For me, the choice is all about what tangible thing I could buy with the lower value. If 600 pays my rent, I’m taking 600. I’m fortunate enough to be past that point in my life but if I wasn’t I’d certainly take it. With 6000 I could buy a hydraulic dump trailer. It’s something I’ve wanted for a while.
I can dream about the infinite things I may want, but tangible things are better than dreams.
Once again, you’re missing the point of the question(s). Obviously if you have enough trails you take the better odds. That’s not particularly interesting. What’s interesting (to me at least) is at what point of reward you switch your strategy (which is what is being shown in the successive polls for different amounts.)
And perhaps among those who understand odds, they tend to separate those who understand that utility functions are non-linear from those who don’t.
Yeah, even tho the odds are good, I’d just take the $6M. I dont need $20M.
I could really use $200K, so i’d flip the coin.
I feel I would generally choose the smaller but sure amount of money. Either amount would be a windfall for me and it’s not like I have any specific plans for the money that could be accomplished with the large amount but not the small one.
To me, it’s not a choice between some free money and three times as much free money. It’s a choice between a 50/50 chance of free money and a guaranteed free money. In my mind, the odds factor outweighs the amount factor.
That’s interesting. It would never have occurred to me to think of it that way, but I can see how that’s perfectly reasonable. If I understand correctly, you’re saying that one unexpected windfall event in which you end up getting some free money would makes you feel good; and that 1 dose of feelgood factor derives from 1 windfall event occurring, it’s not proportional to the quantity of money in the event.
Yeah, expected return has no value to me on a single coin flip,. It’s just whether or not the amount I’d get is significant enough that I’m willing to take a 50% chance on losing it.
Six dollars is no big deal. I might barely be willing to lose $60. But $600 is enough that I’d keep it, and thus every factor beyond that.
What I would find interesting is taking the lowest amount someone would risk, and seeing how high the second number has to be before they’d no longer see the risk as worth it. For me, it would need to be at least double at 60, but I’d risk $6 even to try and win $7.
Yes, I realise that the offer of more money is a jolly good bet … but I like certainty too.
Here in the UK we have a popular horse race ‘The Derby’.
My office held an annual sweepstake on it @ £5 a go, winner takes all. There were 35 of us, so £175 on offer.
In 1981 I drew the red-hot favourite Shergar. 
Coming into the finishing straight, Shergar was over 10 lengths ahead - a truly massive margin. 
At that point I sold my winning ticket for £100 - just in case Shergar tripped. 
And one reason that I would take the bet, despite being risk-averse, is that, over the course of my lifetime, I will have many opportunities to take positive-expectation bets. And the sum total of all of those positive-expectation bets is much greater than $600 or $2000, so I’m not really making decisions about this one specific event; I’m making decisions about my general strategy for all of the many events like this. And if I always take the bet, the amount I end up with, net, over my entire lifespan will be very close to the expected value.
At $6 million vs. $20 million, though, that’s no longer true. Either way, that’s probably more money than I’ll ever have: It dwarfs all of the other financial decisions I will ever make. I will certainly not end up with anything close to the expected value on that bet: I’ll either get much less than the expected value, or much more. And so now, risk aversion says to keep the $6 million.
Yet another factor is the fighting-the-hypothetical factor: In the original situation, I believe it’s on the up-and-up. A game show like that is plausible, because they’ll get much more value worth of entertainment (as measured by the ads that they can sell) from filming me than the cost to them of the prizes. And it’s not likely to be a scam, because the cost to a scammer to set this up and make it believable (with all of the equipment they’d need for a film crew and so on) would be more than they could hope to get out of their marks. But as you increase the dollar amounts, the plausibility of a game show decreases, and the plausibility of being a scam increases.
On the topic raised by @peccavi & @Chronos in their back and forth …
There is a fundamental feature of “expected value” that IMO is often ignored.
“Expected value” absolutely does play in the “long run”. There’s no mathematically literate debate there. And can be legitimately spread across lots of unrelated financial decisions as @Chronos says just above. It doesn’t absolutely need to be just repeated trials of the exact same game.
But … expected value does not really completely play in the absence of a "long run ". And most significantly, the definition of “long run” depends crucially on the odds of winning.
For coin flips, playing 10 times is quite likely to come out near 50/50, the true long-run odds.
OTOH …
For, e.g., 10 Powerball tickets, the outcome is quite likely to still be zero. 10 tickets isn’t enough to “activate the long run effect” in Powerball, while it is enough to (begin to) activate the effect in coin flipping.
The EV math remains the same in either case. But a practical gambler is more interested in the shape of the variation. e.g. Over the 10 trials, what are the odds of the various collective outcomes? Given you know you’ll get 10 trials, the shape of that curve is what you want to pay attention to.
As to Powerball under current rules, the draw is done twice weekly. A person who lives to age 100 could participate in 52 * 2 * 100 ~= 10K drawings. Even buying 1,000 tickets per drawing = $4K per week, you're only buying 10M tickets over a lifetime. As against a roughly 300M to 1 chance of hitting the jackpot.
Conclusion: Humans, except very wealthy gambling addicted ones, simply don’t live long enough to encounter the “long run” as it applies to something as unlikely as the Powerball jackpot. Therefore EV analysis is not the correct way to evaluate the financial wisdom of playing Powerball.
Late add:
Bottom line: And of course this same logic can be applied to other less lopsided games. Including the ones proposed by the OP’s various posts.
I really hope you’re not saying that anyone who understands gambling and odds will always, necessarily take the choice with the highest monetary expected value. Or that they will necessarily make the same choice for a single trial that they would given many repeated trials.
If real life was a series of bets with well defined odds, I might say that. But in life, the bets are complex and the odds uncertain, so no, I’m not advocating this across a lifetime, though I feel that risk aversion can be as deleterious over a lifetime as over-confident betting.
The truth is, in my scenarios while I would take the 10 flips without hesitation for all values, at 5 flips I’d hesitate and think really hard at the high end even though the odds of walking away with nothing are only a few percent.
As Colibri pointed out, it’s not that people don’t understand the odds - everyone here can do math. It’s that $600 is money you can afford to walk away from, but $6 million isn’t.
Yes. I’ll might buy a lottery ticket for $1 at a million to one odds since a dollar isn’t a significant loss. But I wouldn’t buy a lottery ticket for a million dollars even if the odds were double or nothing. It has nothing to do with the odds; it’s about how much I am willing to lose.
You have to know when to fold 'em.
I’d probably take the chance, but I’d feel guilty about it. I believe that encouraging gambling is immoral, particularly when you are being paid to do so, and if I won, it’s not something I’d be proud of.
At $6k I lean towards the coin flip and at $60k I lean towards the guaranteed.
peccavi, if the bet was a guaranteed $10M vs a 50% chance at $20,000,001 are you claiming that all mathematically literate people flip the coin?
One thing a mathematically literate person might ask is how much those amounts would be after taxes.
Richard Thaler (Nobel Prize winner) did a lot of work in this area. He virtually invented behavioral economics. In short, the pain of losing $x is worse than the pleasure of gaining $x. When people have something in hand, they tend to suddenly value to it more just because they have it.