• March 29, 2015, 06:48:48 PM

### Author Topic: The automatic gratuity  (Read 1046 times)

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#### DottyG

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##### The automatic gratuity
« on: April 26, 2013, 12:22:22 PM »
Haven't had coffee yet this morning, so my brain is fuzzy.  I wanted to check this math out.

If there's a large group that gets charged the AG, there's no difference in the amount the server gets as to whether the bill is lump or if everyone splits it and gets their own, right?

What I'm getting is (for example):

\$100 check - lumped 18% would be \$18.

If split into separate bills of 10 people, it'd be \$10 each which is \$1.80 tip on each.  So \$1.80 X 10 = the same \$18.

Am I right there?

#### Cat-Fu

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##### Re: The automatic gratuity
« Reply #1 on: April 26, 2013, 12:37:31 PM »
Yes, there is no difference if the percentage is the same.
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#### Virg

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##### Re: The automatic gratuity
« Reply #2 on: April 26, 2013, 12:38:26 PM »
A lump bill will tend to draw a slightly smaller tip because most people tend to round up for tips, so the total will end up slightly lower.  However, more checks is more work so sometimes it isn't worth the extra work.  That said, if an auto-calculated gratuity is spread across several checks, the total sum of them will tend to add up since the computer will just do a straight calculation as in your example.

Virg

#### MrTango

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##### Re: The automatic gratuity
« Reply #3 on: April 26, 2013, 12:51:33 PM »
The distributive property of multiplication states that X*(A+B+C+D) = XA+XB+XC+XD, so in pure math, there should be no difference.

However, as Virg said, people tend to round.  When calculating tip, I tend to do a fair amount of rounding, but the last thing I do is always round up to the next whole dollar.

For example, a \$49.12 tab becomes \$49.  10% of \$49 is \$4.90 (which is about \$5).  Half again is \$7.50.  Finally, round \$7.50 up to the next whole dollar, and my final tip is \$8.

In that example, I'm thinking the tip will be about 15%, but in reality due to rounding each step to make the mental math easier, the final tip is a bit over 16%.

#### DottyG

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##### Re: The automatic gratuity
« Reply #4 on: April 26, 2013, 12:53:11 PM »
Forget human rounding.  I was just talking about a straight amount.

#### Twik

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##### Re: The automatic gratuity
« Reply #5 on: April 26, 2013, 12:53:40 PM »
Another problem is that with a group, there will often be That Guy, who decides he can skimp on the tip, because no one will notice. The more people in the group, the greater the odds one will be That Guy.
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#### WillyNilly

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##### Re: The automatic gratuity
« Reply #6 on: April 26, 2013, 12:56:34 PM »
Yes it would break down to \$10 + \$1.80.

But if you really were part of a group of ten, personally I would think everyone should leave \$12 total, because its hard to wait on a group of 10. The additional 20 cents per person likely won't be felt by them at all, its only 20 cents, but getting \$2 extra dollars will be noticed by the waiter, especially because it means they aren't dealing with a ton of coins.

Another problem is that with a group, there will often be That Guy, who decides he can skimp on the tip, because no one will notice. The more people in the group, the greater the odds one will be That Guy.

^ This is another good reason for people to leave \$12!

#### MrTango

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##### Re: The automatic gratuity
« Reply #7 on: April 26, 2013, 01:01:47 PM »
Forget human rounding.  I was just talking about a straight amount.

In that case, the math doesn't change.  X*(A+B) = X*A+X*B

#### DottyG

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##### Re: The automatic gratuity
« Reply #8 on: April 26, 2013, 01:21:03 PM »
Thanks MrT.  That's all I needed.

#### Zilla

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##### Re: The automatic gratuity
« Reply #9 on: April 26, 2013, 06:06:13 PM »
Thanks MrT.  That's all I needed.

Did something other than what you described in your OP happened?

#### daen

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##### Re: The automatic gratuity
« Reply #10 on: April 26, 2013, 10:06:57 PM »
Probably Bistromathics - the fact that numbers written on a waiter's bill pad within a restaurant behave differently than numbers written anywhere else in the known Universe. The correct application of Bistromathics allows one to navigate space ships in ways previously impossible.
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