I am used to carrying a minimal amount of cash while traveling to a destination and using my ATM card or credit card to get the local currency when I get there. That was the wrong approach for Japan and we would have been in big trouble if we hadn't had a friend who lived there.
I quickly learned that our American ATM card didn't work at cash machines or banks there and our credit cards were virtually worthless. We learned from our friend, Tom, who was living there, that Japan is a cash society and we needed to get used to carrying lots of money around. When I expressed concern about doing so, I was told not to worry because there is little crime or theft in Japan.
An example our acupuncturist gave us was, "If you forget your sweater on this bench, you can come back in a week and it will still be there, neatly folded with your money still in the pocket." She explained that the lack of crime is largely due to the high social and economic penalties for breaking the law and, even more devastating, the shame that committing a crime brings to the families of those who do it.
A news story that broke while we were there emphasized her point. An executive and his wife were found dead of suicide and it was attributed to their son having been convicted of embezzlement the day before.
So, when going to Japan, bring a lot of cash tucked into the back pocket (the one next to your body).