Excel / Maths problem - please help!

getmore4less

This is an integer problem so the inputs should be the integers not a pre calculated rounded %.

Your second post has 322 games with a win rate of 59.36% that does not match the potential wins of 191(59.32%) or 192(59.63%)

you also have the issue that each time you add a game it could be a win or a lose that moves the % a bit
That means the target may be hit over a range of games depending on the win/loss of the next game

if we allow you could have a winning streak over short number of games say upto 20  while up to that point you have been playing to the rate of those those 322 games never going below that rate 
you could go over 54% by 1450 games  by 1500 you only need a win run of 15 and by 1550 8 in a row.

Using 191/322 as the input never going below that ratio of wins,
you hit 54% for the first time at 1600 but you need to have played 1611 games to stay over 54% with that win rate.
 

new games	new wins	total % wins
1595	947	53.9995%
1596	947	53.9948%
1597	948	53.9988%
1598	948	53.9941%
1599	949	53.9981%
1600	950	54.0021%
1601	950	53.9974%
1602	951	54.0014%
1603	951	53.9967%
1604	952	54.0007%
1605	953	54.0047%
1606	953	54.0000%
1607	954	54.0040%
1608	954	53.9993%
1609	955	54.0033%
1610	955	53.9986%
1611	956	54.0026%
1612	957	54.0066%
1613	957	54.0019%
1614	958	54.0059%
1615	958	54.0012%

WaywardDriver

Leaving aside the maths, who are the OP's opponents? Other players online or a computer program? I'd guess the OP would want to improve his game by playing against more skilful opponents which would affect his win %'s.  Are the online players random, does the computer opponent have a skill level?