score:5
Most answers to this kind of question say that, as a foreigner, you should have it with you.
The probability that you will be stopped and asked for identification is really low (not zero, but close to it) while doing simple tourist activities.
Be safe, just keep it in your belly pouch; in day to day operation, you should not have to handle it, so not a big hassle.
If you want to leave it at your place, you could have photocopies of your passport with you.
Anecdotal, I leave it at my accommodation, never had problems, never was stopped by police or asked for it (other than normal usage when check-in hotels or traveling)