The Semi-Adventures of a Nomadic Mathematician Rotating Header Image

The Intricacies of Tipping

Tipping is a procedure nearly as complicated as cooking. It introduces so much complexity into transactions that I believe a part of the human brain evolved with the sole purpose of taking care of tips. This part of my brain is chronically underdeveloped.

The mathematical part of tipping is easy: you are given a parametric equation that regulates the amount of the tip. The parameter depends on the country: in the US, it is 30 to 50 per cent, in Japan, it is zero. So you have to pay a bill of a figure x in the local currency, plus the tip as regulated by the parameter p. The total is (1+p)x. So far so good.

Restaurant in Japan

No need to tip here.

This value is a real number, and you have to discretize it to match the denominations of the currency. Furthermore, you must also pay attention to what denominations are available to you. Now we are talking about an NP-hard problem. This is a nasty instance of constrained integer optimization. Solving it takes an exponential amount of time.

If the optimization problem has a valid solution, pay the amount. If you do not speak the local language, and you cannot get the message across that you no longer claim ownership of the money handed over, just leave the money there and dash off.

Awkward situations arise when the optimization problem does not have a valid solution, and you have to tell them how much money you are willing to part with, and how much change they should return. This is the true complication in the transaction.

Some countries make it easy for you. In Japan, for instance, nobody would accept tips, so you are saved from all the trouble. China is theoretically similar, tips are rare, but they get around it. Fake bills are common. If the staff feel they need a tip, they take your money, and return to you in a minute with a fake bill, claiming you used the fake bill to pay. In turn, you must pay again with a real note. This ritual relieves you of a hundred yuan every now and then.

Singapore sanitized the whole affair and introduced a legalized version of robbery, marked by a varying number of plus signs after the price of the items you covet. The number of plus signs is correlated with the percentage that will be added to your bill. Even if the service is disastrous — which is often the case — and you do not want to tip, a service charge will be added to your bill. You will be able to pay by cash, cash card, your public transport card, local electronic payment system, Chinese electronic payment system, debit card, credit card, and even by check.

The complication remains unresolved in cases when you have to calculate and handle things manually. The US is awful in this regard, as a huge percentage of tips is customary — tips make up the majority of the earnings of the service personnel. Places frequented by Europeans often have signs reminding patrons that tips are higher than in Europe. You get the evil eye if you are being a cheapo and tip only 20 per cent. The good thing about the US is that many people speak at least some English, so in most cases, you can pay exactly the amount as the solution of the parametric equation requires.

Wall St

Tip here generously. The nation is built on tips.

The exchange becomes even more convoluted when you are clueless about the local lingo. Try to get your correct change back on a fifty-euro note in France for a bill of thirty euros plus tip. That takes a lot of patience. I often found myself not tipping to save effort. I earned countless despising looks for doing so.

One fine day I decided to dedicate a budget for tipping to understand the intricacies of the mechanism and get comfortable with it. I forced myself to tip, and prevent myself from bailing out without tipping. No matter how terrible the service was, even if they ignored me for an hour and brought me scorched bits of dead animals instead of the lovely vegan dish I ordered, I tipped. I churned the calculations of the constrained optimization problem. I introduced a secondary storage of smaller bills in a pocket to always have a stash to tip with. And I kept smiling at the grumpiest waitresses as they were collecting their reward for being part of my experiment.

The experiment was terminated by a specimen of my great enemies, a taxi driver. Technically the monster was an auto-rickshaw driver, but it is the same category of brain structure, or lack thereof.

We haggled in advance, fine, I agreed to pay double the rate, I was used to that. In India, you will never get a bargain. Then he chose the longest route with the biggest possible traffic jam. I was cheerfully yelling at his intelligent face to follow the GPS and get us out of there, but he suddenly forgot his English. He further pretended he never saw a map before. This was probably not just pretending. At some point, he mooted I should pay more, as we were — rather unfortunately — stuck in a jam, which he was not expecting at all. I barked some kind words at him to indicate I disagreed.

Auto-rickshaw in Jaipur

Enemy spotted. Never tip them.

Keeping with my experiment, I had to tip him at the end of the journey, but I still had twenty rupees to get back. Then he pulled the usual trick: “sir, no change.” A bundle of ten-rupee notes were sticking out of his shirt pocket. He overrode the solution of my constrained integer optimization. Some people do not deserve to be tipped. Most people do not deserve to be tipped. These days I go into the effort and pain of tipping if and only if I was blown away by the service, which, of course, seldom happens.

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