So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like
[....]
Your reasoning is correct, but the problem is that only the number of winning bets is not enough to tell you whether you will make profit, because you also need to consider the expected value for the odds.
For example... if every bet has odds of 2.00, then you lose 1 unit when you lose and win 1 when you win, with a mathematical win probability of 55% in the long-term edge is on your favor.... so far, so good! The problem is that, in the real world, the odds usually are n0t 2.00, they are generally lower. When this happens the probabilities work against of you and you have to rely more on luck to make a profit.
And there's another point... none bankroll is immune in the long run. Even if you find value bets, there may come a time when you hit a losing streak and several consecutive losses wipe out your bankroll.
Anyway, mathematics is perfect but sports betting goes far beyond mathematics alone, so do not trust blindly on numbers.