Recently I was around a physical bet shop close to my area and I observed a man who was shabbily dressed walking in the gambling house. I got into the place to observe what his intentions were. He walked straight to the gaming attendant, placed his bets in a highly coordinated manner and quietly walked out of the physical gambling house. From the way he was well organized, you will never know that he was mentally unsound apart from his dirty clothes and unkept hair and beard.
When I inquired from the attendant, she said he was a regular customer and that he usually raised money for gambling through the manual jobs he does around the area. She also told me that he has never misbehaved and acted violently in the gambling house so she was comfortable with him.
My question now is are there any moral, ethical or legal obligation to bar a person from gambling after physically observing that he is mentally unstable?
Frankly it is a slippery slope to try and judge whether someone is mentally unstable, or what is behind their actions. You start entering the area of discriminating against someone for a disability or how they look. While most shops are free to reject doing business with anyone they like, you'll find that casinos or bookmaker shops are some of the last places you'll see someone being prevented from entering to bet. If someone has gotten very angry or even aggressive then they should be removed, but that is probably the only reason they would stop someone betting there. You can find some rather rich people who don't necessarily wear the nicest clothes or even look after themselves particularly well, but they should not be rejected on appearances only.