## Lottery and "special" results?

Here's something I always think about when filling my lottery tickets... the chances that the result would be 1, 2, 3, 4, 5, 6 are the same as the chances of getting 3, 7, 12, 13, 18, 27, right? So why is it that people would rather bet on the latter set of numbers? Is it because they consider 1, 2, 3, 4, 5, 6 to be special and therefore the chances of it winning are smaller?

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 Hey Chen You always bring up interesting topics Anyway, this actually sounds more like a pyschology question if you ask me. I don't think there's any rational for picking 1,2,3. etc... but as the 1,2,3 sequence seems more orderly and hand picked to the average person, it contrasts most with the random process of lottery picking more in the person's head than another random number (relative to the person), so that person is inclined to pick the number that seems as "random" as possible. I guess in other words when someone choses 7,5,2 over 1,2,3 for example, they realize the uniqueness of 1,2,4 and the incredible odds against them of that number being picked, due to their familiarity of it, but not the uniquness of 7,5,2 because it has almost zero meaning to that person, so they are inclined to pick a number which is not so blatently non-random. It's not random to them, so they don't pick it, but its random to the number-chosing machine which is why its as good as any other number ;) Mabye that made sense :-| So I think your original reason sounds right basically, 1,2,3 seems unique + special and therefore less "chancey" of it being picked
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## Lottery and "special" results?

My guess is that "people who buy lottery tickets would rather bet on...." is that people who buy lottery tickets are very bright to begin with!

 people in question correctly observe that combinations which they are familiar with almost never win, but they do not realize that it is simply because they are familiar with a very small percentage of possible combinations.

 Quote by HallsofIvy My guess is that "people who buy lottery tickets would rather bet on...." is that people who buy lottery tickets are very bright to begin with!
I only buy tickets once a year when the grand prize is like 50 million NIS!

Actually, it would be better to choose a sequence like 1,2,3,... not because the chances of winning are different, but because your chances of having to split the prize are lower if you do win. Also, it is a good idea to pick numbers larger than 31, due to the large number of people using their birthdays.

There is actually a way to increase your chances of winning small prizes in a lottery if you usually buy several tickets for each lottery. For example, the UK lottery pays ten pounds if you get three out of the six numbers correct. If you choose a sequence 1,2,3,4,5,6 for your first ticket, 2,3,4,5,6,7 for the next 3,4,5,6,7,8 for the next etc. then you increase your expected winnings from 10 pound prizes compared to picking sequences with no numbers in common. It is an elemenatary exercise in probability to figure this out. Unfortunately, this does not change the probability of winning the jackpot. Another elementary exercise in probability will convince you that no selection can.

 I only buy tickets once a year when the grand prize is like 50 million NIS!
It would be interesting to know the statistics of how many people do this sort of thing. Since a lot of people only enter when the prize is high, the chances of having to split the prize are higher and it might mean that the expected payout if you win is not that much larger, or even possibly lower than if you eneterd when there is a normal jackpot. If you are enjoying elementary exercises in probability, you can calculate this, assuming the number of people entering is a function of the prize money. If you are really enjoying this, then you can try to figure out a good statistical model and a way of estimating the function from data about lottery entries. Then you can figure out the optimal prize money level to enter the lottery. If you did that well, then you can apply for a job as an analyst in a financial institution, where the expected payoff is far larger than from the lottery.

 Well, think about it this way...the vast majority of possible picks are seemingly "random" sequences like 2, 17, 18, 25, 30, 32. So the probability that a random sequence will be picked is higher than the probability that an ordered sequence will be picked. So therefore you have a higher chance of winning if you pick a random sequence. (Of course, most people would reason this out thinking something less methodical like "almost all of the picks I've seen were random") Of course, this is a very good demonstration of very poor knowledge. The fact that the chances of a random sequence winning are higher doesn't mean that an individual random sequence has a higher probability of being picked than any other sequence. So while in reality it doesn't matter if your sequence is ordered or not, it seems like an ordered sequence is unlikely because there are relatively few ordered sequences.
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 You cannot increase the expected payoff by buying more tickets.
That's not what I meant. Suppose you do already buy several lottery tickets each week. Suppose also that there is a small prize for guessing a subset of the numbers rather than just a big prize for guessing all of them. Then, your expected payoff from the small prizes only (ignoring the possibility of winning the big prize) is larger if you choose overlapping sequences of numbers than if you don't.

Of course, I should have said expected loss is lower rather than expected payoff is higher.

 Think of the lottery as a wheel of fortune. The wheel would be about 25 miles in diameter for a 6 ball lottery. Each 6 digit lottery number would be .1 inch high so you could read it. You can, in theory, write down every possible lottery number, starting from 1 2 3 4 5 6 and ending with 45 46 47 48 49 50 for the old 6 ball type. That is what is on the wheel. There are 15,890,700 numbers in this simple old system. That is what you write on the wheel.