If it helps the stats, after my whining about the $50, I ultimately chose that option in the poll as a way of saying, “I’d only ever want to go for the minimum,” - in an effort to not fight the hypothetical.
Poker players understand probability and for the most part are not risk averse (you can’t be a good gambler if you are excessively risk averse).
You probably will win, but, still 13% of the time you would be out $5K. Is that within your risk tolerance? If so, at what point would it not be worth it to you?
So, in essence, the question becomes would you spend $50 for a game you will win 2% of the time, or $5000 for a game you will win 87% of the time. Your preference seems to be the latter. My preference is (slightly) the former. I can explain to my family losing $50. Heck, I don’t think I would even need to explain it, as it wouldn’t be noticed. But that slightly better than 1 in 8 chance that we end up poorer $5K might be a little more difficult. I think my wife would understand it fine why I made the bet, but, still, the realistic possibility that I might lose would probably prevent me from making it (which is why I’m not a regular gambler.)
I agree. This is the point I was trying to make but you’ve made it more clearly.
Take away the amounts. Present it as a game where you have forty-nine chances of losing and one chance of winning. Do you play? Presented that way, the answer is obviously no.
An economist would argue that the game is balanced if the winning reward is fifty times better than the losing penalty. But even economists know that isn’t true; they know that the value of money doesn’t scale linearly. Fifty thousand dollars is not the same amount of money to Warren Buffet that it is to me.
See below. Dupe.
It’s not obviously no. With no stakes involved, of course I’d play it. Why not? I do so when I play games like some versions of solitaire where I’m lucky if I win once every 50 times.
Really? I mean, good lord. Median household wealth in the US is $80,000: we’re talking about increasing your household’s wealth by roughly 60%. That’s going to be life-changing for yer median household, whereas the loss of $50 is going to be a week’s worth of restaurant bills. Eat at home for two weeks to cover your loss, vs. massively increasing your household’s net worth for a win; you’re saying the latter is less than fifty times the former?
That said, I think it’s strange to characterize declining to take the bet as “extreme risk aversion.” Answers that are very common are, by nature, not extreme answers. It may be that walruses have a higher tolerance for risk than other folks :).
Heh. Fair point. Not as high as poker players, apparently.
Perhaps severe risk aversion? As you point out, the risk is relatively small. Most people can in fact absorb the $50. Being unwilling to risk it when the average reward so outweighs the cost suggests a very high level of risk aversion.
Perhaps it’s not extreme in the sense that it’s an outlier. But it’s extreme in the sense that it is very far from optimal.
The calculus is different for people who really can’t afford to lose the $50. If being $50 short this month means you can’t buy your kids food, or can’t afford the bus to get to work, then it makes sense to be unwilling to risk that.
Several people have claimed that it’s rational not to make this bet because money doesn’t have linear utility. I think that claim is weak. You are absolutely right that money doesn’t have linear utility, but on the scale we’re talking about, I don’t think that explains the behavior.
It makes sense that the average person values, say, $10 million less than twice as much as $5 million, and $5 million less than twice as much as $2 million. Because all those amounts reach the “lifechanging” threshold. If you win enough money that you don’t have to work any more, winning more than that isn’t as important.
But, for most people $50k is not some pie-in-the-sky amount. It’s a large chunk of money on a scale that they deal with regularly in their lives. It’s a year’s income (give or take a factor of 2-3) for a whole lot of households.
Imagine someone who makes $40k a year getting a 20% raise. Are they going to think “That’s nice, I suppose, but the marginal utility of that extra $10k a year isn’t really that much”, or are they going to be ecstatic? My money is on the latter, which is not consistent with the claim that it’s rational to discount the value of this bet by a factor of 20 because of the declining marginal utility of money. $50k is worth a lot to 99+% of people.
utility($50k) / 50 should be worth a lot more than utility($50).
So, then. The fifty dollar bet?
(also: reported)
I just picked $5k at random. If I invest, say $20k, it is a near certainty that I will win the $50k. I mean, even if you didn’t have $20k, it would be worth it to take a cash advance on a credit card for that deal.
I think that is when EV calculations work: when I can repeat it enough times to be substantially certain to reap the EV. If we are talking about only ONE SINGLE PLAY, I pay $50 for a 1 in 50 chance of winning $50k, I would rather keep my $50. Why? Because 49/50 times I will simply be out $50 and be unhappy, even if it won’t bankrupt me.
As a poster upthread stated, the EV of a game of russian roulette is a serious wounding, even though that particular outcome will never happen in any game.
While I know the financially logical thing to do is to take the bet at any listed level, I went with $250 because I think that’s the highest amount I could lose without fretting about the possibility of my wife scolding me. Not all value is measured in dollars and formulae.
