You also have to take prizes other than the jackpot into account when calculating EV.
Just be sure to diversify. Don’t put all your money on one number. 
At the minimum payout of 15-20 million, those will make a difference in the EV. At a payout of around half a billion, they become much less relevant.
Ah, it’s like a rounding error. Makes sense.
One way to generate your own random numbers is a Bingo machine. However, Quick Pick is so easy and convenient, why bother?
The only reason that I would question that is how random the Quick Pick is.
If it uses a pseudorandom generator based off a seed, and two locations have the same seed, then all the numbers picked at the two locations would be the same.
Even if not, any pseudorandom generator is going to create patterns that wouldn’t be evident in “real” random generators.
Honestly, I don’t really know exactly what that means in the grand scheme of things, but it does seem as though, if they aren’t all truly random, then it will increase your chances of matching someone else’s ticket. By how much is hard to say without knowing far more about the systems than I think the Lotto will divulge, but it’s higher than zero. And then of course you also have to win in order for that to matter.
The randomness of Quick Pick doesn’t have to be perfect. it just has to be better than the randomness of your own methods of picking your personal numbers vs. the randomness of the millions of other mathophobes who play the lottery*.
c.f. running from bears.
* FTR, I have several current Powerball chances in my pocket right now. Plus several from recent drawings. I’m no mathophobe. But the vast majority of players are, and they’re your “competition” in the sense of who you’d share a win with, if not in the sense of whether they’ll win or you will.
In other news, lightning has to land someplace. If you’re not out in the rain, it won’t be where you are.
Would they? Don’t they also add “noise” like the internal clock or some other variable?
If everyone does quickpick, and the quickpick isn’t truly random, then that’s who you are up against for matching tickets and splitting pots.
Eh, and right now a ticket actually has a positive expectation value as long as you don’t split it. (Even after taking the cash option and after taxes.)
I have no idea how they generate the quick pick numbers, and a moderately deep google search doesn’t come up with anything close to definitive. Maybe it’s out there, but I haven’t come up with it.
Quite right as a matter of strict logic.
But the practical difference between pseudo-random, random, and cryptographically secure random is pretty small from the POV of a player.
If someone plays each and every e.g. Powerball drawing over their adult life, that’s 2 games per week times 52 weeks times e.g. 70 years = 7,280 draws. That’s not a lot of trials for the hair-splitting differences between the various qualities of “random”1 to show up.
Even if we assume our player spends a rather hefty $100 for 50 picks per drawing (IOW, $10,400 per year, $728K per lifetime), they’re still only making 364K lifetime picks out of the vast state space of possible picks and draws.
Though the differences between pseudo-random, random, and cryptographically secure random may well be statistically significant from the POV of the lottery authority. Which is why the game is designed so it doesn’t matter to the lottery authority whether or not there are dupes, or non-randomness, or even outright collusion amongst the ticket buyers.
- Just as long as the lottery doesn’t follow XKCD’s take on random:
Obviously, no matter what method you use, you aren’t likely to split the jackpot, because you are not likely to win the jackpot in the first place.
But, assuming that someone will win, that person will have a higher chance of having to split the pot if the system used to generate their numbers isn’t truly random.
Obviously, all talk of maximizing your ticket value is purely mathematical, and only matters in the real world if we are actually buying hundreds of millions of tickets. I just find it interesting to talk about probabilities that start to seem counterintuitive because they end up being larger than we are able to grok.
BTW, I was wrong when I said a current ticket has a positive EV if you don’t split. I was thinking along the lines of a $1 ticket, but I forgot they are $2 now. The cash reward would have to be about $1.2 billion for that to happen, around $2 billion for the annuity.
If the immediately upcoming drawing does not hit, the next one will probably surpass that threshold.
I also screwed up my calculations above. My arithmetic was good but I forgot they now have three Powerball draws per week, not two. So there are 50% more trials (and expense) per lifetime than I said.
[aside]
I recall a fascinating discussion we all had about 15 years ago on the topic of “expected value” in the context of modern lotteries. Sadly I’ve not been able to search for it successfully.
