Making Change 1129
Roland Piquepaille writes "There are mostly four kinds of coins in circulation in the U.S: 1 cent, 5 cents, 10 cents, and 25 cents. But is it the most efficient way to give back change? This Science News article says that a computer scientist has found an answer. "For the current four-denomination system, [Jeffrey Shallit of the University of Waterloo] found that, on average, a change-maker must return 4.70 coins with every transaction. He discovered two sets of four denominations that minimize the transaction cost. The combination of 1 cent, 5 cents, 18 cents, and 25 cents requires only 3.89 coins in change per transaction, as does the combination of 1 cent, 5 cents, 18 cents, and 29 cents." He also found that change could be done more efficiently in Canada with the introduction of an 83-cent coin and in Europe with the addition of a 1.33- or 1.37-Euro coin. Check this column for more details and references." The paper (postscript) is online.
Forget it. (Score:1, Insightful)
More and more transactions are done electronically. Does anybody really want to go back to shilling, farthings, etc etc?
Instead... (Score:5, Insightful)
Why not round prices to dimes ? Or even quarters ?
Re:Instead... (Score:3, Insightful)
Re:I hate math... (Score:3, Insightful)
For the pure maths side of it it's pretty neat, all the same - just not completely useful when it comes to Real World Stuff
More to transactions than number of coins. (Score:4, Insightful)
You give them a 29 cent piece and see how fast things get.
I'm willing to bet that most of the "coin cost" or whatever you want to call it comes from pennies, anyway -- if the dollar amounts are random, every 5 transactions are going to involve (0 + 1 + 2 + 3 + 4 = ) 10 pennies, or 2 pennies per transaction. Rounding prices to the nickel would be simpler, easier, and more efficient.
Actually, i think it started to help prevent (Score:4, Insightful)
If the price is 1.00$, the person working the regster can just take the buck, or five, or whatever, and slide it into their pocket. If its
typical Computer Science logic (Score:3, Insightful)
Re:Instead... (Score:3, Insightful)
This is why Human Interface Design is important (Score:3, Insightful)
The ivory tower academics are certainly earning their reputation for foolishness.
Why not 99 different coins? (Score:2, Insightful)
Re:Instead... (Score:2, Insightful)
Those prices have been proven to influence buyers. They won't go away until people quit acting like idiots.
Pet peeve (Score:5, Insightful)
Math != Arithmetic
I just hate it when people say... "Oh, you're a mathematician! Can you add up these numbers for me?"
I suck at addition. Give me a theorem to prove!
Re:I hate math... (Score:5, Insightful)
The logic for determining change is really easy for a cashier. start with the largest coin and work your way down until it all adds up.
Re:Instead... (Score:4, Insightful)
I suppose they could just print out signs with an average price, and take a hit in certain areas, and make a much larger profit margin in others. It might balance out in some areas, but possibly not in others. And if you are a consumer in one of those higher profit margin areas, then you are getting screwed as well. It would work, but I don't think anyone would be too terribly happy with it
Bad Assumption (Score:2, Insightful)
I understand that an assumption like this is necessary to even begin an anaylysis using our western logic system, but this assumption makes the study useless.
There's no way that the distibution curve is flat. People spend a lot of time and money price setting as described here [slashdot.org] and you better believe they know how to price their goods to maximize profit.
This study also doesn't take into account people like me, who make a game out of minimizing the number of coins in my wallet/pocket. If I can prevent getting 94 cents in change by carrying and relinquishing a penny and a nickle, I'll do it.
Get rid of 1c pieces! (Score:3, Insightful)
Sure, people will bitch and moan for about 6 months, but then noone would ever consider going back.
All you need to do is 2/3 round at the till. It's great!
Re:Instead... (Score:3, Insightful)
Who are you kidding? Of COURSE they're fooling someone. It's a proven fact that a given good will sell more units at $9.99 than at $10.00. YOU may not think you're being affected, but the truth it is works. Retailers price their goods at a level that will maximise sales.
Theoretical Math != Reality!! (Score:0, Insightful)
I happen to be one of the people all the math geeks are making fun of. I AM the idiot who pulls out a calculator just because I don't trust my sucky arithmetic. I'm just bad at it; always have been, always will be. Round-number coins are the best for quick computation.
