noy2222
Joined: Nov 18, 2009
• Posts: 113
January 27th, 2014 at 1:26:42 PM permalink
Say you were offered to take part in a game:
In front of you is a bucket that contains 999 small black balls and a single white ball and a shipping container filled with 1 billion dollars (because as Hollywood doesn't tell you, a lot of money takes A LOT of space).
If you can successfully pick out the white ball from the bucket (without looking, of course), all that money is yours.
To make it easier, you can remove however many black balls from the bucket, but for every ball you remove, a million is taken out of the container, meaning you can remove all 999 balls and have guaranteed million.
What would you do?
thecesspit
Joined: Apr 19, 2010
• Posts: 5936
January 27th, 2014 at 1:28:00 PM permalink
You can send me the Million, please.

No variance, same expected value.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
KB1
Joined: Jul 9, 2013
• Posts: 128
January 27th, 2014 at 1:40:48 PM permalink
Quote: noy2222

Say you were offered to take part in a game:
In front of you is a bucket that contains 999 small black balls and a single white ball and a shipping container filled with 1 billion dollars (because as Hollywood doesn't tell you, a lot of money takes A LOT of space).
If you can successfully pick out the white ball from the bucket (without looking, of course), all that money is yours.
To make it easier, you can remove however many black balls from the bucket, but for every ball you remove, a million is taken out of the container, meaning you can remove all 999 balls and have guaranteed million.
What would you do?

When you ask "Would you gamble with a huge amount of money?" you confuse me.This implies that I own a huge amount of money that I can willfully gamble with.
Did you mean to say gamble for a huge amount of money?
Sure anybody would play that freeroll.
What does it cost me to play the game?
Sorry to say this noy2222 but what a horrible post.

KB1
Puckerbutt
Joined: Sep 24, 2013
• Posts: 173
January 27th, 2014 at 1:43:01 PM permalink
Quote: noy2222

In front of you is a bucket that contains 999 small black balls and a single white ball..........you can remove all 999 balls and have guaranteed million.

How would the million be "guaranteed"? There are 1000 balls in the bucket. It would be possible for the white ball to remain after picking out 999.
If'n I'd a knowed you wanted to have went with me - I'd a seen that you got to get to go.
Maverick17
Joined: Mar 4, 2011
• Posts: 323
January 27th, 2014 at 2:05:06 PM permalink
Quote: Puckerbutt

How would the million be "guaranteed"? There are 1000 balls in the bucket. It would be possible for the white ball to remain after picking out 999.

While it wasn't completely clear, I belive it would cost \$1m per ball, BEFORE you actually make your draw.

So if you paid \$999m there would only be one ball left in the bucket, and you would be forced to pick the white one, and win the remaining \$1m.

The real question is why the ball gotta be white?
Statistics don't lie, they deceive.
noy2222
Joined: Nov 18, 2009
• Posts: 113
January 27th, 2014 at 2:08:53 PM permalink
Because 999 fuchsia balls and 1 vermillion ball might be confusing.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
January 27th, 2014 at 2:16:51 PM permalink
Quote: thecesspit

You can send me the Million, please.

No variance, same expected value.

Ditto. Plus, the marginal utility of the first \$1M in winnings is (to me) far, far greater than the marginal utility of subsequent millions of dollars. I hope that will change at some point in my life, but right now I don't have 8 figures in the bank so I can't afford to be passing up a million risk-free dollars.

As a follow-on question, suppose there were only two options: draw at 1/1000 for a billion dollars, or take a guaranteed X, where X <= one million dollars. How low would X have to be in order for you to draw for the billion? Ex: If you were offered \$800,000 risk-free, or a 1/1000 chance of \$1,000,000,000 (with \$0 otherwise) which would you choose? (I'd choose the \$800,000).

To the OP: look at prospect theory for more on these sorts of questions.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
noy2222
Joined: Nov 18, 2009
• Posts: 113
January 27th, 2014 at 2:27:00 PM permalink
In my mind, a 1/1000 chance to win a billion just seems like a waste. Sure, I'd be excited to win, but prepared to lose and I'd kick myself for giving up any significant amount of money for it.
I imagine a year or two salary is a good trade off not to play.
ChampagneFireball
Joined: May 2, 2010
• Posts: 118
January 27th, 2014 at 2:37:59 PM permalink
Quote: MathExtremist

As a follow-on question, suppose there were only two options: draw at 1/1000 for a billion dollars, or take a guaranteed X, where X <= one million dollars. How low would X have to be in order for you to draw for the billion? Ex: If you were offered \$800,000 risk-free, or a 1/1000 chance of \$1,000,000,000 (with \$0 otherwise) which would you choose? (I'd choose the \$800,000).

Looking at the utility of money being the log of your net worth, a person with a net worth of \$100k should take \$925 over a 1/1000 chance of \$1billion. And someone with a net worth of \$1 million should take \$6,933. I think my answer is way above my net worth, but way below \$800,000.

I'd probably take \$100,000, but first I'd try to sell my position to someone else. What would you pay for a 1/1000 chance to win \$1billion.
s2dbaker
Joined: Jun 10, 2010