1. Money has a declining marginal utility. Winning that $130 isn't nearly as positive as losing it would have been negative. The author neglects to mention what happens the other 53% of the time when someone with mounting bills loses the last money they had. Debt spiral is usually the result. Even if the odds were 50/50, or in fact even if they were slightly favorable but it were a one-time deal, it would be better not to gamble. You should really only gamble in situations where the expectation is more than enough to offset the declining marginal utility, or is repeatable enough to accomplish that.

#2. If someone has the discipline to go into a casino, double their money, and leave without gambling further, then they probably had the discipline to avoid this situation in the first place. Casinos make billions of dollars because most people can't do this.

#3. It's fairly rare in the real world that there isn't some option better than gambling. Even a payday loan place probably gives you a higher EV than a roulette wheel. Borrowing from a credit card probably does as well. Do either to bridge the gap while looking for a second job. Also driving with a suspended license is an option.

#3.5 (bonus reason): You're much better off making a don't pass bet at a craps table while you're there. I think that's the best bet you'll find in a casino that doesn't require skill. (There are better, some that are even positive expectation, but I'm assuming our person isn't a professional video poker player.)

Granted it's an oversimplification, because that $130 could be used for something, and yes, #2 and #3 are probably better. (Though with fees and multiple rollovers, the payday loan could be ouchy).

Still - declining marginal utility is not always the case. There are plenty of situations like this one, (especially for a corporation) where having half of the money necessary gets you nothing.

Of course, there are also almost always better ways of securing that financing, unless you're the only person that perceives the odds that way.

Here's an interesting example in my life - if I get a windfall, the marginal value starts off low (I don't change my lifestyle), rises somewhat (it becomes enough for me to take a breather from my job and spend more time working on my startup), and eventually declines as I no longer need more to work.

Or in other words, I can't retire because I got $10k. Not useful. But if I can make that $50k, I can survive for a year+ and try to launch a company - that's useful. The value of that $50k is more than 5 times as much as the $10k. (Though the $10k does get me that much closer to having enough...)

In the real world, where you're never faced with two simple options like retire on $10k or start a business for $50k, money's marginal utility is effectively always diminishing.

I question this because you're already in the red: do nothing, and you'll be left with $130 in the bank but $250+$100=$350 in liabilities that eventually have to be paid, so you're at -$220 by default (even if you've still got $130 in your pocket, that's not really your money; as I commented elsewhere, I probably should have set up the example so that Mary had already purchased food for the week, to avoid questions of starvation).

When you're starting in negative territory the usual rules about marginal utility of money don't necessarily apply, I'd actually argue that there might be more utility gained when you go from -$50 to +$50 than there is going from -$150 to -$50 because of the debt spiral effects that you mention.

As for your other points, I agree, there are issues with the false dichotomy that I've set up, ones that I expected to be called out on. Perhaps I should have worked out a better example where there were fewer options available, c'est la vie.

Even in the face of marginal utility differences, though, if you were to accept (unreasonably, of course; thought experiment disclaimer goes here) that you only had the two options given (do nothing and owe another $100 to the state, or take the bet, coming out $130 ahead or $230 behind), would you really suggest that doing nothing is the better option? How good would the odds need to be (and how little variance) for you to take the bet, if so?

If I laid out this payoff structure without placing it in a real world context where there are many other obvious potential solutions, I think you'd probably argue in favor of taking the bet - the expected loss is so much lower that I think it's difficult to make a marginal utility argument against it. I suspect that what's really making you argue against it in this example is that there are so many better ways to deal with the situation in real life that it's hard to even imagine having to make a choice between the two alternatives on the table.

The most likely result of gambling is that they will still have to pay the BMV bill plus now have to recoup $130 (which is hard for them to come by) to pay other bills.

Tax brackets are another classic example. Sometimes you get much more by being paid a little less.

Edit: The tax thing was a brain glitch and not true IRL. Check Matt's comment below. There may be true life examples where you come out ahead but they are likely to be scholarships or insurance policies or something with similar hard cutoffs that form step functions.

