On 12/16/09 11:08, Le_Forgeron wrote:
> For optimising my happiness' function, I will take the first box and say
> good bye, not wanting to know which case I was playing.
>
> Playing otherwise might diminish my happiness' value, and that's not
> something I would risk.
>
> That's not rational, but I'm human, I have the right to make error (as

	Nope - that's rational.

	The economists use "rational" in terms of choosing the path that gives 
you the most money. Unfortunately, too many people tend to use the same 
definition outside the sphere of economics.


-- 
Would the capacity of a Palaeozoic Hard Dive be measured in Trilobites?

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"Le_Forgeron" <jgr### [at] freefr> wrote in message
news:4b2913f1$1@news.povray.org...

> That's not rational, but I'm human, I have the right to make error (as
> in 'to err is human') and to seek happiness rather than optimal
> solution.

For some, happiness *is* finding the solution.

> P.S.: tuning the numbers, what if the amount ratio instead of 1:2 is 2:3 ?
> Found 300? under your choice, swap for other ? (450? or 200?)
>

>
> and what about 1:100 ? (100, 1 or 10000)

You are onto something here.

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somebody wrote:
> You are on a game show. The host says he has hidden money under two cups,
> one amount being double the other one. You pick one at random, he turns it
> over, it's $100. He gives you a second chance (that he would do so was
> determined before the game and not dependent on which cup you'd turn over):
> You can switch, or take the $100.
> 
> You figure: If I switch, I will either get $50 or $200 with equal
> probability. Expected return is thus $50*1/2 + $200*1/2 = $125, which is
> larger than the $100 I'd spend to "play" this second game. Looks like a good
> deal. Is it?
> 
> 

There are actually four cups. Two cups in the $300 total universe and 
two cups in the $150 total universe. No amount of switching will change 
the universe in which you exist and that universe was selected before 
you chose a $100 cup.

  -Shay

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Shay wrote:

> 
> There are actually four cups. Two cups in the $300 total universe and 
> two cups in the $150 total universe. No amount of switching will change 
> the universe in which you exist and that universe was selected before 
> you chose a $100 cup.
> 
>  -Shay

Yes! You've got it. :-)

-- 

Best Regards,
	Stephen

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Stephen wrote:
> Shay wrote:
> 
>>
>> There are actually four cups. Two cups in the $300 total universe and 
>> two cups in the $150 total universe. No amount of switching will 
>> change the universe in which you exist and that universe was selected 
>> before you chose a $100 cup.
>>
>>  -Shay
> 
> Yes! You've got it. :-)
> 

Here's how the math really works out, as well as a better explanation of 
where Andrew got it wrong.

Andrew counted the built-in profit of the system as "winnings" he showed 
for switching.

Four cups, right?
{$50 | $100} ------ {$100 - $200}

I'll change the scenario just a bit to make it clearer. Contestant is 
allowed to select one set of two cups ($50-$100 and $100-200) and to 
then select one of the two cups from his selected set. His expectation 
from this game? ($50 + $100 + $100 + $200) / 4 = $112.50. That's what 
he's being *given* for playing the game, so that amount must be 
subtracted from his winnings to reveal the profits of his strategy.

So, subtract $112.50 from each of the four cups to get
{-$62.50 | -$12.50} ------ {-$12.50 | $87.5}

Now, back to Andrew's premise. The contestant turns over a cup to find 
-$12.50. Should he switch?
Possibility 1: He's in the low set[1] - expectation = -$37.50
Possibility 2: He's in the high set - expectation = +$37.50
A 50% probability either way.

That's the honest math.

  -Shay

[1] Actually, not *the* but *a* high set. There are two ways that could 
go, but it doesn't change the problem.

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somebody wrote:
> You are on a game show. The host says he has hidden money under two cups,
> one amount being double the other one. You pick one at random, he turns it
> over, it's $100. He gives you a second chance (that he would do so was
> determined before the game and not dependent on which cup you'd turn over):
> You can switch, or take the $100.
> 
> You figure: If I switch, I will either get $50 or $200 with equal
> probability. Expected return is thus $50*1/2 + $200*1/2 = $125, which is
> larger than the $100 I'd spend to "play" this second game. Looks like a good
> deal. Is it?

Yes.

Regards,
John

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