I think what what ottoerotic was saying was that if you look at the entire population of people who have won lotteries, and group them into sets of “people who won playing their own numbers” and “people who won using quick picks,” the “people who won playing their own numbers” set would be bigger, NOT because those people’s sets of numbers win more often, but when they do win (which is just as likely as the “quick pick” group), MORE PEOPLE win with them.
I.e., if you survey lottery winners, you’re probably going to have more people say “I won with my own numbers” but those people’s winnings will probably be less on average.
Oh, I’m sorry, did you think you were debunking something?
The only time the money involved enters the picture is when you are deciding if the prize pays off according to the odds. The odds remain, as you stated in you earlier post, one in 146 million. You can decide to play those odds for $10mil or $200mil or whatever you like. There’s still a 145,999,999 in 146,000,000 chance your dollar is not coming back to you.
Let’s say we have a long-running, growing jackpot in a twice-weekly lottery with the odds you describe. Joe Blow spends $2 on each drawing for two chances, twice a week, until the prize is won (not by him, sad to report). Let’s say it goes on for five weeks. He’s spent $20, with nothing personal to show for it. If it had gone on all year he would have spent over $200. Some of the ticket money goes to increasing the prize pool, but a lot of it goes right into the state coffers (admittedly, often earmarked for specific purposes).
Do you think if his state Rep had announced they had just voted in a new tax that would raise the average citizen’s expenditures by the equivalent of $200 a year, even temporarily, that Joe and his neighbors wouldn’t scream for their ouster.? But if you offer him a half a hair’s breadth of a chance (72,999,999:1 against) of making a bundle off it, he gladly forks it right over to the state.
Unfortunately, your math is completely wrong. You assume that because the jackpot was $177 million, and your odds are 1 in 144 million of getting all the numbers exactly, that your expected value is greater than $1, the entry prize. This is not true. Your chance fo getting $177 million is not 1 in 144 million, because you neglected the odds of splitting the pot. You also neglected the taxes paid on the $177 million, which are enormous. In your example, your expected value is not precisely known (since you don’t know how many tickets are bought), but it is clearly less than $1.
Because prime numbers are mostly in the lower numbers, this is a poor strategy, not much different than picking birthdays. The best strategy would probably be to pick all numbers above 31.
Well speaking purely from math/economics level, most lottery analysis assumes that
$100 is 100 times better than $1 and $1000000 is 1000000 times better than $1, but practically speaking that is not true due to human lifetimes being finite. The amount of money one has/gets is an exponential curve of utility up until a certain ceiling (otherwise known as “more money than he knows what to do with”). $1,000,000 is billions of times better than $1, and even disregarding the psychological utility of playing the lottery, it’s a pretty good deal mathematically.
Fear Itself, you didn’t debunk jack shit and you are way over your head. What you are not understanding, even though it has been explained a few times, is that your true payout is the jackpot minus taxes less the odds that the jackpot will be split.
I won’t even follow you down that irrelevant hijack rabbit hole.
You missed my point entirely. What I was tring to get across is that the lottery is a tool by the state to get revenue they could not get otherwise. As long as people remain ignorant or in denial of their real likelihood of walking home with the jackpot, the state can rake in dough they could only dream of of getting through legislation.
And don’t forget to eliminate all those sequences on the back of chinese cookie fortunes.
There might be a corrilation between how often people play, and picking thier own or doing the quick pick, and that might tend to make one way look better than onother, simply because more tickets are bought that way.
Your argument is specious. You’ve given Joe zero expectation on his bet. Let’s say Joe Blow spends $2 and wins the jackpot. Smart guy that Joe fellow, always has been! Joe Blow doesn’t care who is profiting from the lottery because it’s not relevant at all to the analysis of the game. I have played the lottery a few times. I lost overall. That doesn’t make my decision to play at the time wrong (or right).
No. I am using math as well. The key to math is knowing what formula to use in a given situation to get the right result. I know that you didn’t come up with your answer on your own so I don’t hold you fully responsible.
However, the calculation you are using is only a part of a complete formula. It isn’t the end of it. Whoever came up with it needs their Ph.D. revoked because it is NOT a complete formula.
Expectation is a concept that needs to be applied a the individual level when it comes to gambling. It isn’t a one-shot deal. All bets get added together over a lifetime to form the overall expectation.
If someone gets to play a game very week that costs $1, had 1-in-10 odds but pays out $11 dollars, they would be fool not to play. If they start playing at age 20, live for 72 years and bet $1 a week, the median lifetime winnings is about $2600. That is the formula that needs to be used with individuals.
If someone plays the lottery for $5, $100 or even $1000 a week, the median expectation for lifetime winnings is $0 for a jackpot and only a small amount for the consolation prizes for hitting 4, or 5 numbers.
There is nothing but math there. It is simply an alternate method of calculating expectation using reasonable bets and lifespan combined with median winnings.
