Wouw... Thank you for this charitable interpretation. I'll try to respond.
(1) You don't have to construe the gamble as some sort of coin flips. It could also be something like "the weather in Santa Clara, California in 20 September 2012 will be sunny" - i.e. a singular non-repeating event, in which case having 100 hundred people (as confused as me) will not help you.
(2) I've specifically said that if you have enough trials to converge to the expectation (i.e. the point about Weak Law of Large Numbers), then the point I'm making doesn't hold.
(3) Besides, suppose you have a gamble Z with negative expectation with probability of a positive outcome 1-x, for a very small x. I claim that for small enough x, every one should take Z - despite the negative expectation.
What's your x, sunshine? If 0.01 isn't small enough, pick a suitably small x. Nick Bostrom in Pascal's mugging picks 1 over quadrillion to demonstrate a very similar point. I picked 0.01 since I thought concrete values would demonstrate the point more clearly - I feel like they've been more confusing.
In fact, people take such gambles (with negative expectation but with high probability of winning) everyday.
They fly on airplanes and drive to work.
(4) Besides, even if we construe the gamble being repeated like a coin toss, I feel like with 0.99^99 = 0.37, you stand to lose 10M with probability 0.37 . I don't know about you but I wouldn't risk 10M with those kinds of odds. It helps to be precise when you can and not to go with a heuristic like "on average there should be 1 W in every 100 trial"...
(1) You don't have to construe the gamble as some sort of coin flips. It could also be something like "the weather in Santa Clara, California in 20 September 2012 will be sunny" - i.e. a singular non-repeating event, in which case having 100 hundred people (as confused as me) will not help you.
A coin flip is not fundamentally a less singular non-repeating event than the weather at a specific location and specific time. There are no true repeating events on a macro scale if you specify location and time. The relevant difference is how confident...
Two or three months ago, my trip to Las Vegas made me ponder the following: If all gambles in the casinos have negative expected values, why do people still engage in gambling - especially my friends fairly well-versed in probability/statistics?
Suffice it to say, I still have not answered that question.
On the other hand, this did lead me to ponder more about whether rational behavior always involves making choices with the highest expected (or positive) value - call this Rationality-Expectation (R-E) hypothesis.
Here I'd like to offer some counterexamples that show R-E is clearly false, to me at least. (In hindsight, these look fairly trivial but some commentators on this site speak as if maximizing expectation is somehow constitutive of rational decision making - as I used to. So, it may be interesting for those people at the very least.)
A is a gamble that shows that choices with negative expectation can sometimes lead to net pay off.
B is a gamble that shows that choices with positive expectation can sometimes lead to net costs.
As I'm sure you've all noticed, expectation is only meaningful in decision-making when the number of trials in question can be large (or more precisely, large enough relative to the variance of the random variable in question). This, I think, in essence is another way of looking at Weak Law of Large Numbers.
In general, most (all? few?) statistical concepts make sense only when we have trials numerous enough relative to the variance of the quantities in question.
This makes me ponder a deeper question, nonetheless.
Does it make sense to speak of probabilities only when you have numerous enough trials? Can we speak of probabilities for singular, non-repeating events?