https://de.wikipedia.org/wiki/Lotto#Verwendung_der_Einnahmen
50% for is the gamblers
23% is diverted towards the charity you mention.
16.7% is taxes
7.5% is commission
2.8% is for running the business
In other words, the "Aktion Mensch" gives around 1/4 to those in need.
* Correction, "Aktion Mensch" give close to 1/3 to those in need and less to gamblers (also 30%). But they keep more to themselves.