For example we through a coin 100 times and the amount of heads and tails aren't the same. Now we bet the next toss will be the one that happend less.
We will repeat this process until we got enough data (no idee how to define enough but that's not relavant).
Will bet more often right then wrong? And why?
From a pure mathematical point of view what happens in the past should not influence the present toss. If you obtain head 100 times in a row but your coin is fair, the probability to obtain head at toss 101 is 1/2, and the probability to obtain tail is 1/2 as well. This is the key probabilistic notion of independence.
On the other hand, if you play this game in real life, you can adopt a statistical point of view. If 100 tosses gives head, you might assume that the coin is unfair, and biaised towards head (typically if in fact for each toss, P(head) = 0.99, 100 head in a row is not so unusual). So in some sense if you know nothing about the coin at first, the best strategy is probably to follow the momentum, i.e. to bet on the result that has appeared the most.
