Cecil’s column on the lotteryunsurprisingly states that it’s not possible to develop a winning system for choosing numbers. I remember hearing someone on the radio while driving (years ago) who said that some mathematical thing or other meant that it was usually stupid to play the lottery, but that it was permissable if the payout rose to twice the odds against winning. At which point it was not totally stupid to buy one ticket.
Whoever it was never said that it was a good idea to buy lottery tickets. You were still unlikely to win. And you should never buy more than one because multiple tickets don’t improve your chances noticably. They just said that it was excusable to buy a ticket during a 2 to 1 payoff to odds ratio.
I suspect that this is BS, but I was driving and not listening too hard, so I don’t know the name of the thing he was citing. Was it totally BS?
With any bet, the odds and potential return determine if there is a positive or negative expected return. It’s harder for a lottery since you have no idea how many people will choose the right numbers, which will potentially reduce your return. But folks can make educated guesses based on human patterns. If you bought every possible ticket combination and it costs you more than the expected outcome then the bet will have a negative expected return no matter what you do. The return (jackpot) will have to be much higher than that to make the bet positive.
The odds of winning most lotteries is really, really, really small for any particular ticket. Buying two tickets with different numbers will double your odds, but 2 times a very small number is still a very small number. Once there is more money in the pot than usual the odds turn in your favor, but more people will buy tickets so it’s a balancing act to find a lottery that is in your favor.
If you buy tickets for entertainment value, do you get more enjoyment from two tickets than you would from one? Because in most cases that’s the most tangible return you can expect, a few hours of daydreaming.
You know, I think that’s the best way to look at it. For two tickets. Or so. If you can afford it. I remember one local lottery winner being quoted as saying he had been “investing” $25/week from his minimum wage job for a year and was starting to lose patience . . . so he had been considering doubling his “investment” to make it pay off sooner.
My jaw dropped. I figure for every winner who’s done that there are thousands of non-winners doing the same thing. That is such a very, very bad idea.
I’m not going to link, but you could google Wizard of Odds for a breakdown of lotteries, blackjack, and a lot of other gambling.
Short version: if the pot gets big enough, sometimes a lottery ticket is a good bet. Far more often, it’s a sucker bet worse than slot machines.
I think this depends on the notion that winning sixty million dollars is twice as good as winning thirty million. In fact, for most people, that is not true. There is little or no difference in how much pleasure, security, or whatever, two such large amounts can bring you. Either way you can buy all the toys you can play with, and are set up for life.
It’s possible for a lottery to have a positive expected return. If you bet $1 your expected return is, say $1.5. Now, most of the time you’ll win nothing. But if the odds are 1/100,000 that you win and the payout is $150,000 then the odds are in your favor. But situations like that are very rare. And there’s no way to be sure that only one person will buy the winning combination.
Yeah, it’s a gambling site. SDMB is sketchy about stuff like that. (link)
The payout is in proportion to the odds, not that the odds are in your favor.
House Advantage drops to zero or becomes negative, rather than being 90+% as is typical for lotteries.
In the 80’s, when legal lotteries became more common, people started to notice that if the Jackpot got big enough, you could win by buying all the tickets. Even though say 50% of the money went to tax and profit, if the jackpot is 200%, then you win 200% * 50% = 100%. If the jackpot is more than 200%, and the tax + profit take less than 50%, you come out ahead.
An AUS company worked this out, got a large number of investors, and came over to the USA to invest in lotteries. They couldn’t buy all of the tickets (other people were buying too), but they bought enough tickets to win – and came out ahead.
Then the executives took the money and moved to Israel. (For historical reasons, Israel has no extradition treaties for some classes of people).
So that didn’t work out so well for the investors anyway.
From a straight profit point-of-view, lottery promotors don’t care who buys the tickets, and who gets the prizes. However, from an overall promotion-point-of-view, they decided that they prefered the prizes to go to ordinary suckers, to encourage them to keep playing and voting, not to foreign companies, playing only when it was profitable and taking the money out of the community.
So many if not most lotteries have changed their jackpot and payout rules to spread out doubled-up jackpots and prevent doubled-up cash payouts.
Does it ever make sense to buy one or two lottery tickets? That is a deeper question. You will have to make your own answer.
Here is the math (part of Game Theory, I believe) behind why playing the lottery doesn’t pay off.
A lottery ticket usually costs $1. If you buy the lottery ticket, that money’s gone. So you have a 100% chance of spending that money.
The chances of winning a lottery are so infinitesimal that only super huge jackpots make it worth taking a chance on such a purchase.
Let’s take the hypothetical circumstance of a lotto where you have a 1 : 1000 chance of winning, with a payout of $100. Sounds like a good deal, right?
Nope. That $100 is only worth $100 * 1/1000 = $0.1. So at best, your lotto ticket has a 10% return on investment, and 999/1000 times you win nothing at all. Actual lottos have much worse win chances to jackpot ratios, even when figuring in non-jackpot winnings.
And that’s not even figuring in how lotto winnings are paid out. See, most states don’t actually have a couple million bucks lying around to give to you in a (ceremonial) check or suitcases full of bills. So they set up an annuity that pays over a long period of time, so that when figuring in compound interest, you’re technically getting paid in full. If you’re impatient and want a lump sum, you’ll get a much smaller check.
And then there’s Uncle Sam. You’ll get docked either in Capital Gains taxes, federal income taxes, or state taxes.
