Ok hope this helps. We do carpet cleaning and are fully trained by Prochem in Chessington.
There guide suggests
Apply
Solvex and blot and note if ink is readily released. If so, this indicates a solvent soluble dye. Repeat as needed. Blot, do not rub, to avoid spreading spot. If stain persists, apply
Citrus Gel (or Stain Pro for water-based inks). Rinse thoroughly with water and blot until dry. Note: All inks are not the same and different approaches may have to be evaluated.
Although I dont clean casino tables, I do have a casino table. I have had ball point pen on it. Kindly put there by one of my kids having an artistic moment. Let me say I was not best pleased. But I did remove it with the Citrus Gel.
There products can be obtained on the website.
http://www.prochem.co.uk/chemicals.htmI will just add here, be patient. Very patient. Do not rub at all, Casino cloths are delicate and you could end up having to recover the table. So blot by pressing down on absorbant tissue, White.
ALWAYS TEST AN INCONSPICUOUS AREA! ON EACH TABLE YOU CLEAN.
Dave