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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

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?

mattmaroon 16y ago
Actually EV "makes sense" even when applied only once. You should take any positive EV gamble you can at any time you can, and avoid the opposite. 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.
- Dn_Ab 16y ago
  I see your point. But I would say maximize your utility but even that is questionable. As Daniel Bernoulli (St. Petersburg Paradox) showed, the concept of expected value to the real world is not straightforward. 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.
  - mattmaroon 16y ago
    Let me put this another way. If you take every suitable gamble you can, even if they're one time deals, you'll end up further ahead in the long run than the guy who only takes suitable gambles that are repeatable. Thus whether or not the gamble is repeatable should have no bearing on your decision. (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.)
Dn_Ab 16y ago
I see. I did miss the part about the $100 late fee. And you know what, I would still take option A because the expected loss is not meaningful to me, I don't intend to have this happen again. For one, I should not have been speeding or whatever and then compounded the problem by ignoring the punishment. I deserve that penalty and gambling it away is missing the point. In fact, I'd rather the money go to the local municipality than some casino's pocket. Or I would take another bet with better odds or payout :) 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.

mattmaroon 16y ago

Actually EV "makes sense" even when applied only once. You should take any positive EV gamble you can at any time you can, and avoid the opposite. 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.

Dn_Ab 16y ago
I see your point. But I would say maximize your utility but even that is questionable. As Daniel Bernoulli (St. Petersburg Paradox) showed, the concept of expected value to the real world is not straightforward. 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.
- mattmaroon 16y ago
  Let me put this another way. If you take every suitable gamble you can, even if they're one time deals, you'll end up further ahead in the long run than the guy who only takes suitable gambles that are repeatable. Thus whether or not the gamble is repeatable should have no bearing on your decision. (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.)

Dn_Ab 16y ago

I see. I did miss the part about the $100 late fee. And you know what, I would still take option A because the expected loss is not meaningful to me, I don't intend to have this happen again. For one, I should not have been speeding or whatever and then compounded the problem by ignoring the punishment. I deserve that penalty and gambling it away is missing the point. In fact, I'd rather the money go to the local municipality than some casino's pocket. Or I would take another bet with better odds or payout :) 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.