Forecasting Lottery I do understand that all lottery has a negative mathematical expectation but I am wondering, if we have a set of historical data of the winning numbers, is it possible to increase the winning chance? 
I also do understand that each round is a independent event but according to this theory where you roll a dice $n$ times, you each side should get $n/6$ times as $n \to \infty$.
So my questions is, does such a function exist to increase the winning chances of a lottery?
 A: While Joe Zeng's answer is certainly theoretically correct, as the practice shows sometimes it is quite possible to increase the chances to win a lottery. All of us (well, most) remember the story of Smoke Bellew by Jack London, that noticed that one roulette was dried and got some numbers with greater probability than others. Here is another story which shows that good knowledge of statistics might be very helpful. I will leave all the details to my link, the story is really worth reading.
A: No.
Because different events are (meant to be) independent, the probability of each lottery being a certain result is unaffected by previous results.
The theory you are referring to is the Law of Large Numbers, which is only a statistical trend (rule) and not a certainty.
A: In many lotteries, one shares the grand prize with all the people who picked the winning set of numbers. 
Lotteries in the main pick the winning numbers by a process that simulates randomness well. However, the number choices by lottery players are anything but random. If one stays away from the popular sorts of choices, one can increase one's probability of not having to share, in the highly unlikely case that one happens to pick the winning numbers.
A number of lotteries maintain and publish statistics on the numbers that bettors have chosen.  
A: About rolling the die, I will explain by example: Suppose that you have a six sided die, numered 1 - 6. The "expected value" of a roll is 3.5. This means that if you roll the die many times, say 1000, and write down the number that you get each time, the numbers will average out to 3.5. It does not mean that you can forecast that on the next roll, you will have the number 3.5 come up. If the person rolling the die is trying to make it land on a certain number, then it is equally likely to land on any one side when rolled.
The organisers of the lottery also calculate expected value. If many people play the lottery, then on average, they are making a profit. 
I have read a story about a team calculating the physics of a roulette wheel and placing bets accordingly.
