Hi
The discourse around the USA reaching a milestone has caused me to look at this list
https://en.wikipedia.org/wiki/List_of_modern_sovereign_states_by_date_of_formation
And im confused. 1801 certainly is a key date for the UK, but so is 1706. So is 1066 for that matter. And 1922. I cant really find a reason 1801 is the listed date that also makes sense with Germany being 1867 instead of 1991.
Any help greatly appreciated.
I have tried to find this and have found lots of methods for particular cases, but it strikes me as strange that there isnt a named standard probability distribution for a fairly standard type of game.
Two players play many rounds. Each round can be won or lost but not drawn. The game ends when on player has won 1+(N/2) rounds. Best of N.
It feels like it should have two inputs p = probability of player A winning a round (which we assume is constant and independent of previous round) and N the most possible rounds played. I am happy if we reconsider N as rhe number of required wins (first to N).
What id really like is some kind of hypothesis test where we see a result like 7-4 and we get some kind of confidence that the winner was actually the better player.