Again this analysis would only be correct if getting $2 would be equivalent to getting a $1 and then another $1, but it is not. If someone gets to play a game every week that costs $1 and has a 1-in-10 odds but pays $11 dollars, it is a good deal. If someone gets to play a game every week that costs $1 and has a 1-in-10000 odds but pays $5000, it’s not necessarily a bad deal - the lifetime expectation is negative, but it’s easy to see if you consider a ridiculously short lifetime:
Say you have $1 and you live 24 hours. You can either spend your $1 and have $1 worth of something, or you can buy a $1 lottery ticket and have a chance of having a much bigger amount of money to spend in your 24 hours. In this situation there is simply no reason not to buy the lottery ticket since the benefit of winning, however remote, outweighs not having that chance, regardless of the odds. Practically the difference between having $0 or $1 is negligible.
That’s the beauty of the lottery, your negative lifetime expectation can never be less than what you spend on the lottery, and have you spent that money or invested it instead it would not make a distinguishable difference in your life (or you wouldn’t have bought the lottery tickets to begin with). Nobody will turn down a completely free lottery ticket, and for a low number of tickets they are functionally indistinguishable from free.
I don’t recall passing any judgements, on he rightness or wrongness, either morally or logically, of buying a lottery ticket. Often, when I notice the jackpot greatly exceeding the odds (which means they’re giving a fair payout based on the risk), I’ll buy a couple of quickpicks. I have no problem with lotteries.
This thread is about number-picking strategies. All I’m trying to get across is that any plan to go for a lottery prize needs to be evaluated in light of the fact that a state or multi-state lottery is not structured to put money in the hands of the players. It’s structured to put money in the hands of the state, and any expectation of riches needs to be adjusted accordingly. For instance, in California, only about 50% of the revenues for the last 20 years from the state lotto have been dsitributed as prizes. The rest goes to administration of the lotto and education.
Whenever your local news reports on a big jackpot, take note of the number of tickets bought. That’s the money that people willingly gave to the state in those few days with no actual guarantee that anyone was going to win anything. Ask yourself if the state legislature would ever have the nerve to risk voter ire by taking that sum of money in that space of time through legislation.
Once you’ve grasped this, you havethe essence of my point.
Think about your use of the words “remote”, “regardless”, and “practically”. When you transform those into mathematics, you’ll see why you are incorrect.
And as long as you’re providing irrelevant thought experiments – in your example, you would be crazy to buy a lottery ticket. You couldn’t get your winnings while you were alive!
Ok, here’s the breakdown. Right now, if I instantly win $1,000,000 I will derive billions (for the sake of math, let’s say 25 billion) times more utility than keeping my $1. This utility multiplier is dimished the more lottery tickets I buy since the purchase starts affecting my net worth in a sizable manner. The utility of money, especially changes in net worth, is not linear and is first and foremost subjective and relative. The 25 billion number comes from me and only I can evaluate that for myself.
It’s almost meaningless to analyze money as if it was linear. To some, $1,000,000 is chump change and risking even a $1 to win that much is pointless. They derive way less than million times the utility from $1,000,000 than they do from $1. For others, $1,000,000 would completely change their entire lifestyle and the utility is significantly more than a million.
You shouldn’t be dividing your payout by your odds, you should be dividing expected utility by the odds.
I buy them on the theory that if I don’t, I have zero chance of winning. If I do, I have a greater than zero chance of winning. It may be microscopic, but it’s there.
Congratulations, Fear Itself, you’ve just demonstrated perfectly why people get conned into buying lottery tickets. Others have pointed out that you have to take taxes into consideration, but when you factor in the likelihood of multiple winners, this is definitely a losing proposition.
You debunked nothing. Even assuming you never bought a lottery ticket unless there was a “rollover” jackpot, your odds of coming out ahead are inconsequential.
Look at the big picture: half of the money taken in is paid back out in prizes. On top of that, they pay out over a 20-year period, so the lottery commission gets to earn interest on your prize money for a couple of decades–or you can take the discounted net present value of your prize…what a scam! On top of that, the “big prize” isn’t even that full 50% of what comes in, because a big chunk of the money (which varies from lottery to lottery) is paid back out in the little $1, $2, and $5 winners. The odds are very thoroughly stacked against you.
I recommend a book called Innumeracy: Mathematical Illiteracy and Its Consequences, by John Allen Paulos. It can help you understand how lottery advertising convinces people of this kind of fallacy.
I’ll check out the book, but I don’t see how it’s a fallacy. It’s trivial to see that the utility of money does not behave in a linear fashion at all. Just imagine three families, one making $10,000 a year, another $100,000 and another $1,000,000. The practical lifestyle differences between the lower class and the middle class is much greater than that between the middle class and the upper class families. Second, the nature of money is such that you’re always better off with the maximum amount of money now rather than over a period of time. Assuming 0% inflation, getting $1,000,000 one year and not earning anything for the next 9 is better than getting $100,000 a year for the next 10 years.
