Gamble more acceptable?60:40 chance of gaining or losing $10000 or 40:60 chance of gaining or losing $1?Why?

Question

Gamble more acceptable?60:40 chance of gaining or losing $10000 or 40:60 chance of gaining or losing $1?Why?

Answer 1

Using a blind expected value approach would tell you the first gamble is preferrable, as it has an expected gain of $2000 while the second has an expected loss of 20 cents.  And if you were able to play 1000 times I'd certainly take the first one!

But assuming you only get to play once I'd take the second gamble.  Why?  Because what I value isn't the money in of itself; it's what I can buy with that money, and the first dollars you have are spent on more necessary items, and vice versa.  If I gain 10 grand, I may spend it on a nice vacation; if I lose the same amount, well, there goes a good chunk of my retirement.  60 chance of gaining a nice vacation vs. 40 chance of making my retirement less cozy, and suddenly it doesn't look like such a gain anymore.

Answer 2

If you played the first game 100 times, on average you are going to win 60% of the time and lose 40% of the time.  So you'd win $600,000 and lose $400,000.  So your net gain would be $200,000.

On the other game it is the other way around, and you would win $40 and lose $60 for a net loss of $20.

So provided you had enough money to cover any initial swings (variance) then the first game is better.  Of course if you could only afford to play it once (say you only had $10,000) then it might not be such a good thing because it could wipe out your bank roll in one go.

But provided you could afford it, and afford to get 'unlucky' a few times near the start, the more expensive game is long term profitable.

Answer 3

Depends on how much money you can afford to lose.