Deal or No Deal Conundrum

#1
This will be for the ones good at maths.

We all know the game Deal or No Deal where you get 22 boxes with different amounts of cash in them and you try and make the most money. My friends and I were having a (rather heated) debate about whether at the end you should stick or switch?

I will explain...

Let us assume that the banker is irrelevant and you have got down to two boxes with either 1p or £250,000 within them. Considering you have one box in front of you...

...do you stick or switch?

I believe you should ALWAYS switch since it will drastically increase your chances; I will explain:

At the beginning you have a 1/22 chance of picking the box with the £250,000 in.

Therefore there is a 21/22 chance that the box with the £250,000 in is out in the boxes that you have not selected.

Having whittled down the boxes you find yourself with two left one with 1p and the other with £250,000.

Technically you should switch since the chances it's in the box NOT in front of you is 21/22.

I believe this is just a scaled up version of the Monty Hall Problem.

My friends are adamant it remains a 50/50 chance even though I'm adamant it's a matter of statistics.

Any thoughts/want to argue the matter

Edd
 
#3
But thats statistics which have no impact on chance.

With two boxes left there is a 1 in 2 chance (i.e 50/50) that you hold the 1/4 mil.

edd, both you and your friends are correct because you are talking about two differenct mathematical things.
 
#4
Nonsense, Shrodingers Cat applies here too, the chance that the prize is in the box is 50/50, it either is or isn't,but until you open the box (TAKE THE MONEY!) you don't know.
 
#5
The odds change after doing away with each box.

At the end you are left with 2 boxes.....therefore it's 50/50.
 
#6
In your statement above exchange 1p for £250,000 and £250,000 for 1p. I think you will then come up with the answer.
 
#7
smudge67 said:
The odds change after doing away with each box.

At the end you are left with 2 boxes.....therefore it's 50/50.
Have to agree.

3 boxes left it's a 1 in 3 chance.

2 boxes left it's a 50/50 chance.
 
#8
Spank-it said:
smudge67 said:
The odds change after doing away with each box.

At the end you are left with 2 boxes.....therefore it's 50/50.
Have to agree.

3 boxes left it's a 1 in 3 chance.

2 boxes left it's a 50/50 chance.
Of course, because I'm right :)
 
#9
Similar question which has been argued in the pub for about 2 years.

They say that the odds of winning the lottery are 1:14,000,000.

My argument is that for each extra ticket you buy, the odds would simply be reduced by one... so if you get ten the odds are now 1:13,999,990

My dumb ass mate reckons that by buying another ticket you are doubling your chance of winning (2:14,000,000), therefore you are halving the odds (1:7,000,000). Personally i think he's talking bollacks as by this logic you would only need to buy 25 tickets to get the win.

Help me out. 8O
 
#10
Social_Handgrenade said:
Similar question which has been argued in the pub for about 2 years.

They say that the odds of winning the lottery are 1:14,000,000.

My argument is that for each extra ticket you buy, the odds would simply be reduced by one... so if you get ten the odds are now 1:13,999,990

My dumb ass mate reckons that by buying another ticket you are doubling your chance of winning (2:14,000,000), therefore you are halving the odds (1:7,000,000). Personally i think he's talking bollacks as by this logic you would only need to buy 25 tickets to get the win.

Help me out. 8O
Make him buy 25 tickets. If he wins the jackpot then he was right. If not then you.

Easy and no long winded discussions needed.
 
#11
Steven said:
Social_Handgrenade said:
Similar question which has been argued in the pub for about 2 years.

They say that the odds of winning the lottery are 1:14,000,000.

My argument is that for each extra ticket you buy, the odds would simply be reduced by one... so if you get ten the odds are now 1:13,999,990

My dumb ass mate reckons that by buying another ticket you are doubling your chance of winning (2:14,000,000), therefore you are halving the odds (1:7,000,000). Personally i think he's talking bollacks as by this logic you would only need to buy 25 tickets to get the win.

Help me out. 8O
Make him buy 25 tickets. If he wins the jackpot then he was right. If not then you.

