I'm glad you mentioned your major, so I can go in to actual math instead of simplifying things as I did last time.
First, I'll apologize for misreading gamblers ruin instead of the gamblers fallacy - although I'll comment that we're in a case of the former rather than the latter.
My comments on the binomial distribution weren't to say that for large n it's impossible to attain k < n/2, rather as I said it was to show that the probability diminishes rapidly with large n. The comment on 16 billion years demonstrates the difference between my theoretical University and your more practical learning (via physics) - I'm branching on to the concept of infinite. Regardless if you are 0 out of a million trials, another 9 million trials would have expectation of 5m successes and 4m failures so that you would break even if you beat the expectation. If not, you apply another 90m trials, then 900m, etc... No matter how bad your luck is, I have an infinite number of chances to succeed on a 50-50 coin flip - I'll win eventually.
Anyways, explaining my previous post aside, time for the real content - this is a renewal theory problem (often known as the gamblers ruin).
The most basic version of the problem is set up as a random walk: starting at 0 you move up 1 with probability p and down 1 with probability (1-p). The walk is finite in the simplest version, and you find out the probability of returning to 0 exactly 0, 1, 2, etc... times for any value of p. The next step is an infinite walk, where the same applies but the walk goes on forever. Again, for given p the interesting problem is to determine the probability of returning to 0 a certain number of times before the walk wanders off to positive or negative infinite.
The gamblers ruin problem is the next step. It basically says you start at a certain amount of money, say $k, and move up $1 with probability p and down $1 with probability (1-p). You then find the probability of ruin for various p, I.e. The probability that the gambler ends up at $0. Typically you consider p <0.5 and the gambler doesn't quit, so he inevitably eventually loses everything and ruin ($0) is guaranteed. Next steps involve introducing an upper limit that the gambler decides to quit at, and given k and p you determine the probability of ruin.
Anyways, back to this particular problem, I stated that gamblers ruin does not apply - which is true because there is no lower limit, you can't reach a ruin of $0 because there is no $0. Rather, we're in the second case I mentioned in this analysis, an infinite random walk. With a simple random walk (p = 1/2) it has been proven that given infinite time every value will be crossed an infinite number of times. Thus, even with a 50% chance of the afk being on either team, you're GUARANTEED to not only break even, to not only reach breakeven an infinite number of times thereafter, but also to reach any arbitrarily (but pre defined) large number of extra benefits and extra disadvantages of afks. The flaw being that you have to let it go on for an infinite number of trials (ain't nobody got time for that! ). Alas, I am speaking in terms of infinite (again, see my 16 billion years comment as 'waiting forever') - this isn't wrong as you can always play more games. Anyways, from that point, it should be obvious to see what happens when we increase p to > 0.5, or in this case p= 0.55556.
If not, we can look simply at the problem where you want to get ahead. I.e. starting at 0, what is the probability that within an infinite number of steps we'll reach +1? The solution to this is {1 if p> 1-p, p/(1-p) otherwise}. Since p > 0.5, p > 1-p, and thus the probability is 1. In other words, given enough time you are guaranteed to come out ahead - exactly the point I made in the first place.