Just wondering if everything else being equal does OG affect FG? For example, if I make two batches with one having a original gravity of 1.050 and one having an original gravity of 1.070, The Grain bill is exactly the same except for amount, with appropriately increased yeast for the higher gravity beer, both mashed at the same temperature, and everything else kept equal, will the final gravity be the same or will the higher gravity beer finish higher for some reason and why? Somehow I remember when I first started Brewing if you try to make a very high gravity beer you have to add sugar to get a dry beer?
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If you truly keep everything equal except the OG, then the attenuation of the yeast should be equal. The attenuation is the percentage of sugars consumed by the yeast. If your attenuation is 80% for both batches, then your FG would be higher for the batch with the starting OG. It is easier to work with gravity points instead of specific gravity, so your batches would start with 70 and 50 points. The final points would be OG*(1-A), where A is the attenuation. If A is 0.8, or 80%, then the final gravity points would be 14 and 10, or FG of 1.014 and 1.010.
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To add to Richard’s explanation, if your grain bill includes a percentage of unfermentable sugars from, say, Crystal or roasted malts, there will be more of that in the final volume of the higher OG wort, resulting in a higher FG. Adding sugar (corn=glucose or candi=glucose+fructose) does give you a higher percentage of fermentable sugar and, perhaps, a higher apparent attenuation. But in general the %attenuation will be the same in both batches. The FG includes a percentage of the fermentable sugars (attenuation) plus the unfermentables.
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