Easy and no long winded discussions needed.
Don't even waste the £25 quid. Your mate's clearly a spastic.
 
#12
OK, tech geek head on (all figures to 3 sig fig)

You buy a ticket and you are sitting there all damp with excitement. Lancelot has got the balls rolling around and they come out, you have a 6 in 49 chance of your first ball being pulled (6/49 or 0.122) then its 5/48, 4/47 and so on until you have a 1/44 chance.

When you do stats you have to multiply the chances together, therefore 6/49 x 5/48 etc etc which ends up with a figure of roughly 0.0000000709 (its a slow news day) and to find out what your odds are you divide 1 by this number. Hence a one in 14 million



I've got to get out more and get myself a woman I know........
 
#13
sparky8 said:
OK, tech geek head on (all figures to 3 sig fig)

You buy a ticket and you are sitting there all damp with excitement. Lancelot has got the balls rolling around and they come out, you have a 6 in 49 chance of your first ball being pulled (6/49 or 0.122) then its 5/48, 4/47 and so on until you have a 1/44 chance.

When you do stats you have to multiply the chances together, therefore 6/49 x 5/48 etc etc which ends up with a figure of roughly 0.0000000709 (its a slow news day) and to find out what your odds are you divide 1 by this number. Hence a one in 14 million



I've got to get out more and get myself a woman I know........
Yes........yes you do.
 
#14
sparky8 said:
OK, tech geek head on (all figures to 3 sig fig)

You buy a ticket and you are sitting there all damp with excitement. Lancelot has got the balls rolling around and they come out, you have a 6 in 49 chance of your first ball being pulled (6/49 or 0.122) then its 5/48, 4/47 and so on until you have a 1/44 chance.

When you do stats you have to multiply the chances together, therefore 6/49 x 5/48 etc etc which ends up with a figure of roughly 0.0000000709 (its a slow news day) and to find out what your odds are you divide 1 by this number. Hence a one in 14 million



I've got to get out more and get myself a woman I know........
'kin ell, I thought I was dull... you must be a riot at parties :wink:

Cheers Smudge, i'll let him know that some random internet bloke agrees with me, that'll settle the matter for sure :D
 
#15
No, you are dull, you're just in denial ;)

I did apologise and its OK, Smudge does know exactly how dull I am but has to be nice Cos Ive got ALL of the Corps wristbands for AvN.

If not, I think he quite justifyably may have called me a cnut!
 
#16
I think it's 50/50 for the last box. Because...

Effectively when you choose the box you put in front of you, you also choose the box you are not going to pick from the rest of the pile.

Whatever your strategy for picking the boxes is, the decision to leave one is made effectively right at the start because no new information is added during the game. It doesn't really matter what the middle boxes are that you eliminate.

Bit difficult to explain. But, I reckon it's 50/50. Though I might be wrong. My head hurts.
 
#17
sparky8 said:
No, you are dull, you're just in denial ;)

I did apologise and its OK, Smudge does know exactly how dull I am but has to be nice Cos Ive got ALL of the Corps wristbands for AvN.

If not, I think he quite justifyably may have called me a cnut!
On that note, did you get the email I sent you?
 
#18
Yeah, no offence but giving all requests a good ignoring until Feb at the earliest!
 
#19
CQMS said:
Nonsense, Shrodingers Cat applies here too, the chance that the prize is in the box is 50/50, it either is or isn't,but until you open the box (TAKE THE MONEY!) you don't know.

Terry Pratchett goes further than Shrodinger and postulates a 3rd option:
Mainly the cat is bloody furious at being locked in a box.
 
#20
theiftaker said:
CQMS said:
Nonsense, Shrodingers Cat applies here too, the chance that the prize is in the box is 50/50, it either is or isn't,but until you open the box (TAKE THE MONEY!) you don't know.

Terry Pratchett goes further than Shrodinger and postulates a 3rd option:
Mainly the cat is bloody furious at being locked in a box.
Are you both attempting a wah? The cat is both in the box and not in the box at the same time until you open the box to find out.
 

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