The punchline I and a couple of other folks ended up defending against overwhelming numbers of other posters was that “expected value” is certainly computable on one trial of a random process like a lottery draw, but only becomes a meaningful decision-making metric when the number of trials is large compared to the state space.
IOW, if you’re repeatedly playing a dice game with a single D6, then after e.g. 100 rolls an a priori EV calculation will have proven highly predictive of your actual experience. After only 3 rolls, not so much. After just 1 roll it’s not a good predictor at all.
A lottery like e.g. Powerball is equivalent to a dice game rolling with a D292200000. It takes a lot more rolls to adequately explore that state space than there will ever be, much less than you can personally participate in.
The bottom line being that EV is very, very, very close to a meaningless concept when applied to hyper-unlikely events like winning a lottery. Best not to even bring it up. Or at least that was my and another couple of math geeks’ contentions. Although as I say we were soundly in the minority with our views.
If you win the jackpot, you won’t care if you have to share it. They will have been the right numbers.
I agree if you are having a serious discussion about investments, but in much more loose talk, I like to call it having “pot odds”. In poker, you may find yourself in a situation where you only have a 1 in 3 chance of winning, but the pot is 4 times what you need to call. Even though you probably won’t win, the proper move is to make the call, because if you follow this strategy, you will end up winning more than you lose in those situations, over the long run.
Same with the lottery, if you only play when you have “pot odds” you will end up winning more than you lose over the long run, it’s just that the long run is very, very, very, very… long.
I read an article a while ago that said your expected value on these large lotteries is basically never positive because sales of tickets increase rapidly with large prizes which increases your risk of splitting the pot faster than the extra tickets sales grow the pot.
Not necessarily. If you know that other peoples’ selections are systematically biased (like picking dates) you can theoretically reduce your chance of sharing the pot by systematically avoiding the numbers that others are systematically choosing. For the effort that would take though, using the lottery’s random number approximator is good enough for me.
I can’t tell you how many people I’ve heard saying they have a “system” for buying their tickets. It’s all nonsense. The odds for hitting on any one particular set of numbers is EXACTLY the same as for any other set of numbers. What increases your odds is buying MORE tickets. If you buy 100 tickets instead of one, your odds are 100 times higher. Unfortunately, that is still very, very, very long odds.
In most of my posts, I have caveated with “and you don’t split” which is the point of trying to choose numbers that no one else chose.
Sure, that becomes harder as ticket sales go up and there are more “clones” out there, but the last massive jackpot was won by a single winner.
Of course, if you do that, then you are now picking out of the pool of numbers that those who avoid the numbers others are systematically choosing are using.
Same here, but I also don’t know that it would actually improve anything.
Interestingly (or maybe not) of the 50 largest jackpots in US history:
Three way split: 4 times
Two way split: 9 times
One ticket: 37 times
Eh, not exactly. They do use a physical system with ping pong balls that are only calibrated to the limits of our capabilities. If you did a hundred billion drawings, you’d probably actually see a bias towards certain numbers that are on balls that are slightly lighter/heavier/smaller/bigger.
But, for all practical purposes, it is random.
Just an hour or so ago, I had a conversation with a client who believes that there is a system to scratch-offs. He’ll hang out in the gas station until someone wins something, then count a certain number of sales, then buy a certain number of tickets. He claims to be “up.” If he’s right, then the lotto is doing a terrible job of randomizing their scratch offs, but I’d say it’s more likely that his math skills that lead him to think this is a winning strategy also prevent him from properly accounting for losses.
Mathematically, every combination is just as likely as any other combination - assuming that the randomizer is working correctly.
But, as others have said, the risk comes that you will have to split with someone.
So really, what you want to do is to figure out the sorts of patterns that people are prone to and, if a number matches that pattern, then discard it. After that, you just want to make sure that you have no duplicates (not that you’re liable to, given the vastness of the number space).
There’s no real advantage - in terms of getting a hit - of putting out your nets in this little bit of space versus that little bit of space. There’s no law that the randomizer won’t pick a number that looks like a number that a person would choose. But, likewise, there’s no danger of putting all of your numbers into the space that others are less likely to go. Your only risk is an overlap with someone else. So you may as well try to avoid that.
That’s the best you can do unless you can find a flaw in their randomizing methodology.