Whether the odds are consequential or not depends on the payoff attached to those odds. A 1 in 100 chance to win 10 times the entry fee is an inconsequential chance. A 1 in 1000 chance to win 10000 times the entry fee is a considerable chance. Now, usually, even rollover lotteries are still bad bets by this rubric (owing to taxes, the possibility of splitting the pot, etc.), but it’s at least conceivable that a lottery might be a good bet if it rolled over enough.
If more people choose their own numbers than use quick-picks, then most winners will have chosen their own numbers. If more people use quick-picks than choose their own numbers, then most winners will have used quick-picks. The clumpiness does not affect this result at all.
Sure it does, these type of relationships occur all the time in nature. If you have a radiation source, being two times closer means quadrupled exposure. The inverse square law is an example of a strict relationship. There’s also non-linear subjective relationships that aren’t strict, doubling dosage of a drug does not necessarily double the effects for example.
To me, having a single dollar is almost indistinguishable from having nothing. Having a million would drastically change my life, resulting in benefits far exceeding million times that negligble difference between $0 and $1.
I accept your point about expected utility. However, since that is a subjective number, you can’t make general statements about it. Not having any other information, any mathematical argument has to start with the premise that the worth of one dollar is one dollar. Like you say, the 25 billion is subjective.
Having said that, it’s hard to believe. The utility to you of one million dollars is 25 thousand times the million dollars!!?? Particulary when the utility in economics of an additional dollar goes down as the absolute number goes up. (That is, the slope of the curve levels off, it doesn’t increase). So let’s not “just say” 25 billion. Let’s step back and think about what that number actually is. I accept all your qualitative arguments, but that number seems way off.
I’m curious, if you truly believe that, what do you consider the marginal utility of $100,000? $10,000?
The number was used as an example, but for me it starts going up early. $10 is already significantly more than $1, simply because $1 almost doesn’t have any purchasing power, and $10 does. With $10 I can get lunch, with $1 I can’t even get decent gum. There’s no way to get even a shitty lunch for $1, so having just $1 cuts an important thing out of your life. Each increment you listed, $10,000, $100,000 and $1,000,000 opens up new categories of spending that were not available at all before, the mental important you assign and the utility you derive through these categories define the utility of money.
For example, it’s been my lifelong dream to get a pilots license and own an airplane. I simply cannot afford that right now. There’s a certain amount of money after which that becomes affordable, I prioritize, spend the money and my life changes. The projected amount of happiness and utility derived from this change has nothing to do with the monetary amount invested, yet it was not possible without that monetary amount. I can be happy without any money at all, I don’t need it to be happy, but the amount of benefit one derives from spending usually is not related to the amount spent. I’ve bought paperbacks that have given me more enjoyment than my car ever did.
Linear, dollar for dollar, analysis is not necessarily the only way to treat money. You can certainly attempt to use a gaussian distribution or whatever else you like, and it would be just as correct. Gaussian would probably be more accurate for most people anyway.
I get what you are saying but it seems to be largely irrelevant to the OP, which was answered by the first two or three posts. Your point is also irrelevant to the individual trying to decide whether or not to play the lottery. For instance 50% of a lot of money is still a lot of money. Why should I be concerned with the profits of the organizing entity? If I feel the lottery is not attractive I am free not to play, unlike taxes. I really don’t see what the problem is with people paying the state to play the lottery.
The truth is that it simply does not really matter to you as an individual player. Yes, Quick Pix will slightly increase the expected payout because they choose numbers over 31 (you could do this yourself by choosing numbers over 31. Same difference) but only because it increases the payout of a jackpot. Most lower end prizes are still exactly, or very nearly, the same.
The truth is that it makes little difference to you if you get half of a $17 million jackpot, or the whole thing; beyond a certain number it’s a Life Changing Amount of Money. From that perspective the only thing that matters is whether you win or lose. Choosing the numbers 14-29-32-37-44-46 because they’re unlikely picks (four numbers over 31, none 21 or below) only gives you an advantage over, say, 5-7-11-20-25-29 if you actually win a big prize. And with respect to winning a big prize the only thing that matters is whether your numbers win. 5-7-11-20-25-29 are still the right numbers to play if they win, and they’re always the wrong ones if they lose.
