So, this causes a lot of people a lot of confusion, so I thought I'd explain what I think I've figured out and maybe someone can explain Combustion Heaters? Most importantly, nothing in the mod, as far as I know, is random chance. All of the percentages, at least for the below machines, are just decimal/fraction math.
Alchemical Fusion Table
They're actually pretty simple.
Each recipe has a "% of catalyst used", and the fullness of the green bar to the right of the catalyst slot shows you how much of the last piece of catalyst you used is remaining.
The "yield" on each type of catalyst (i.e. Primus at "75% yield", Secundus at "175% yield") tells you how much of the purple bar to the left of the catalyst slot each piece of catalyst will fill per batch of input items. You will get 1 output for each 100% "stored" in the purple bar at the time of the operation.
For Primus dust, this means that:
The first use (e.g. first batch of input items) gives 75%, so it will use up 1 set of input items but give no output!
You'll need a 2nd batch of inputs to reach 150%, which will give you 1 batch of output (however much the recipe you're using gives) and leave 50% in the purple bar afterward.
A 3rd batch adds another 75% for 125% in the bar, so you'll get another batch of output and 25% will remain in the bar.
Lastly, a 4th batch adds a final 75% to the bar for 100%, so you'll get a 3rd output batch and nothing will remain in the purple bar.
Since the 1st batch using Primus will always "waste" your input items, you may wish to first "prime" the Fusion Table by sacrificing a relatively inexpensive set of inputs (like a piece of glass) for the first 75% of purple. Your next 3 input batches will then yield 1x output each.
Secundus dust improves to 175% yield, so your first batch will give 1x output, and your next 3 batches will give 2x output each, for a total of 7x output for 4 input sets. You could, of course, prime this with glass instead, to get 2 Crystal Shards and 6x output for the next 3 input sets.
Tertius dust yields 450% per, so your 1st batch will give 4x output, and your 2nd batch will give 5x output and reset the cycle (so you'll always get 4x, then 5x, then 4x, then 5x, etc.)
Condensers get more complicated. First, you'll always use 1 block of Liquid Crystal (and thus 1 Crystal Shard) or 1 Stone per output item. An incomplete output does not use any Liquid Crystal or Stone, but will waste Alchemical Dust. But figuring out how much Alchemical Dust is used requires some math. Here's how to do it:
Each pair of Casing and Condenser give you a different Speed and Efficiency/Production, which you can see inside the Condenser interface (or calculate yourself, by taking the Speed of the Condenser and multiplying the efficiencies of the Casing and Condenser). For your 1st Condenser, Stone/Stone is recommended, which give 80% Speed and 100% Efficiency.
Next, each Condenser recipe has a Tick duration and % (Alchemical Dust) per ingot. For example, Liquid Crystal and Iron Alchemical Dust have a 249 tick duration (at 100% Speed), and use 0.2875% of an Alchemical Dust per tick (at 100% Efficiency).
To adjust this for Stone Condenser & Stone Casing, we divide the duration by our speed as a decimal (80"%"/100 = 0.8). So 249/0.8 = 311.25 ticks. But there's no such thing as a partial tick, so this is (AFAIK) rounded up to the next whole number (312 ticks). Our efficiency is 100%, so the 0.2875%/tick is not changed.
Next, we multiply our tick duration and %/tick together to get a % Alchemical Dust/output. In the current case, this is 312 * 0.2875 = 89.7% AD/ingot.
To figure out how much Alchemical Dust you'll need to get a certain number of ingots, just multiply this result by the number of ingots you want and convert the percentage to a decimal and round up. So 4 ingots would take 358.8% of an AD, which is 3.588 as a decimal, rounded up is 4 AD.
The green bar to the right of the AD slot shows how much of the last AD is remaining.
You can experiment with a calculator or use tools like this or this more complicated but more complete tool to find AD and ingot numbers that give you a little extra! Keep in mind that only fractions greater than (or, technically, equal to) the decimal are valid. For the others, you will be 1 ingot/ore short. So for the 89.7% = 0.897 as a decimal that we found before, approximations include 9/10 (so 9 AD for 10 ingots) = 0.9, and 61/68 (so 61 AD for 68 ingots) = 0.8970588235294118. Those are the basics. I'll leave it to other users to link spreadsheets for AD/ingot pairs they've found.
Note: to use the 2nd link, make sure "Only Better" is checked and put the maximum number of ingots you could possibly want to make at once (manually) into the "Limit" box. The first number on each line can be taken as the amount of Alchemical Dust used, and the 2nd number as the number of ingots made. The 3rd number (a decimal) must be negative or 0 for the line to be valid.