You don't need to know number of wins and loses in a best of # series. You only need to "pick" which team will ultimately win the series. Hence the name pick'em. However: your math is waayyyy off if you think you have a 1 in 40 shot at getting the skin. To get the Riven skin you need to get ALL group stages correct and in the right order, and essentially get quater, semi, and finals correct too- all of them, not just some of them.
So you have to predict all 16 teams, in all 4 groups in the proper order of their performances (1st through 4th place) per group and only 1st and 2nd place gets to move on. I hate to break this news to you, but to successfully predict the group stage alone is
1 in 331,776
That's not even calculating the probability of the knock-out stage (quarter, semi, and finals)
The reason the number is so high, is because you have to predict the order too, so it's no longer 4 x 4= 16 x 16 x 16 x 16 (4 groups), but it's 4 x 6 = 24 x 24 x 24 x 24 (4 groups).
The probability of getting 1 group correct is 1 in 24 (because there are only 24 outcomes) based off order. However it gets much more complicated when you're calculating the probability of getting multiple groups right. Now to get two groups correct you have a 1 in 576 chance, because there are 24 times more outcomes for each group you add. Since this is multiplication this number grows faster the more groups you stack on it.
Only 1 Group Correct: 1 : 24 (4 x 6)
Only 2 Groups Correct: 1 : 576 (24 x 24)
Only 3 Groups Correct: 1 : 13,824 (576 x 24)
All 4 Groups Correct: 1 : 331,776 (13,824 x 24)
The reason you multiply by 24 passed the first group is because you can use the probability of the chances to correctly guess the first group, and stack them with the probability of getting 2, 3, or all 4 groups correct.
Here's my google docs for proof on Group Stage: https://docs.google.com/spreadsheets/d/14n17ew2lUoY8rJV93IJmFe5F2N4mxdYKScdf0_4tYmE/edit?usp=sharing
Your best chances, believe it or not, is to not just fill answers in with this insane amount of people to get different results, but to use past-team performances. Since these team's aren't random number generators you have a better chance at actually playing the pick'em the way it's meant to be played. For instance SKT T1 and LDG have really good chances of making it through groups, so you have a 50:50 shot (assuming I'm correct) at placing them in 1st and 2nd place in their respective groups.
Good luck with your search for ~500,000 people (don't feel like doing more math for the quarter,semi, and finals) :d
