re: Which Method Will Give a Richer Stock?

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Drop a bouillon cube in a half cup of water and another in a gallon of water. Which will have more flavor?

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The better analogy would be to then reduce that gallon of water to half a cup.

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If I put a bouillon cube in a cup of water, it will be weaker than if I put a cube and a half in 4 cups of water and reduce that down to 1 cup.

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Correct but you asked if the amount of water made a difference and it does. If it didnt you wouldnt need to reduce it.

Option C for me too.

The answer is method B but the difference would probably be slight.
If flavor is soluble, then using more solvent will ensure the maximum amount of flavor is being dissolved into the solution.

Solubility increases with temperature/pressure so that's why many of us use a pressure cooker and reduce to desired consistency/flavor.

I have some chem/math background but not an engineer.

Nooo that’s not how it works... sorry kosmo

Because. It just doesn’t. I don’t know the science but I know that it makes a difference

Stock is comprised of four components. A nutritional element (bones, meat), a vegetable element (mirepoix & aromatics), seasoning (bouquet garni of herbs & spices), and liquid (cold water).

Bones contain collagen which is responsible for giving stock its flavor & gelatinous texture. Starting the bones in cold water allows for maximum collagen extraction. The longer you cook the bones the more collagen and other flavoring elements will dissolve into the water.

Method A does not provide a sufficient amount of water to achieve maximum collagen extraction. In this method, cooking the stock long enough to dissolve all of the collagen will evaporate the water down past the bones leaving them above the water line. If the bones are exposed to the air, then they aren't contributing to the flavoring of the water. The only remedy is to add more water to keep the bones fully submerged which sounds like a PITA. Method B solves this dilemma by providing sufficient water to account for loss due to evaporation during the extraction process.

I'll stick to how Escoffier recommends to make stock and therefore my answer is Method B.

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In the medical terms that I'm more familiar with... It may give a statistically significant difference but whether or not there is a clinical (real world) significance is questionable

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Optometrist

How do you know that the solvent in scenario A is saturated? If it’s not saturated then adding more solvent isn’t going to hold more solute

But as you reduce it down, does the water continue to hold the solute beyond the saturation point?

I guess what I’m askin is if X amount of water is capable of holding X amount of solute, and you can’t dissolve said solute in X amount of water in the first place due to saturation, what checmial change takes place in the water during reduction that now allows the same volume of water to hold solute beyond saturation?