Statistics was always a weak area for me... (Score:5, Insightful)
The paper assumes all amounts in 0..99 are equally likely in making change. Is this a fair assumption? Wouldn't there be patterns in the amount of change returned based on varying "psychologically appealing" decimal retailer pricing schemes, local sales tax percentages, the average total price of a transaction, etc? Wouldn't the optimal selection of coins in making change therefore be influenced by the peaks and troughs of this change function?
Re:Instead... (Score:5, Insightful)
Re:Yeah Right... (Score:3, Insightful)
-
Bad Assumption (Score:2, Insightful)
Is obviously not true - prices are clustered at certain points, eg 95c or 99c, so the typical amount of change would be skewed as well. Would be nice to see the experiment using real data for typical prices.
Also, I wonder to what extent the demoninations of currency in use effect the prices of goods?
dave
===== Tech, Ramblings, Photos --> davidgoodwin.net
Re:I hate math... (Score:2, Insightful)
Make sales and other taxes round prices up to the nearest nickel. Banks could still have rolls of pennies for those desperate for Mr. Lincoln's face, but otherwise I'd be happy to see them disappear.
Re:I hate math... (Score:3, Insightful)
A poor family, in a foreign country, that sends their child out to work selling stuff on the corner would do poorly on an IQ. They'd lack the skills you get from going to school necessary to actually take an IQ test. You learn basic things, like pattern matching and some minor analytical skills.
Take that child, and ask that child who has to properly make change daily, and does it, could do math quiet well. Easily better than others since that's what he was able to learn. He has potential.
Now, going back to this $18 cent coin biz? Quick, how many times does 25 go into 200. Now how many quarters are in two dollars? How about 10 dollars? Really stupid, but easy associativity. 98/18 isn't so hard if you remember that 100 and 20 are very close. it's 4 times. But you know what. 4*18 would be easy after a few months of people re-learning the relationship of coins and math.
I hate math too.. but it's amazing what you learn when you aren't trying. But hey, please. Still hate math. Stupid recipricals. riciprocols? recipie-cols.
Re:The quarter is hard enough (Score:2, Insightful)
Wanna see those tables? Here you go.
tens digit:
-------------------
9 - 0
8 - 1
7 - 2
6 - 3
5 - 4
ones digit:
-------------------
9 - 1
8 - 2
7 - 3
6 - 4
5 - 5
0 - 0
It's very simple math. Most likely, that blank stare you get from the cashier is your own damn fault for making it more complex. Then again, there are a lot of clueless cashiers out there... Maybe I'm just a change-giving genius.
Re:I hate math... (Score:3, Insightful)
Re:Yeah Right... (Score:5, Insightful)
It's funny (in a VERY sad way) that to him, the cash register was this magic oracle that told him what to do, and that it didn't occur to him that what he was doing was even knowable without its use.
I am a High School math teacher, and I can't agree with this statement enough. Somedays I laugh, somedays I cry, but it is always sad when I see a student need the calculator for the most BASIC of operations (And I am not even counting the OP's example as "basic", that would be "basic+")
I think it all comes from the fact that students are allowed to use calculators at such an earlier point in thier schooling. I am only 29, but I was not allowed to use a calculator in school until somewhere around 11th grade. It really hones (sp?) those basic math skills. I'll step off my soap-box now Sorry ;-}
Re:I hate math... (Score:2, Insightful)
Re:I hate math... (Score:4, Insightful)
Don't you think that the current denomination systems are designed specifically so that the greedy change-making algorithm will work?
The poster you were replying to seemed aware of that; They were merely saying that since the current denominational system has this property, it is easy to use. The problem with adding 32- and/or 18-cent coins is that the greedy approach may no longer make the most optimal change.
The Math is just WRONG. Here's why (Score:4, Insightful)
first,
that the price of goods is not partly determined by the demoninations of coins. for example, the reason why a candy bar is 50 cents or 65 cents and not say 48 cents is because we have nickels dimes and quarters. or that the reason a price is 5.95 cents and not 5.96 cents. etc..
