Lottery Pool mechanism

Now, there is a chance for everyone to select the ticket number he wishes. According to the lottery mechanism, there is a 61313/(141414*14) = 0.02639525198 chance for a ticket to match exactly two numbers with the winning number. And 0.001353602666 chance to match exactly three numbers. It means that if someone chooses the ticket numbers strategically, he can find a winning ticket for three numbers matches prize with at most buying 1/0.001353602666 = 738.76 tickets. The same argument is applicable for the two and four numbers matching prizes. We can have some lottery pools that people can delegate the right of choosing the ticket number to them. The winning prizes are directly sent to the winning ticket holders and there would be no prize sharing mechanism among users in the same pool.

This way not only the number of winning ticket increases, but also the probability of prize splitting will also decrease since the lottery pool tends to issue tickets with different numbers.

Another interesting thing could be allowing everybody to design their own lottery pool and strategy, and the pool owner can charge some amount of premium from the ones who want to participate in this pool. Hence, the better the strategy, the greater the premium.