So, walk me through this process, because at each step, you have to make the same decision, to wager $50. And your odds of future success don’t get any better just because you’ve lost in the past. Thinking otherwise is the gambler’s fallacy.
You bet the first time, and very likely lose. You’re down $50. Then you bet again. You’re down another $50. Then you do it again, and so on.
Now imagine you’re down $1000. Still gonna make the next $50 bet? On average you have to make this bet 30+ times before you get to 50/50. Gonna keep going when you’re down $3000? Down $10000? You’re no more likely to win this time.
If so, why wouldn’t you make that bet when you weren’t down a bunch of money?
Is it just the sunk cost fallacy?
I’m not convinced that “dead” plus “not-dead” average to “seriously wounded” in the same way that monetary values average. Going back to the marginal utility argument, the utility value of being dead is very very negative. Far more negative than, say, 6 times being wounded.
Wrong. The more times you play, the higher the probability that your total winnings will exceed your total bets (as long as your individual bets do not exceed $1000).
But, as I have pointed out, you don’t get to play a statistical simulation. You get to make bets one at a time, in chronological order. And the outcome of previous bets doesn’t change the probability of future success.
So, if you’re not willing to make the first bet, why are you willing to make additional ones?
I think it very much is that a 1 in 50 chance at winning seems really low. It almost certainly won’t pay off. And so it doesn’t matter how big the winning pot is to most people, because they’ve already decided it’s not going to happen. So they’re only willing to bet an amount they won’t miss, which is under $50. The exact amount of the bet vs the amount of the reward and the probability of winning doesn’t matter, because all their mind sees is: small, large, and small.
It sort of reminds me of a time I went with some buddies to the Casino, for the seafood buffet. But of course we have to gamble too. And my buddy’s game was Keno, because it was mostly just sitting around watching numbers, shooting the shit, and drinking. Didn’t require any thought, it was just a way to pass the time.
Anyway, the point of Keno is that you pick 5 numbers from 1 to 100, and the house picks some random numbers, and if your random numbers match the house numbers you win. So just to be an asshole, I picked 1, 2, 3, 4, and 5. And my buddy was pissed at me, because obviously that combination was not going to win compared to a more likely pick like 37, 42, 19, 75, and 22. That set of seemingly random numbers seemed much more likely to randomly come up than my highly ordered set.
Except of course that they really were picking random numbers, and so every set of five numbers was exactly as likely to win as any other. My pick was just as good as any other…but it didn’t SEEM that way to my innumerate buddy.
So the point is, $50,000 just means “a lot”. 1 in 50 chance just means “not going to happen”. So putting any real money on that bet is just a waste, because it’s not going to happen, so you should only bet a really really small amount of money.
And I also suspect that there’s quite a lot of fighting the hypothetical, because our intuitions of how things work are created in an environment where people really do try to cheat other people. And that’s why I wonder if the game were presented as part of a game show it would have been more palatable. Some guy at a bar asks you this, and you know it’s got to be a scam, because of course it is.
So instead of a guy at a bar, pretend it’s Pat Sajak.
This has nothing to do with the probability of winning or losing.
No one here is saying if you lose, you’ll be more likely to win next time. Everyone here knows the odds of winning an individual bet are still 1 in 50.
I voted 0, for the record.
This is not true, as you yourself point out later.
That is correct. It’s not fighting the hypothetical to calculate the EV of a transaction, determine that anyone offering that deal will bankrupt themselves long-term, and decide not to partake in it for that reason alone. I’d call making this calculation the opposite of being innumerate.
It’s also not risk aversion or being too poor to gamble, as I’m willing to bet $50 in a casino with far worse odds. The difference is that I can see their angle and I understand why they are offering me the bet. In this case, I can’t see why even a Bill Gates type would bother to do it, and that leads to assuming bad faith.
Yes, I did later consider the fact that people are fighting the hypothetical.
I guess it depends on why you’re not participating? If you feel it’s not morally right to take someone’s money on a bad bet they’re offering, then I agree it’s not fighting the hypothetical.
If you’re saying that, because the EV is positive for you, and it’s negative for the person offering it, then they’re probably not really going to pay out, then that’s exactly fighting the hypothetical.
See the reference to game shows and scientific studies. There are cases where deep-pocketed parties will offer games not in their favor and still pay out.
See, I don’t at all see a 2% chance as being something crazy low, especially when it comes the possibility of winning $50K. 2% is unlikely, but not crazily so. It wouldn’t be until about 1-in-1000 that I would start getting concerned about the odds of winning being too low, but even then it would depend on what the reward is. Even though I am generally risk averse, a 1-in-50 shot of winning $50K is hard to come by and absolutely worth the shot, especially for $50. That’s a no-brainer to me.