At such an extreme example, of course, one can argue whether the bet has a positive EV at all, since we’re getting to the point that the additional money has no utility. For an ordinary schmoe like me, the utility of the first $100 million is enormous, while the next $300 million has very little measurable marginal utility.
Another example that comes up sometimes: You’ll occasionally hear of a class of students having a mock-stock exchange challenge. Everyone is given $1000 or whatever of virtual seed money, and have to pick stocks, and after some period of time, you see how much everyone has left. The catch is that, often, it’s structured as one student being the winner, with everyone else getting nothing. In a case like that, you absolutely need to take high-risk, high-reward bets, even if they’re negative EV, because the winner is going to be someone who made a high-risk bet and won.
No it isn’t. Losing $1 in a bet is completely inconsequential for most people, but losing $50 would have real consequences for many.
Nearly every point you’ve attempted to make throughout this entire thread has been completely off-base.
It’s not surprising to me at all, insisting that people’s real-world decision making is based on ‘very rudimentary heuristics’ because they’re averse to making the ‘right’ decision in a completely impossible hypothetical situation is not reasonable. People develop their decision-making apparatus in the real world, and in the real world no one sensible would take a bet structured like the one in the OP because it’s almost certainly a scam; there’s no reasonable motive for the ‘house’ to offer it. Also people’s cut-offs for how much they’re comfortable betting with a high-chance of loss are generally based on likely real-world bets, and may not give the ‘correct’ answer on an impossibly good bet. If someone’s decision making is good in the real world but bad in completely unrealistic hypotheticals, they’ll be better off in their real lives, even if they’d be poorer in the world of spherical cows and frictionless roads.
Also, the heuristic of “If a bet is +EV of course I take it” is a pretty rudimentary one -
and self-destructive. If the people who said they’d take the $900 version of the original bet without a second thought each have a $200,000 bankroll for betting, half of them will end up broke by applying the heuristic of ‘always take the +EV bet’. Any non-rudimentary evaluation of +EV has to take the risk of ruin into account, and it doesn’t look like a lot of the ‘of course I’d take it at a high amount, duh’ respondents did - because they need to have much more than the $50,000 prize available to have a decent chance of not going broke chasing the payout.
That’s true. But it seems like some people wouldn’t bet $50 even if the chances of winning at least $50 were 99.9%. That’s the strange thing to me.
Hold up: there’s a difference between EV and the chances of winning. Try a different bet:
Same deck of 50 cards, same gameshow. Pay $50, and if you draw anything except the Ace of Diamonds, you win $1000.
Does anyone change their answer?
With a 98% chance of winning, I suspect a lot of folks would change their answer.
If by ‘a financial perspective’ you mean ‘purely in terms of dollar figures’, sure. But if you mean real-life finances, it depends highly on what the actual cost to the person is of the $50 loss they take 98% of the time. If the loss means they have to cancel a date and look dumb, that may well outweigh the small chance of a financial windfall. Note on ‘looking dumb’: nothing in the OP gives you any ability to persuade people that the bet was good; a real person is more likely to think you fell for a scam than had a magical ‘can’t be a scam’ bet. And as far as the ‘yeah, but it’s a +1000 EV goes, how can a date be worth that much?’, bear in mind that $1000 is a 3-year subscription to match or eharmony, and some people really only get a handful of promising dates in that time.
Sure, the initial statement implied something like “if you’re not in extreme poverty and don’t take the bet at $50, you’re clearly innumerate or stupidly risk averse”. By changing it to acknowledge that someone can notice a $50 loss without being in ‘extreme poverty’, and accepting that the risk aversion might be reasonable, you’re no longer dismissing everyone who disagrees with your conclusion as what amounts to ‘stupid or super poor’.
I pointed that out when I discussed the quadrouple or nothing bet earlier 
But when you’re going into that kind of analysis, I think you’re leaving behind the standard definition of EV, which (AFAIR) is purely numeric. You’re still in a similar conceptual area (evaluating the value of winning vs cost of losing), but I don’t think you’re within what’s generally meant by EV.
I hope people change their answer
Perhaps another poll could be “How high of a chance of winning would you need to wager $50 to win $50,000?”
In theory, yes. The problem is that there may be hidden costs for that bet, depending on how much money you actually have. Hidden costs can bite you in the ass, if you don’t have a big enough bank roll.
Another flaw in reasoning is that you cannot compare the value of the bet against the value of not betting. You have to compare it to the value of the best thing you can do with the money other than the bet. For example, instead of betting the $900.00, you could buy a CD with a guaranteed interest rate. Or maybe you can pay your rent or your credit card bill and avoid a late fee.
I had this friend – he was a math major, so it was shocking to me that he made this kind of error in reasoning. He bragged to me that he made a thousand dollars in the stock market in the past year. I asked him how much he had invested, and he didn’t understand why that would matter – turned out it was a pretty significant chunk of change. And after he told me, I had to explain to him that, in effect, he lost money, simply because he would have made more with something less risky. This is a math major, and he didn’t quite understand that comparing investing to doing nothing with the money was not how you evaluate the value of an investment.
Well, no one bats 1.000, I guess 