Should I pick entirely different numbers on each lottery ticket? I was discussing optimal lottery ticket purchasing strategies with a friend, and an interesting question came up. 
Suppose you doing the following:


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*You purchase multiple tickets for one draw

*You select the option to pick the numbers at random for all tickets


It occurred to me that if the numbers are selected at random, then it would be possible - indeed quite likely if you buy several tickets - that some number(s) may appear on multiple tickets. A quick Google confirms what I expected - that the random number selection process for my local lottery is independent for each ticket even when you buy them together and for the same draw, so this would be entirely possible.
This had me wondering, does this factor decrease your odds at all, and if it does, could one improve upon the process of randomly selecting each ticket independently to improve things? Perhaps this is just a more specific version of the general question - should you avoid repeatedly selecting the same number across multiple tickets on the same draw?
The parameters of the draw are:


*

*Numbers are 1-59

*Six numbers are drawn

*Prizes start at three numbers, increasing in size up to all six


Having not studied maths in any depth since my college days, I'm unsure how to frame the problem mathematically, so I'm interested both from a mathematical point of view and practically.

For the jackpot, you only care if the set of six numbers is different between your tickets.  Having tickets 1,2,3,4,5,6 and 1,2,,4,5,7 gives you the jackpot on two different draws and gives you twice the chance of winning that you would have from buying only one ticket.  
The downside of these two tickets is that many combinations of three numbers are repeated.  You are not increasing your chances of the smaller prizes as much by buying these two tickets as you would by buying two tickets that do not share numbers.  Even for this, you only care if at least three numbers match between two tickets, so having 1,2,3,4,5,6 and 1,2,7,8,9,10 is as good as having two tickets that disagree completely.
Presumably if you get a set of three on multiple tickets you get paid multiple times.  That means the expected value of two tickets with overlap is the same as two without overlap.  You will win less often, but some of the time you do win you win more money.  
The arguments of picking unpopular numbers only matter if there is a jackpot that is divided among the winners.  In that case you want unpopular numbers so you share less.  If the payout even for six of six is a fixed amount, you don't care about the popularity of the numbers, but the operators do.
