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?
Ask HN: How do you choose powerball numbers if you play?
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Re: Ask HN: How do you choose powerball numbers if you play?
#2My 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.
Re: Ask HN: How do you choose powerball numbers if you play?
#3My 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. ht…
thanks Pat, like I said I do it for fun sometimes.
Re: Ask HN: How do you choose powerball numbers if you play?
#4My 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.
Re: Ask HN: How do you choose powerball numbers if you play?
#5The 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?).
Re: Ask HN: How do you choose powerball numbers if you play?
#6My 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. ht…
There have been other lotteries which were pseudo random and were statistical won because the assumption "the coin is fair" was incorrect.
Re: Ask HN: How do you choose powerball numbers if you play?
#7The 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.
Re: Ask HN: How do you choose powerball numbers if you play?
#8My 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. ht…
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)
Re: Ask HN: How do you choose powerball numbers if you play?
#9A 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.
Re: Ask HN: How do you choose powerball numbers if you play?
#10The 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.
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).