Sorry for answering for John, but when you put a puzzle in front of me I compulsively have to answer it. Completely understand its annoying, and you want Johns answer not mine. I had to do the math myself though, figured Id share in case anyone wanted it too.
The math is really difficult, changes wildly week to week, and is largely impossible to predict ahead of time. If you start with a simple permutation on this weeks small slate of two games, decide to play all chalk and say 3 QBs are playable, 5 RBs, 7 WRs, 2 TEs, 2 defenses, and 3 kickers there are 75,600 different possible lineups. From there you need to be able to predict ownership in order to get a feel for exactly how far outside the box you need to get. If you were to play the most popular player at each position and say their ownerships are as described below:
QB: 40%
RB 1: 75%
RB 2: 50%
WR 1: 80%
WR 2: 66%
WR 3: 60%
TE: 40%
Kicker: 40%
Defense: 40%
The likelihood that someone has that exact lineup is .3%, not 3%, but .3%, so its still very unlikely. If you have 172,000 entries though that lineup can be expected about 524 times. That scenario is the definition of negative EV. You would need a contest of atleast 658 people to expect that lineup to duplicate. That isnt really true though, the reason is at the end.
If you change the 60% owned WR to a guy like Janis, who lets say is 1% owned then youre looking at 8.7 duplicate lineups expected in a field of 172,000. To get to the point where you expect to have a unique lineup in a field that large youd also need to swap the 75% owned RB with a 25% owned one, and the 80% WR with a 25% one. In a small field, or with lots of options like during the regular season full slate contests you really dont need to get all that cute to get to the point where you expect a unique lineup. If anyone is interested I coded a quick excel spreadsheet to do that math for me, youre welcome to it if you want it.
The problem is that that math doesnt really work for DFS purposes, each position is not truly a unique event. If you play Cam this weekend you are likely going to play Olson over Gronk, and youre almost certainly not going to play the Cardinals defense either, even though simple probability formulas are going to assume you will with an equal likelihood. I dont think its possible to predict that ahead of time with any kind of certainty either. Im sure theres more complex formulas ( and I have a rough idea of how to long form it in a spreadsheet thatll Ill add to) that would do a better job, but theyre well above my head.