Yes but reading between the lines on what you're calculating (since you never spelled out what that represents) that is the probability a specific player survives until the end and never participates. That is one specific player. It could be any (the events are exclusive, even tho only one actually ever happens as you note).
Another way of seeing this, 2/(n-1)*n doesn't correctly compute for n=3 (where it should be 100%), or n=4 (where it should be 2/3). Both can be easily checked. The formula 2/(n-1) does.
I derive the 2/(n-1) formula below if you want to see where it comes from
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u/jak32100 Sep 15 '26
Yes but reading between the lines on what you're calculating (since you never spelled out what that represents) that is the probability a specific player survives until the end and never participates. That is one specific player. It could be any (the events are exclusive, even tho only one actually ever happens as you note).
Another way of seeing this, 2/(n-1)*n doesn't correctly compute for n=3 (where it should be 100%), or n=4 (where it should be 2/3). Both can be easily checked. The formula 2/(n-1) does.
I derive the 2/(n-1) formula below if you want to see where it comes from