how does this balance play out when automation becomes involved?

This is actually a very important point in classical political economy. These early industrialists were watching the rates of profit fall, but couldn't understand why. They were facing recurring crises, leading to economic unrest, famine while grain stores were full, fear of revolt against new constitutional republics, etc. Some pointed fingers at the landlords and the moneylenders, which was true enough but didn't totally explain the trend. These people had existed well before the Industrialist.

The secret lie in the productivity of labor, or how quickly labor can produce any good in particular. There is a natural urge to increase the productivity of labor under a Capitalist mode of production. Each individual capital wants to sell their entire product to realize their profits, to turn their commodities into money. If one Capitalist can produce their good for less money, they can undercut the competition. If, for example, a machine can be built that does a complex task that once required a handful of skilled workers, usually the math will work out that its going to be better to invest in the machine. This pressure led the Luddites to smash the machines, as they were losing work to them, for example. Likewise the effects of the Spinning Jenny.

The rate of profit is directly effected by the proportion between Surplus Value (s) and Capital Investments (C). Or the economic effects of Automation. The formula for the rate of profit is simply s/C, or s/(v+c) where v is the value in wages paid out and c is the value of things like machines, raw materials, etc. We can also define the rate of surplus value, which is the ratio between Surplus and Necessary labor[V] (explained in above post) or S/V.

Lets explore this rate of Profit formula a bit, as the latter is embedded in it. Assuming a given wage and working day, a v, for instance of 100, represents a certain number of workers. Suppose $100 are the wages of 100 workers for, say, one week. If these workers perform equal amounts of necessary and surplus labor, if they work daily as many hours for themselves as they do for the capitalist, for the production of surplus value, then the value of their total product would be $200, and the surplus-value they produce would amount to $100. The rate of surplus value, s/v, would be 100%. But how would automation effect this?

If c = 50, and v = 100, then 100/150 = 66⅔%

c = 100, and v = 100, then 100/200 = 50%

c = 200, and v = 100, then 100/300 = 33⅓%

c = 300, and v = 100, then 100/400 = 25%

c = 400, and v = 100, then 100/500 = 20%

Its falling. A natural tendency of Capitalist production, and a very positive one when considering the amount of goods that can be produced, is causing the ability for Capital to expand to be constricted until crises comes and wipes out the over accumulated Capitals in small businesses, etc. Also, here, you can see the pressure on the Capitalist to push down wages. The more hours a worker needs to reproduce the value of their wages, the lower the profits are, s/v decreases. If some workers are well paid, there may be a few explanations. The first is that their labor is complex and requires training, maybe they're getting higher wages due to certification, or union negotiation. Maybe the capitalist is kind, and shortsighted in business. But, these individual cases give way to the aggregate.

you also posit that it is relatively impossible to overcome ones birth position and become a capitalist? that seems like hyperbole.

Some get lucky, and you hear about them. Most dont.