Tax rates are marginal. So for instance if the tax rate was 20% up to $100k, then 30% afterward, you'd pay 20% on your first $100k, then 30% from $100,001 and up.

That introduces some distortions into house pricing, making it very difficult to sell a house in the £250,000 to £265,000 range - because you are competing with houses just under the threshold which work out significantly cheaper for the buyer. As someone selling a house which falls into that price range, you might be better off asking for slightly less from the sale (versus asking for just over the threshold and waiting much longer to find a buyer).

But the step function thing was the point, not the taxes. I'll put in an edit and get that last bit ignored.

(1) Be careful what you take as truth when young and don't rethink later.

You only pay the higher rate for income within that bracket.

Making an extra dollar pushing your taxable income to $34,001 as a single American in 2010 does not raise your Federal taxes from $5100.00 to $8500.25 by naïvely applying the higher rate — it actually raises your taxes by 25¢ from $4681.10 to $4681.35.

(I know it's a smaller house edge than roulette by some way, but not too familiar with craps)

Also some of the EV comes from blackjacks (typically paying 3:2) so there is some chance you'll end up with more money than you need. You could walk out with $325. Again since marginal utility is diminishing the extra risk is bad.

If she just gets socked with the fine and loses her license, she can still make other gambles that have a lot better expected value as overall utility, not just money. She can make the gamble of driving without a license, as the risk of being caught by the police is a lot less than losing everything by betting on black. She can use the $130 to buy a bicycle or a moped, and maybe that's enough transportation to get by for now. And so forth.

The author has a good point in that the expected value in a gamble is often a better choice than the status quo, but reducing everything to dollars and coming up with the conclusion that "if you're screwed, put everything on black," is a fallacy.

Yes, this is a very good point, perhaps the way I should have phrased the example was that she had $130 left in the bank after obtaining the necessities of life, to remove that concern. In that case, I think the logic goes through a bit better.

She can make the gamble of driving without a license, as the risk of being caught by the police is a lot less than losing everything by betting on black.

In my example, that's exactly what I did (I drove as little as possible, but on occasion I had no choice), and I did, in fact, get away with it long enough to get my license back (it's worth noting that had I not gotten away with it, getting my license back would have been a much more troublesome process). But be aware, I was pretty lucky - if your license is taken away, your plate will get flagged if the car is registered in your name, and you'll absolutely get pulled over if a police officer sees you driving and has nothing better to do. My girlfriend was pulled over several times while driving my car during that period, and then immediately let go when they realized it wasn't me behind the wheel.

reducing everything to dollars and coming up with the conclusion that "if you're screwed, put everything on black," is a fallacy

Indeed, it's not always the right solution - but it's also wrong to assume that just because the odds are against you in a bet, you shouldn't take the bet, if the other option is to do nothing, especially if doing nothing leaves you screwed anyways.

When I landed myself in this situation, that was exactly the problem: I felt like the Big Bad Court System would never cut a stupid kid like me any slack, and it just never occurred to me that I should talk to them and see what could be done about it. After trying unsuccessfully to deal reasonably with the DMV on the issue, I sort of assumed every aspect of the government was always out to screw me over in any way possible.

Live and learn, I suppose.

Of course, assuming any reasonable credit is available at all, and that the person is not in permanent deficit unable to eventually pay back a loan, would give rise to a dominant option C, where enough is borrowed to avoid the penalty. But maybe this same effect is what makes 'payday' loans at astronomical effective rates attractive to some people.

Is there some other 'guardian angel' business model possible from this effect -- protecting the liquidity-challenged from disproportionate late fees, via an automatic loan of just-enough to save the fee, splitting the savings with the affected person?

As in: seconds before BofA or some other institution is about to pillage someone for $30, the 'angel' swoops in with a just-in-time loan, charging the person (in fees and interest) any amount less than $30 -- and lower with more competition.

It's called a credit card or savings account.

If you have a credit card, you can't overdraw it. Or you can link your checking account to it, avoiding the "we're loaning you money even though you didn't ask for it" fee. Or you can have a savings account, and dip into that when your checking account runs out of money. Or you can just not run out of money.

