I agree with Donny & Eddie re: the private party type gigs, but for regular 'on going' 4-5 hour club/piano bar gig dates, it's generally 45-50 on / 10-15 off per hour, but you soon realize you can't go by these rules if you want to keep the house happy and make great tips as well. Flexibility is crucial. If the room's really hopping, and the bar is selling lots of drinks, you skip your breaks(s) and take longer breaks when the room slows down, sometimes never. You have to pace your playing to the 'mood of the crowd' which can be unpredictably different every night.
Though I no longer play piano bar gigs, I do remember quite a few nights having to play 4-5 hours straight without a break.

I appreciated the lucrative tips

but now I think I'd prefer the breaks instead. The number of tunes I'd do in a set vary from 10 to 14 songs, depending on how much stage patter (which is also important) there is. This also has a lot to do with the energy of the crowd too. On a busy night, you might squeeze in more songs whereas on a mellow slow night, you can take a lot longer to chat & smooze between songs. The bottom line, you need to pace your set to the mood of the evening. As you can tell, being a good musician is only a small part of the requirements of a solo musician-performer.
I remember a bartender telling me (when I first started out gigging years ago) to intersperse my set with fast - slow - fast- slow songs etc. I quickly learned how ridiculously inappropriate that was. Every evening, and crowd is different. You quickly learn to gauge each night 'as you go' as to what 'appropriate' songs should be played, and when. There are a number of techniques used to draw the audience in (group participation songs, hi energy numbers, etc), but once you got them , you can then take them where you want : sophisticated ballads, originals, etc. As performers, we are responsible for orchestrating the mood of the crowd. It's our job to know WHO your audience is and what they want on a given night. Psychology 101.

Scott