Interesting question, which necessitated some research. My normal routine is a two pass, with and against, DFS, sometimes DFS+. Three gets BBS. The block often produces a mild sting unless I try to go to bare metal on a tough spot, then it gets serious. By the way, daily shaver after shower.
Methodology: After each pass, rinse the residual lather and apply the alum, evaluate, then wash face with soap and rinse well.
First trial, a blade with two shaves on it (Usually get 3-4).
First pass (WTG) - No stinging whatsoever, but the alum block was scratched pretty heavily.
Second pass (ATG) - Very slight sensation, not quite stinging, no scratches appearant on block.
Third Pass (XTG) - Very slight stinging in some places, block smooth.
(Not the standard order, but it works for me.)
Second trial, new blade.
First pass (WTG) - No stinging whatsoever.
Second pass (ATG) - No stinging.
Third Pass (XTG) - Very slight sensation.
I had expected a greater amount of sensation/stinging than I encountered, and the shaves were very smooth.
Could the effect of using the alum, even though washed and rinsed well between passes, have "tightened" my skin leading to a closer shave?
Been using the crystal alum sticks as a deodorant for years with good results. However, they do not prevent perspiration, that's aluminum chlorohydrate I believe.