I got hit with an overdraft fee back when I was in college even though I explicitly opted out. I didn't make that mistake again. I stopped using a debit card and started using a credit card again... and now I even get 1.5% cash back. (If this happened to me now, I would have just filed a complaint with the state's attorneys general office. Customer service doesn't want to help? Enjoy the fine and new regulations.)

The theory of the 'guardian angel' service is that it handles things even when you forget. It presupposes that there's some way to give the service total visibility into your imminent payment deadlines -- of course right now that doesn't exist, and the businesses that rely on late fees for their margin may not want it to.

But this might be an appropriate area for an industry consortium or even regulation to create a clearinghouse. If you're about to fine someone $X for an amount due up to $Y, you have to broadcast it on some confidential national clearinghouse an hour before assessment, allowing a contracted representative of the target to settle it on their behalf. If you do this, your fine is considered reasonable and customary; if you don't, it's presumed to be trickery and held to a higher standard.

I agree it's farfetched. But when we're talking contrived scenarios where people living hand-to-mouth should play roulette, the imagination wanders!

Yeah.

But this might be an appropriate area for an industry consortium or even regulation to create a clearinghouse. If you're about to fine someone $X for an amount due up to $Y, you have to broadcast it on some confidential national clearinghouse an hour before assessment, allowing a contracted representative of the target to settle it on their behalf. If you do this, your fine is considered reasonable and customary; if you don't, it's presumed to be trickery and held to a higher standard.

Who pays for this? What's the penalty for "trickery"?

Compared to electronic stock markets, or check/charge clearing, or even the Twitter firehose, this "identity M is about to be fined $N" live book is pretty simple. The 'angels' or regulators could pay for the system, but those who wish to assess late fines would be responsible for their own prompt reporting.

For example, the law might be: "To charge a late fee that represents an effective interest rate more than 10 times the prime rate, electronic notices of intent-to-charge must be filed both 1 day and 1 hour before assessment, and electronic payment from third parties must be accepted."

The other portion is the fact that the $250 is a sunk cost. Future decisions should be independent of that money lost. Rationalizing gambling using cost relativity since gambling on an already expensive bill "will save you money" is not logical. It won't save you money unless you keep doing stupid things at which point you are already losing alot of money - its on average meaning repeated trials. Simply irresponsible. I'm either gonna win $130 with 47% chance or lose $130 with 53% chance. My $250 bill is sunk and completely independent of this decision and outcome. Otherwise any time I have an expensive bill to pay and will be left with only about $130 why not gamble it save the amount I need to pay in the long run. This is the start of a gambling problem.

No, you're missing the point: the $250 is, indeed, a sunk cost. The $100 fee that's going to add on if it's not paid on time, however, is not.

Stripping away all the irrelevant details of the problem, the (completely contrived and artificial, indeed) choice is between:

A) Certainly losing another $100, B) A near 50/50 shot (minus a single-digit house edge) of either winning $130, or losing $230 (lose the $130 bet, plus have to pay the $100 "late fee")

The $250 owed is irrelevant to the problem except to trigger the late fee and set up this payoff structure.

Firstly the concept of expected value only make sense over repeated trials of the same experiment and using it here on a one off is a misapplication.

Whether or not expected value calculations are valid for single shot deals, are you really saying you'd choose option A in this situation, which loses you twice as much as the expected loss in option B?

Then there is the other part.

You can't ignore utility. Heard of loss aversion before? How people prefer more risk when it is supposed to mitigate a loss? This is a textbook example of that psychological fallacy. Am I willing to risk a further $130 to avert my loss? No, not in this situation, considering my actions and the increased utility the money has to me as a poor college student. But phrased this way most people would take the risk!

I look at it this way. I am not willing to take an even odds bet of $130 that a coin will turn up heads, especially when I already owe $250. Are you? Most people are risk averse when the situation is phrased properly. If you are willing to take the bet then you derive less utility from the money and so are not applying the correct mental context of a cash strapped individual. Unless a poor appreciation of money is why this individual is cash strapped in the first place.

