You need to understand how yeast works; it’s different to what you appear to think.
Yeast doesn’t want to make alcohol at all, that’s it responding to an environment where it can’t reproduce which is what it really wants to do.
In a wort yeast will make yeast until it runs out of any one of a number of "nutrients" that it needs. We as brewers make a wort, in it are things we want and some stuff we don’t want but that yeast will metabolise. The most important are Oxygen, Lipids (fats/oils) and some Proteins (among others).
Part of being a good brewer (or kit manufacturer) is to have all the bits and bobs in balance so that the yeast eats (metabolises) all the things we want removed from the wort at about the same time.
It also reaches a large enough population to turn the remaining sugars into alcohol in a timely manner, without making too many nasties like Diacetyl.
We are left with a wort that will make good tasting beer without much of the stuff that could cause harm to the flavour (see above).
In theory if you added 1 yeast cell, or 1,000,000, you would end up with the same amount of yeast (roughly) by the time the vital nutrients were used up in yeast reproduction.
The problem is that during reproduction the yeast will make some off flavours along with some we like (i.e. esters that give fruity flavours and aromas). Smaller pitches (amounts of yeast added at the start) will spend longer getting up to population and will make more off flavours.
The other big problem is that the smaller the pitch, the bigger the chance of bacteria getting a start. As bacteria can reproduce at least 20 times faster than yeast, a small number at the start can become a raging infection pretty quickly. Note there probably has never been a wort that isn’t infected to some extent, fortunately most of the things that get a start in our beer are benign.
And here come the really clever part:-
Yeast when it can’t reproduce will start making a really powerful bactericide (Ethanol) that kill its neighbours so that when conditions change it can have somewhere to live. Its conducting chemical warfare and that makes us happy
Add all the bits up and that’s why there are recommended amounts of yeast to add, and recommended amounts of oxygen to dissolve in your wort. Not so important for dry yeast but really matters if you are reusing a yeast slurry from another brew.
Sadly kit makers supply a bare minimum of yeast (often less), most brewers opt for better and bigger yeasts.
The amount of yeast to do the best job is usually given in the form of cells/mL/oP
Cells - number of yeasties; mL - the volume in millilitres; oP - the wort gravity in Plato
To get from SG to Plato the rough enough equation is SG=(4*oP)/1000+1. We can rearrange this into
oP=(SG-1)/4*1000
If your SG was 1.050, oP=(1.050-1)/4*1000 = 12.5oP
The "standard" pitch for Ale is 0.4-1Million cells/mL/oP. If you are given a range and don’t have a dam good reason, start in the middle say 0.7M/mL/oP
If you were doing a half sized brew say 11L with an SG of 12.5oP
You would want 700,000*11,000*12.5 = 96,250,000,000 cells in a simpler form 9.625x10^10
In the attachment you can see that US-05 (one of the best selling dry yeasts) there are 6x10^9 cells/g
From there 9.625x10^10/6x10^9 cells/g says you should pitch 16 grams
As it comes in 11.5g packs, you can see why I said kit makers skimp, I would use a whole pack in a half brew.
You can also see it says 50-80g/hL (hL=100L) or 5.5-8.8g in 11L
There have been some pretty lively discussions on AHB over the years on this subject - let’s not start another war (please).
One of my favourite sayings about brewing is "Everything ends up in the glass"
If you change the amount of yeast (or anything else) it will change your beer!
Mark
Sorry
Rainy Sunday too much time on my hands, I hope you didn’t expect simple answers to brewing questions.
Recomended
Ale 0.40-1.00 Million cells/mL/oP
Lager 1.00-1.65 Million cells/mL/oP
Dissolved Oxygen 8-12 ppm (mg/L same same) 10ppm is the sweet spot.
M