Yes, the money is regarded as the server's money in the scenario I described. But it was also considered good form to tip out back of the house. My kid had a great relationship with everyone back of the house because she never neglected this, even on bad nights. In return, her orders were up pretty quick.
I admit that I am really torn regarding tips. I know how much my kids have depended upon tips for their livelihood. They were lucky enough to work in some pretty decent to extremely good places so that helped with the tips. I know that dishwashers get paid crap and cooks don't get paid decently either.
In my ideal world, everyone would earn a decent wage.
I've worked in anti-poverty programs before, so I've seen the problems low wages create (and have lived it, too, although I was lucky that it was brief). My town is extremely working class, with local employers paying very poorly and offering terrible benefits packages. When they can, they limit hours available to just under the minimum required to provide even those terrible benefits. What this does is create a large group of people who live so close to the edge that they often fall off of it, even working two or three part time jobs. The stress that this creates in their life simply makes their situation worse. It greatly increases the amount of substance abuse, mostly alcohol, but not entirely. It exacerbates mental health issues, physical health issues, weight issues, education issues and effectively robs their kids of parents who have the luxury of doing anything other than parking their kids in front of a screen while they try to recover from their day/night. It adds to instability of marriages and other relationships. It creates and maintains an underclass which needs the largess of the more fortunate just to survive. Employers use unreliability of workers to justify low wages, refusing to accept that their low wages create so much stress and financial insecurity that they must juggle multiple jobs, constantly worry about their kids, worry about losing phone and lights (in winter, you cannot have your heat cut in my area), their homes. And so, they drink. A lot. Which is not a good way to solve their problem and only creates more but it is easily available and lets them escape for a few hours from the unrelenting stress of not being able to make ends meet.
Access to better and affordable job training and educational programs would really help--but I know plenty of people with good degrees working some pretty low paying jobs.
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I'd think it's a nice idea if the employers were required it divide the tips evenly, but they were also privy to what servers were getting tipped or not.
And no, I have no mathematical equation to know that I'm right or wrong.
:EDIT:
And if you eat out, you always bring cash
I ALWAYS tip in cash, even if I am charging my meal. And I tip well. Applies to the wonderful woman who does my hair and any other tip-dependent person I encounter.