And finally, there is the fact that this could breed irresponsibility in many people. They do it once, win and a lesson is not learned. Increased likelihood of repeated behaviour and say the bet is lost the next time we have more money lost than if the bitterness of the fine had been instilled. They would have to do this enough times for the law of large numbers to kick in for them to approach their expected loss. Worse is if this becomes a general philosophy toward bills. Oversimplification of course but the point remains.

Life is a series of one time decisions. You might not get the same exact gamble again, but you'll get many others, and if you keep taking ones with positive expectation you'll end up ahead in the long run.

Short of it is: I don't agree. Those other situations are not the same event as this and even often completely unrelated. You cant lump them into the same space and claim positive expectation on their value.

(I'm using the term suitable somewhat vaguely here, since even +EV gambles can be bad ideas in the long run due to bankroll considerations. But for what we're talking about, we're assuming all the gambles are the same in all other respects.)

I don't think this is the common case, but there are cases where that makes sense, for instance if keeping a license enables you to keep a job that will allow you to easily pay off the debt, or, if you multiplied the numbers by 1000, and assumed the poor person was willing to declare bankruptcy. In that case, you might have a point; Really, I think this is why buying a house at a time of obvious volatility is such a good deal, assuming you have no other assets. If prices go up, you have put 5% down on an asset that is appreciating quickly. In the up market, housing was appreciating at north of 10% a year; that's 10% of the total home value, of which you maybe put down 5%. If prices go down? you walk.

The question, in that case, is how much does declaring bankruptcy cost? I mean, you have the up front lawyer costs... then you have the problems associated with having bad credit. but I can see many cases where taking the gamble would make sense.

It's true: I just moved to CT and had to deal with transferring a car title, registration and license from out of state and it was a nightmare. Definitely would've rather spent the 8 hours and ~$350 at a casino, of course.

I always thought state sanctioned lotteries were highly immoral. Sure, they want the tax revenue, but poor people are disproportionately the victims of what feels like fraud. The people believe that have a chance at winning what they most certainly do not.

It's like reverse welfare- taxing the poor and uneducated for the benefit of the masses.

Not at all. In fact, I wrote this up because of a conversation I had a while back with a man buying a lottery ticket at the gas station. I was talking with him about how bad the odds were, and he fully admitted that he was getting terrible odds on that dollar.

But he figured that on the one in a million chance that he hit the jackpot, even if he only saw a quarter of that amount he could actually get out of debt and start making the power of compound interest work for him instead of against him, and after enough time with that money in the bank, the scales would tip in favor of spending the dollar on the lottery ticket.

Now, I don't think that argument really holds water, and I told him so (for several reasons, even apart from my skepticism that he'd actually put any cash he won into a properly managed account without spending a huge chunk of it first; the odds at the lottery are so hideous and the doubling time for a quarter million that you're also drawing money out of to live off of is very long, so it would be tough to make those numbers work out), but it got me started thinking about whether there might actually be situations where a losing gamble could be worthwhile, depending on the current situation of indebtedness.

Gambling where you get the results quickly (pretty much anything at a casino) has no appeal for me though, I see that as simply destroying money.

Also people greatly overestimate their odds of winning big prizes like that. If the odds of winning the lottery were 1 in a million I'd be buying tickets by the truckload.

One could argue that it's better than legalizing casino gambling and inviting Steve Wynn to come into your state and help write the laws.

Maybe that was the best solution? Having to live without a privilege such as your licence seems like one of the best ways to teach you not to let your registration expire next time. Stay on top of things, and don't let the first late fees happen in the first place. If you STILL don't have enough money, you're living beyond your means, plain and simple.

But this is almost always a false assumption. It would be better to borrow money to pay the fee in time. Can anyone think of a case where it actually would be better to gamble (at expected loss) than borrow money?

No gamble: 0% chance of success * 53%

Put it all on black: non-zero chance of success * 47%

I don't imagine this would go over very well with investors, though.