And then there’s the psychological toll of sudden wealth, but that’s beyond the scope of the question.
BTW, treating a bet as favorable when it has positive expectation isn’t really appropriate. For example, suppose your life savings are $10,000 and you make a favorable even-money bet of $5000. Let’s say you have 51% chance to finish with $15,000 total and 49% chance of finishing with only $5000. Is that really good for you? Probably not: the hardship caused by being reduced to only $5000 may outweigh the luxury of $15,000 even though the latter is somewhat more likely.
Similarly, insurance – which offers “unfavorable odds” since the insurer needs a “vigorish” (profit) – may be beneficial. Your savings are reduced to $9,900 after paying the insurance premium, but that’s better than risking being wiped out.
A simple but effective way to incorporate this concept into calculating whether a bet is wise or not is to replace the usual optimization condition maximize Expectation[bankroll]
with maximize Expectation[logarithm(bankroll)]
Ignoring any entertainment value, this means buying a lottery ticket is “bad” even if slightly favorable!
For definiteness, suppose the chance of winning is 1 in 1000; your life-savings is $1000; should you buy a $1 ticket? If you seek to maximize expected bankroll you should if the jackpot is at least $1000. But if you seek to maximize expected logarithm of bankroll, I think you need to wait until the jackpot is at least $1718. (Yes, that’s $1000 * (e-1) )
Similarly, you could make the argument that as long as a lottery ticket is only costing you chump change, it makes perfect sense even when your expected return is only fifty cents on the dollar, as long as the prize is big enough. The enormous probability is that you’ll lose your dollar, but then that would have bought you only a cup of nasty coffee anyway. There is an outside chance that you will make enough money to make your life extremely luxurious. Kind of the other side of septimus’s coin, where the expected gain was actually positive but losing $5k hurt you more than winning $5k would benefit.
I think the above argument is a perfectly sound one, but I’m too mean to waste my money.
I think there’s some confusion here with the mathematical “expected value” of a probability situation. The “expected value” is the expected outcome if you play the game many, many times. The formula is basically the [probability of an outcome] x [payout if the outcome occurs]. So, example: you pay $1 to flip a coin; if the coin lands heads, you win $4; if the coin lands tails, you win nothing. Then the expected value is ($4 x .5) + ($0 x .5) = $2 and the game costs $1 to play, so this game is a “good bet” – if you play the game a sufficient number of times, you have reasonable expectation of coming out ahead.
However, if you only play the game once, then the expected value is a meaningless exercise in theoretical math: you’re either up a dollar or out a dollar. A positive expected value tells you only that the game is a “good bet;” zero says the game is “fair” (i.e., even chances of both sides winning) and negative says the house wins more often than not (like, say, roulette.)
So, the comments above about whether the lottery is a “good bet” (based on number of players vs payout) is really only saying that, in certain situations, the expected value is positive – if you play often enough, there could be a positive result. The catch is that “often enough” in a coin-toss game is probably five or six times, where “often enough” in the lottery is to buy millions of tickets.
All I know is that if I put a dollar in, I have an infinitesimal chance of winning the jackpot, but an infinitesimal chance is infinitely greater than a zero chance.
OK, so I assume we’re talking about a rollover situation, e.g.
A lottery company typically takes in each week $3 million from punters and pays out £2.5 million in prizes (including the big one of $1 million.)
For two consecutive weeks nobody wins the $1 million.
So now the lottery company have an extra £2 million (which they’ve been earning interest on.)
They can thus afford to give a one-off prize of $3 million, plus their regular $0.5 million in lesser prizes.
So for that week, punters pay over their usual $3 million, but stand to win $3.5 million in prizes.
So there is a positive outcome (based on the fact that the punters from the two previous weeks are subsidising it.)
^^^ and as several people have mentioned, there’s an entertainment value to a lottery ticket.
A one-dollar blackjack bet is over quickly and doesn’t change much. A one dollar lottery ticket can be a conversation piece for a week.
Hey, I’ve been to Las Vegas!
A one dollar casino bet with whooping crowds of fellow gamblers, one-armed bandit bells going off and gorgeous cocktail waitresses beats the hell out of losing money in a lottery.
P.S. Here in the UK we have Premium Bonds, which is a lottery with a positive result every week. (Currently 1.3% in our favour, but (from memory) it has been as high as 4%.)
A good theoretical example of the difference in expected return vs. perceived value is the St. Petersburg Paradox. A game with infinite theoretical expected return, but which most people wouldn’t pay an entry fee of more than a few dollars. Some good discussion about the issues in the Wikipedia article.
Anyway, back when, we had a state lottery. I calculated how large the jackpot had to be to be worth entering. (Not easy to do since the jackpot was the annuity amount rather than a straight figure. Plus the value of lesser prizes. Minus taxes.) It was a surprisingly low amount that the jackpot reached at least once a month. Mrs. FtG likes to buy a ticket once in a while so I encouraged her. But then they canceled it since it wasn’t attracting enough interest due to low jackpots. Went to MegaMillions. Much bigger jackpot required to break even. Then they added more numbers to lengthen the odds. Rarely would pay, in theory.
A $5 million dollar payout is plenty. A $200 million dollar one is just going to cause so much psychological stress it really isn’t worth it.
I have told Mrs. FtG that it’s fine to play the lottery as long as she never wins the jackpot.
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