When I was thirteen or fourteen, my father—who was pretty well-off but played the lotto very regularly—let me fill in one of his tickets for a bit of fun. I, being the precocious young person that I was, entered 1,2,3,4,5,6, reasoning that since the lotto was random, any given combination was equally likely to come up. Pleased with myself and with the laws of mathematics, I showed it to my dad, who immediately gave me a massive bollocking-out for having wasted a ticket on a number that was sure never to come up.<p>So I can answer the OP: No, you shouldn't, because you'll really piss off your dad.
This is actually one of the better ways of illustrating how low the probability of winning is.<p>When you pick random numbers, you might think that those look like the numbers that are usually drawn, and "almost every time, somebody wins so why not me?" etc. But then imagine that you chose 11111111. The idea that <i>this</i> is the combination that will be drawn is laughable. You couldn't possibly imagine it. It would be on the news, everybody would talk about it. Well, you have those same odds with your random numbers!
I've heard picking a lot of high numbers is a better strategy than picking pseudo-random numbers.<p>The logic is, sharing the prize greatly hurts the expected value (when N people win with the same numbers, they split the jackpot 1/N). Certain people like to play numbers corresponding to their birthday, anniversary, or other meaningful dates that range from 1 to 31. In the big US lotteries (Mega Millions and Powerball), the numbers range as high as 59, so picking a bunch of numbers in the 40s and 50s greatly reduces the chance of having to share the prize.<p>Another interesting story I've heard (no source sadly): one time the winning numbers were exactly the same as the "lucky numbers" printed on the back of a fortune cookie. An inordinate number of winners shared the prize, all Chinese food eaters who received the same fortune that week.
<a href="http://www.sbs.com.au/news/article/1093277/Identical-lottery-numbers-drawn-twice-in-a-row" rel="nofollow">http://www.sbs.com.au/news/article/1093277/Identical-lottery...</a><p>I'm reminded of this incident in bulgaria where the lottery came up with the same numbers two weeks in a row<p>Notice how EIGHTEEN people had to share the pot (presumably) because they thought they were being clever in picking numbers noone else would pick.
People who think all lottery numbers have equal value are mistaken. Division payouts are divided among the number of winners, so combinations that are less frequently used have a higher expected value.<p>Eg. numbers 1-12 and 1-31 are more often used as people play significant dates, leading to high numbers having higher ev (still negative though).<p>I remember reading a paper somewhere on this but can't for the life of me source it.
It should be noted that for the actual lottery, the advice given is wrong. Because in many real lotteries the first five digits can be in any order, 1 1 1 1 1 would be less likely than, say, 13 23 42 33 2, because, though there is only one way to end up with 1 1 1 1 1, there are 5! == 120 ways to achieve the latter (I am ignoring the "bonus ball").
I'm surprised no answer mentions the Kolmogorov complexity [1]. There's a fascinating link between how a given series seems "probable" to humans and its Kolmogorov complexity.<p>[1] <a href="http://en.wikipedia.org/wiki/Kolmogorov_complexity" rel="nofollow">http://en.wikipedia.org/wiki/Kolmogorov_complexity</a>
I dont play the lotto because the odds are terrible and I dont like the "OMG my life is awful but would be awesome if only I got lucky and hit the jackpot" attitude.<p>Whenever theres a big draw here I just buy 1 ticket of 123456. I really want it to win one day and watch the idiots come out of the woodworks and call it rigged. You would be surprised how many relatively smart people think that such numbers are more unlikely.<p>Its also funny to hand 35 cents over at the newsagents while everyone use is dropping at least $5 on the draw
Back in the 1970's, the Mafia ran a numbers racket in NYC (and Chicago and presumably other cities) that was very similar to the "Pick 3" game run by the New York Lottery. That is, you would pick a 3 digit number and if it matched the last three digits of the balance of the U.S. Treasury that day.<p>To add to the vig, the Mafia would not let you bet on numbers like 100, 111 and such, because they didn't want to have a big payout day. Of course, if any of those numbers came up they wouldn't pay anybody out.
