Question: Exponential Growth - Game Theory

One thing I have always found interesting is that exponential growth/decay
is not symmetrical hence:

100*(1+0.01)^2+100*(1-0.01)^2-200 = 0.0200

For example:

If you start with 100 and bet 1% and you win and then again bet 1% of your portfolio value
and you win again your portfolio value will be PW=100*(1+0.01)^2.

If you start with 100 and bet 1% and you lose and then again bet 1% of your portfolio value
and you lose again your portfolio value will be PL=100*(1-0.01)^2.

Now you would think that PW+PL-200 would be equal to zero but as seen previously it is not!

Can anyone think of a situation where this would be useful ie game theory finance etc ?!
I mean very few games has serial correlation. We need to find for example a binary game {0,1}
where the probability of getting 1 at time t+1 is larger than 0.5 given that a 1 was obtained at time t.