Just some quick mathematics.
For a given engine, let's say the 2.0 TDI CFHD engine in my backyard
Stroke is 95,5mm
Bore is 81mm
Compression ratio = 18:1
Compression ratio = (swept volume + combustion chamber)/combustion chamber
Swept volume = pi * (bore/2)^2 * stroke = 492 cc
18 = (492+CC)/CC --> CC = 28.94cc
Head gasket comes in thickness 1,55mm, 1,63mm, 1,71mm (03L103383BM, 03L103383BN, 03L103383BP)
Volume of head gasket is [1,55 1,63 1,71] * pi * (bore/2)^2 = [7986mm3 8399mm3 8811 mm3]
With standard head gasket, combustion chamber = head gasket + residual volume
So residual volume = 28940mm3 - 7986mm3
Combustion chamber with 1.63mm = residual volume + 8399mm3
Doing some math, the compression ratio with 1.63mm
Compression ratio = (swept volume + combustion chamber)/combustion chamber
CR = (492cc + 28940mm3 - 7986mm3 + 8399mm3)/(28940mm3 - 7986mm3 + 8399mm3) = (492 cc + 29.36 cc) / 29.36 cc
CR = 1 : 17,75
Same trick with 1,71mm -->
CR = (492 cc + 29.77 cc) / 29.77cc
CR = 1 : 17,5
Lowering compression ratio can help an engine with severe boost levels.
Increasing compression ratio can help an engine with efficiency and horsepower