Another point to consider is how is the winning number selected. Here the lottery numbers is decided through a powerball mechanism (<a href="http://en.wikipedia.org/wiki/Powerball" rel="nofollow">http://en.wikipedia.org/wiki/Powerball</a>). So given that there is only a fixed amount of numbered balls the winning number is drawn from, this skews the probability of the winning number being 111111 versus another random number.<p>For example normally, if the numbers chosen are truly random, the odds of 1111111 being the winning number is 1 / 10 000 000.<p>But lets say in the powerball bin, there is 7 '1' balls, 7 '2' balls and so forth, then the odds that first drawn number will be '1' is 7 / 63. That ball is then removed from the bin. The odds that second number will be '1' is now 6 / 62 etc.<p>That brings the odds of 1111111 to 7x6x5x4x3x2x1 / 63x62x61x60x59x58x57 = 2 / 1 000 000 000.<p>Quite a bit less... The effect will vary depending on how many balls of each number there is in the bin, and how balls are replaced once selected. Some powerball lotteries has a preselection draw which determines which balls are in the final draw, but the same argument is still valid.
Since lottery jackpots are traditionally shared among everyone who picked the winning combination, the only skill/logic in picking a number is picking one that you believe is an uncommon choice. That way, should you win, there's less people to share it with. And there probably is statistical evidence to back up the the idea that some numbers are chosen by people more often than others (ie: somehow everyone's lucky number is 7).
Take a coin. The winning flip combination will be a somewhat random sequence like:<p>> heads-tails-heads-tails-tails-heads<p>Now what are the chances that you're going to flip:<p>> heads-heads-heads-heads-heads-heads<p>Is that chance equal to you flipping the winning combination?<p>And I don't mean for this to happen anywhere between the first and the million'th try, <i>but the first try</i>.<p>Sequences have different entropy values, which means they are not equally random.
<a href="http://en.wikipedia.org/wiki/Entropy_(information_theory)" rel="nofollow">http://en.wikipedia.org/wiki/Entropy_(information_theory)</a><p>Edit:<p>Also (but unrelated to the above), can you look at it this way?<p>There are X amount of same-number sequences (ex: 2222222, 3333333).<p>There are Y amount of non-same-number sequences (ex: 2449776, 4553219).<p>Y >> X<p>If that is true, then getting a same-number sequence is not just as likely as getting a non-same-number sequence because if the lotto draws from a pool of all sequence numbers, there are much much more non-same-number sequences in there.
Of course, 1111111 has as good a chance of winning as any other number, but since most lotteries are parimutuel (i.e. the prize is divided evenly among all winners), it makes sense to try and pick a number that no one else is going to pick.<p>The Quebec lottery published their most popular numbers a few years ago [1]. They were:<p><pre><code> 7-14-21-28-35-42
1-2-3-4-5-6
4-8-15-16-23-42 (the numbers from the tv show Lost)
</code></pre>
Also, from personal experience, it seems that more people play "birthday" numbers (numbers 1-31) than higher numbers.<p>And, while I haven't confirmed it, I suspect that in games like Powerball, where winning tickets are determined by two independent sets of balls, people stick with their habit of choosing numbers in numerical order and not repeating numbers, so 4-12-17-24-36 (42) would be a more common pick than 4-12-17-24-36 (24).<p>[1] <a href="http://lotoquebec.com/loteries/nav/en/useful-information/popular-selections/accueil" rel="nofollow">http://lotoquebec.com/loteries/nav/en/useful-information/pop...</a>
Stupid question: the reason he's questioning the equal probability of 1111111 being drawn is because it <i>seems</i> significant. It looks like it is less likely to be drawn. But we know it is equally likely.<p>But forgetting the actual fair drawing process and just focussing on randomly choosing a number from a set of numbers...if you divide a set of numbers into significant-looking and insignificant-looking, would it not be true to say that a random choice is more likely to look insignificant and random, than significant and ordered, purely because there are far more insignificant looking ones?<p>(I'm not saying that 11111111 isn't equally likely to be drawn in a lotto here)
I remember reading several years ago that in the UK lottery 10000 people every week play 123456. And thus would be very disappointed at their £500 payout.
Yes you can use 1111111. The chance that you win is 50%, you do or you don't.<p>Now the 50% is ofcourse a little joke. But there is some truth in it. Randomness doesn't mean the numbers change all the time. The probability that the numbers change is ofcourse very very high. But random doesn't equal change.
For me, the easiest way to visualise that you have equal probability between the two sets of numbers is to simply visualise the balls, but without the numbers. Now, what are the odds of drawing blank set of balls A. Then, what are the odds of drawing blank set of balls B.
This needs to be clarified, because there are some games that play out of a single bin for all numbers and some games that play out of separate bins for each number. In the case of a single bin, a series like 111111111 is less likely to appear than a series like 123456789. The reason is that there are a finite number of balls in the bin. If there 9 count of each number of ball, then the probability of each ball i (from 0 to 8) coming up X in turn is (9 - i) : (81 - i), whereas any other number, in its turn, would be 9 : (81 - i).