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Ask HN: How do you choose powerball numbers if you play?

6 points by tmaly ↗ HN
I play sometimes just for fun. I was using R a while back to do kernel density estimation using the history of each time a number appeared in a drawing. My assumption was that each number should have an equal distribution over time, so anything that did not had a higher likely hood of being chosen. Safe to say, I still have not won. What is your method to choosing numbers for the powerball?

25 comments

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patio11
My assumption was that each number should have an equal distribution over time, so anything that did not had a higher likely hood of being chosen.

I feel like saying Gambler's Fallacy to someone who knows what R is is borderline aggressive but, out of a maximum of good intentions, the thing you've labeled as an assumption is called the Gambler's Fallacy and it is so named because statistics does not work that way.

https://en.wikipedia.org/wiki/Gambler%27s_fallacy

Consider the case of a fair coin. We agree that, if one flips a sufficient number of coins 100 times, eventually one of them will come up with 100 heads, right? Pretend you've got a factory in China filled with people flipping fair coins until one station shouts out "GOT IT!"

Do you think that there's some property that the universe attaches to that coin which makes it more likely to be heads, or more likely to be tails, simply because it "feels" anomalous if one happened to be flipping only that coin and not one of the thousands being flipped simultaneously in the factory?

No, that's preposterous. The universe doesn't care what feels anomalous to us. It's a fair coin. The next shot is like every other shot: 50/50.

tmaly
thanks Pat, like I said I do it for fun sometimes.
possibleNoob
There have been other lotteries which were pseudo random and were statistical won because the assumption "the coin is fair" was incorrect.
an4rchy
Although I agree with what you're saying in principle, there could be other (highly unlikely) aspects to it. What if the coin had a small aberration due to the manufacturing process or it was dropped one too many times, this could lead to some sort of unfair odds. Once again, this is definitely a reach, (maybe not the universe attaching a property to something but just bad manufacturing processes or too much wear etc)
spdustin
Back in middle school, I did a science fair project on this for the Florida lottery. My hypothesis was that each ball was dropped into air-blown hoppers made by the same manufacturer to the same specifications, and each ball had slight variances in weight and aerodynamics due to the (assumed) pad printed numbers on the balls; thus, the "hot numbers" were statistically more likely to be drawn.

EDIT: also, the hypothesis included the average amount of time the balls were being tumbled before drawn.

It was, to my middle school statistical ability, correct at that time (ca. 1980s). The "hot" numbers "won" me over $3,000 over the course of two months. Random numbers? About $20.

Things have very likely changed since then, though.

gregjor
My father used lists of previous winning numbers and a "system" he adapted from Keno (which he mostly lost at). Once I was with him when he was buying lottery tickets and I bought one with the numbers 1-2-3-4-5-6. My dad came unglued, asking me if I understood how unlikely my numbers were to hit. Exactly as likely as his, I tried to explain, but he didn't get it.
jeffwass
Your dad was on the right track though, but for a different reason.

1,2,3,4,5,6 is a (relatively) common choice of numbers people buy in lotteries, so if those numbers win you're more likely to have to split the pot.

cmdrfred
The only way to win at powerball is to never play. I'm up whatever the average player is down (100's of dollars? 1000's?).
eecks
And you miss out on the fun
Gustomaximus
Also I like the thought my few bucks helps someone have the experience of their life.
montbonnot
If you don't play you can't win. $2 can make you rich.
mod
"If you play, you can't win" is true 99.9*% of the time, with a lot of nines.

This isn't kind of gamble you use that phrase about. Blackjack or something, maybe. Non-casino gambles, like taking a new job, yeah.

cjbprime
The only useful strategy for choosing numbers is to choose numbers that other people are not using, so that you maximize your chance of not having to split the pot in the unlikely event that you win.

I think I read that numbers below 30 are vastly overrepresented in lottery ticket number choices.

jerrytsai
I second this. There's little (...or insufficient) reason to believe some numbers come up more often, so you assume any set of numbers may come up. Then any number combination may come up, so you may as well pick the number combinations which fewer people pick. At least one study has shown that numbers below 30 are picked more often than those above 30. So by picking numbers above 30 you increase the chance you do NOT split the jackpot if you win.

From an expected value perspective, however, lotteries are generally money LOSERS. Even at the estimated $1.5 billion for this Wednesday's drawing, the expected value of purchasing a ticket is NEGATIVE.

Here's why: the $1.5 billion is paid as an annuity-- the reported lump sum (present value) payment would be $930 million. Depending on your tax situation, if you live in the USA, you would lose about 40% of that to federal taxes, leaving you with about $558 million. In that it costs you $2 to purchase one number and the odds are 292 million to 1, you would need the take-home jackpot to be 2 times $292 million, or $584 million dollars before the expected value to be zero. (And this assumes a world in which jackpots cannot be split! And that you have no taxes beyond the federal tax!)

So the best play really is to NOT PLAY. From an expected value perspective, it probably would make sense to play when the jackpot is over $2 billion. It would depend on the frequency distribution of split jackpots.

So IF you're going to play, then you should try to minimize the chance you win a share of a split jackpot. But the rational play is to NOT PLAY AT ALL (well, at least not until the jackpot grows larger).

brudgers
A mechanical system such as balls in a hopper is likely to be biased either by design or by active human intervention when the results appear biased. One of the insights at Bletchley park was that Enigma operators had "letter bias" in their selections.
tmaly
it would be an interesting math problem to try to create a model that could detect the bias
brudgers
A mathematical model isn't a mechanical system. The mathematical model for a set of balls will tend to be random just like the mathematical model of a roulette wheel. Yet roulette wheels can be clocked and machine vision can predict outcomes based on wheel speed and the conditions of ball release.

The problem with powerball is obtaining a large enough sample size...the space is much bigger than that of roulette.

o_nate
That's a good argument for playing the numbers that have won more frequently than average in the past, which is exactly the opposite of what the OP had tried. Of course, this is assuming they use the same mechanical system, balls and everything else for each drawing, which is unlikely, but I'll defer to someone who follows the lottery more closely than me.
S4M
There is one trick you can use: all numbers have the same probability to be inthe winning combination, but some numbers are less picked by played less (typically: numvers that can't be associated with birthdays). Pick those numbers and if you will, you will have to share with less people.

Not something l'd recommend though, as I hate games of luck.

logn
I had trouble finding reliable historical data. I didn't trust anybody that compiled the data, as they all had different results, and the powerball set of number has slowly expanded over the years.

I think it's reasonable that some numbers are more likely. Either by their initial placement or by subtle effects of aerodynamics and weight of the painted numbers.

That said I think it's a little absurd to choose numbers. Like it actually matters. Just get computer picks. It's the best chance to not split the pot, assuming a fair computer.

Unrelated: I don't think it makes much sense to buy more than one ticket. The EV is still slightly less than the cost of the ticket and after the initial ticket you cannot boost you odds again like that. Even with positive EV it's still insanely high variance, so I don't see how multiplying your odds makes any difference, compared to raising your odds from zero which your initial ticket does.