not knowing which one has the object under them, there is a guarenteed 1 in 3 chance that one has it. And each person has the same 1 in 3 odds and also has 2 in 3 of not having the object. Now if one gets eliminated then the other 2 people still have a 1 in 2 chance and also a 1 in 2 chance of not having it. And on that occasion its 50:50
- Status
Sponsored Links