Round Robin combination formula?

Hello

This is not my first post as I was on here a while ago seeking assistance with an excel problem that we managed to resolve

I am by no stretch an active forum user, but when stuck on a problem, where better to go than the people in the know, I might not have much to contribute, but I appreciate greatly the contribution of others.

The reason I am back here is that, yes, you guessed it! I am stuck but it is not an excel problem but mathematical and I am quite sure there are more than a few excel experts that also dabble now and then in mathematics and quantum physics and the like.

As it is off topic from excel I thought best to post here out of the way instead, but I really can not stress how much I am hoping someone out there with a brain that functions better than mine can lend assistance in any way!

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If you fancy a challenge and would not mind taking some time to help me out, I really would appreciate it so much!

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If a competition has 8 levels to it, each level has 10 teams competing in it and depending on the level, the teams in each level will either progress to the next round, repeat same level again, drop back a level or be knocked out completely.

Table_view.jpg

If I am correct with even this, then it should require 18,750 level 1's to be run in order to complete one final of 6 in level 8?

Level - - Games Needed
1 - - - - - - 18,750
2 - - - - - - 9,375
3 - - - - - - 1.875
4 - - - - - - 375
5 - - - - - - 75
6 - - - - - - 15
7 - - - - - - 3
Final of 6

If that is even correct then I am getting there, but with each level that is run also automatically assigning teams either to the next, same or previous levels, I know this drastically effects the number of actual teams to enter the competition in order to get the 6 teams in the final?

Example (bad one) - Perhaps only 4,500 games need to be played seen as so many teams repeat and fall back which pushes more and more teams towards the final 6.

New data.jpg

I got that far in attempting to try and work out how many of each level would actually need to be run, essentially and most importantly, how many teams would need to pay an entry at level 1 in order to get enough players to qualify through the system and get 6 qualifiers to play the final level?

Hope that makes some sense and really hoping someone can help? my head really hurts and I end up just staring at the screen like a zombie ;(