You’re ducking the question. Obviously, $10 is worth more than $1. Obviously, $100,000 is worth more than $10,000. The question is, is it worth 10 times more? So again, I ask you for numeric data, not qualitative theories. If you’re going to make a claim that a million dollars is actually worth 25,000 times one million dollars in your personal utility calculus, it deserves to be backed up.
Nobody’s going to follow commands to do a math assignment, but there is a certain logic here.
Possessing $1 has a given amount of utility. Posessing $1 at a million separate times simply does not have the same utility as posession a million dollars all at once; that seems pretty obvious to me. Aside from the fact that we don’t live long enough to possess $1 at a million meaningfully discrete moments, posessing a million dollars all at once is almost immeasurably more valuable than a million discrete possessions of $1 for the simple reason that a million dollars all at once enables you to do things a million individual dollars doesn’t.
Look at it this way; what can you buy for $1? A small cup of coffee. What would a million small cups of coffee do for you?
Now, what would a million bucks buy you? A house and freedom from worry about money for the rest of your life; spent wisely it might in fact extend your life and improve its quality, as you could avoid stress by quitting your shitty high stress job.
That’s why people borrow money for houses and cars and other big ticket items; having a lot of money at once permits things that having a little bit of money at different times does not.
In the last big lottery the after tax payout was $176M (the advertised jackpot was $365M). This does not take into consideration the chance of multiple winners.
I hate to say it because I though he was a nut job the entire thread, but groman seems (to my unsophisticated mind) to be making a lot more sense here.
I don’t buy lottery tickets for all of the “tax on the stupid” reasons already cited. But now, I kind of feel dumb for not doing so. Look: $10 per week is nothing for me. I wouldn’t miss it. I used to smoke that in cigarettes in two days. I’d trade the “fun” of hope for the “fun” of, oh, whatever else I’d just blow the $10 on (extra beer at BW3’s?). On the other hand, even though $10 is totally insignificant to me, $1,000,000 is totally NOT insignificant to me. The only way to get that (short of, you know, actually EARNING it) is to pay the $10 per week that I’d be wasting on something else anyway.
Therefore even though I’m good at math (it’s my profession in a way), now I feel stupid for not playing the lottery.
The fun of playing is an entirely different topic. I play occasionally myself. I think $1 is a good price for the enjoyment I get dreaming about what I would do with the money.
However, that’s not the topic at hand between me and Groman. It’s the second part of your paragraph. Of course $1,000,000 is better than $10. I mean, really, duh. Do we really need to have that discussion? The question is not going from insignificant to significant. The question is whether $1,000,000 is worth so much more than $1,000,000 that it makes the lottery a good mathematical bet for you. So I’ll ask you the same questions I asked Groman.
How much better is $1,000,000 than $10? 100, 1,000, 10,000, 100,000 or more?
How much better is $100 than $10? How about $1,000 or $10,000?
Seems to me that some decide this based on some warped logic where $10 = 0 utility and $1,000,000 = infinite utility. Unless you’re clinically insane, that can’t be true, even in your own personal calculus.
(BTW, you might be interested in The Latte Factor Calculator if you’re never seen it. http://www.finishrich.com/free_resources/fr_lattefactor.php The basic idea is that giving up some small amount on a daily basis and investing it can result in large yields compouned over time. The numbers can get dramatic.)
I’m not following you at all Rick. People borrow money and it allows them to trade “cups of coffee” for larger items. When I pay my mortgage bill, it’s a certain exact amount of money. That amount of money is a certain exact multiple of the price of a cup of coffee. It’s not infinite. Coffee isn’t free. Houses are much more expensive of course, but not infinitely so.
As for asking people to do math – I don’t have much hopes of getting an answer. But if someone is going to make the bizzarre claim that one million dollars is worth 25 billion dollars, and then base a strategy on that and say it’s a proof of anything – that needs to be backed up. Some have claimed that the utility of a million dollars is so high that it makes playing the lottery smart. That is counter to virtually any analysis of the lottery. Extraordinary claims demand
extraordinary proof.