Impeccable logic
- Thread starter Kes
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It's a totally random game, so I don't really see the point in all this tbh.
But my 2p worth anyway. The odds of the other boxes containing the top prize change throughout, as boxes are opened and eliminated. So at the end you have 2 boxes to choose from, the odds of the other box are not 19 to 1 or whatever, it's 50/50. This is shown by the value of the bankers offer increasing as boxes get whittled down.
I believe the banker can influence the decision making process, but this is for dramatic effect, as he has no idea what's in the boxes either.
But my 2p worth anyway. The odds of the other boxes containing the top prize change throughout, as boxes are opened and eliminated. So at the end you have 2 boxes to choose from, the odds of the other box are not 19 to 1 or whatever, it's 50/50. This is shown by the value of the bankers offer increasing as boxes get whittled down.
I believe the banker can influence the decision making process, but this is for dramatic effect, as he has no idea what's in the boxes either.
Having had another think, you (EdSet100) are correct to point out that the maximum and minimum prizes will end up in two particular boxes only twice out of twenty attempts. If the contestant's box is 'A', then the max prize will be in 'B' once out of twenty attempts, and in box 'A' once out of twenty attempts. This implies that there is no advantage in swapping.
However, the original post didn't specify that box 'B' was nominated to be the one that ended up containing either £1 or £250, i.e. that the game was repeated up to 18 times (averaged) in order to create that permutation. Another interpretation of that OP that it is known by elimination what remains in the unopened boxes. Given this ambiguity, it would more natural to assume the game is played as normally as possible, i.e. to base an answer on the second interpretation.
Working to this premise, my belief was correct, i.e. there is an advantage in swapping.
This aligns with Kes' findings in his for the Ace of Spades.
To those posters who think that you can arrive at the answer intuitively, I would suggest that you examine the Monty Hall scenario, which (as has already been pointed out) has been discussed for many years and has befuddled many renowned mathematicians.
To the poster (guess who
) who believes that this is an "argument" that some people are pursuing until becoming blue in the face, it isn't - it's a sensible discussion about the use of statistical theory to derive an answer to a potentially interesting question. If you think that other people's contributions are nonsense and piffle, then you aren't reading them and dispassionately analysing the problem.Someone earlier posted
Whilst I agree that at the start when your single opponent holds 51 cards and you hold one your chances of holding the AOS is lower than his, but at each stage when a card is discarded (akin to opening a box), the odds are reset until when, at the two card stage, the odds of you holding the AOS is 50:50.
No more chance with a swap than without IMHO.
And, if anyone watched this week, the girl would have swapped and would have lost out
MW
Probability isn't accumulative ... If there are 52 people, each with a single card, you each have the same 1 in 52 chance of being dealt the Ace of Spades.
Whilst I agree that at the start when your single opponent holds 51 cards and you hold one your chances of holding the AOS is lower than his, but at each stage when a card is discarded (akin to opening a box), the odds are reset until when, at the two card stage, the odds of you holding the AOS is 50:50.
No more chance with a swap than without IMHO.
And, if anyone watched this week, the girl would have swapped and would have lost out
MW
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To the poster (guess who
I've explained it quite simply for you in the 'apples in boxes' scenario. If you think I've got it wrong (and I haven't) then please show me where. The MH thing is totally different and involves three doors and a host that knows what is behind them. It's the host's CHOICE that removes random chance in the MH thing. If MH was none the wiser about what was behind the doors then there would be no advantage to the contestant.
That particular kindergarten scenario was a hint of what's going on inside your head, not a solution to a statistical problem.joe-90 said:
joe-90, this is typical of your closed-minded approach to debating. There are many times where I align with your view, and respect your awareness of the general good, but this is one of those topics where the "(he won't)" stance won't achieve anything.
If you read my posts you'll see that I'm maintaining an open mind, and although it's not impossible that you're right, and that the probability really is 1/2, I've put a reasonable amount of thought into the problem and I'm satisfied with the answer I've reached and the reasoning I've provided.
I remember a lot of the education I've been fortunate enough to receive on the subject of statistics, and I have to point out that the terminology you've used on this topic reveals that you've not been so fortunate. With many statistical problems it's possible to reach the correct answer using intuition, but with this one most people will get it wrong.
For that reason, I'm happy to agree to disagree with you on this occasion, and I wish you luck with your solution to Kes' problem.
Joe, why does Monty's choice affect the odds? If the door covering the spare goat just swung open, or if the goat pushed it, or if Monty guessed correctly, the odds would still be on swapping. (If Monty guessed incorrectly and revealed the car the swap would of course not be offered.) To be at the point of the swap implies that a goat door has been opened, not how it has been opened.
What I can't get my brain to grasp is that if DonD is 50/50, i.e. no advantage in swapping - and I am coming to that conclusion - then why is it an advantage to swap in Monty's game? What's the element we're missing that divides the two games?
What if Noel had three boxes, holding £250k, £1k, and a goat. The contestant picks a box, then he, or she, or Noel, or blind chance, or the goat, opens either £1k or the goat box (one of which must be on the counter). Monty says swap. DonD says no difference. Why? That's the crux of the OP.
Edit: Aghhhh... I've just typed in "monty hall" "deal or no deal" into Google. I'm going to lie down in a dark corner somewhere...
What I can't get my brain to grasp is that if DonD is 50/50, i.e. no advantage in swapping - and I am coming to that conclusion - then why is it an advantage to swap in Monty's game? What's the element we're missing that divides the two games?
What if Noel had three boxes, holding £250k, £1k, and a goat. The contestant picks a box, then he, or she, or Noel, or blind chance, or the goat, opens either £1k or the goat box (one of which must be on the counter). Monty says swap. DonD says no difference. Why? That's the crux of the OP.
Edit: Aghhhh... I've just typed in "monty hall" "deal or no deal" into Google. I'm going to lie down in a dark corner somewhere...
The banker can and does influence the process. That is the main attraction of the game.
The offer is an extra box of known and variable value. Played to the very end the choice is one of two real boxes with two known amounts or a known value (the offer) between those two known amounts.
At all other times it is a choice of wether the odds about the values of the nest three boxes are worth taking.
I am sure the banker has a statistical program running on a PC that offers the upper and lower limits for the offer. Limits that statitically provide the best chance of the banker taking the player out for the lowest loss to the company averaged over the series of games.
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Softus. It is a simple game with a simple conclusion. I've proven that beyond doubt with the apple scenario. Why are you attempting to read into it some element that isn't there? If you know anything about statistics from your 'brilliant' education you should see quite clearly that you are attempting to fit three-cornered logic into a two cornered problem.
You know I'm right and it pains you to acknowledge that - but acknowledge it you will sooner or later. (probably later
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