Second,
this assumes your change purse is stocked with all denominations. that's true at the cash register but not in my pocket. When I reach in my pocket and I pull out some change there are a myraid of ways I can make 25 cents. 5 nickels, 2 dimes and a nickel, 5 pennies+ etc...,
not so with his optimal set. if I'm nissing any of the denominations its hard to make it up with the others.
third, entropy
again reaching for change in my pocket the goal is not to find the minumum number of coins but rather to be able to pay the bill without thinking too much. that is the more ways I can add up to the same value the more likely I will on a random grab find the right coins to make it. I dont care how many coins.
Re:This is why Human Interface Design is important (Score:5, Insightful)
Assuming that each amount of change between 0 and 499 cents is equally likely, Shallit's calculations show that the average cost of making change would fall from 5.90 to 4.58 coins per transaction with the addition of an 83-cent coin.
That's a pretty big assumption, isn't it? I'd assume that amounts of change would cluster around certain values. That was one thing that caught my interest, so I went to look at the article to find out how they evaluated that effect. Answer: apparently they didn't.
To be fair, it's quite possible -- even probable -- that the original article was a light-hearted, tongue-in-cheek sort of piece, and that the author has been horrified to see it turned into a serious suggestion about actually changing the denominations of coins.
In fact, the more I think about it, the more likely this seems. From TMI's site: "The Mathematical Intelligencer encourages authors to write in a relaxed, expository style and to include pictures and other graphics with articles. Opinion, mathematics, and historical comments can (and often should) be intermingled to make lively reading. Humor and controversy are welcome." So it was probably just a goofy abstract problem, written for entertainment value, not "serious" research. So I take it all back: let's give the guy a break, smile quietly, and move on.
Re:Yeah Right... (Score:5, Insightful)
The thing that struck me about this guy was that it wasn't even that he couldn't do the math in his head
Re:I hate math... (Score:5, Insightful)
And as many people have mentioned, the current system is probably the best because of the ease of addition/subtraction. An 18-cent coin would be a nightmare for most minimum-wage cashiers. The only problem with our current monetary system is that inflation has made pennies freakin worthless.
Re:I hate math... (Score:2, Insightful)
have you ever worked at a place like walmart or target? i have. the average cashier has problems figuring out how to *scan* an item properly. what makes you think they can see
note, that's only the average ones...
What about a 2 cents coin ? (Score:2, Insightful)
Actually, ... (Score:3, Insightful)
So your argument is moot: The cashier does actually have to use math to give you back your change.
A "Scientist" wrote this!?!?!?!? (Score:5, Insightful)
The US does not need another coin. Indeed, the *opposite* is true. If you get rid of the penny, you can increase efficiency tremendously, to only 2.75 coins per transaction, and a whopping 45% of transactions would require 2 or fewer coins!
Many people oppose the elimination of the penny, but bear with me for a moment. Consider the following issues:
- Pennies cannot be used in vending machines, and therefore are not as "spendable" as all the other coins.
- Prices will not rise as people think they will; they will fall instead! Everything that is priced at $n.99 will now be $n.95 instead (marketers HATE to price in round dollars because it makes their prices look higher). All other numbers will be rounded to the nearest $n.n5.
- The US government makes 12 billion pennies at a cost of $100 million each year (http://www.retirethepenny.org/), which could be put to better use than filling up my coin jar.
- Half of these pennies will disappear from circulation within a year! (http://www.shepherd-express.com/shepherd/19/41/n
- Counting out pennies costs the economy an estimated $20 billion in productivity annually (http://www.retirethepenny.org/)
- The U.S. Mint loses $8 million a year manufacturing pennies. (http://www.shepherd-express.com/shepherd/19/41/n
Think about it - do you *really* want another coin in your pocket? Thank God that politicians don't listen to us all the time!
-Mark
Re:I hate math... (Score:2, Insightful)
The whole notion of altering the face value of coinage is a bit silly. First of all, judicious use of a 50 cent piece would make many transactions much simpler, as would actually taking advantage of the two dollar bill. I used to work in a restaurant (as both a financial manager and a cashier) where we used all available denominations under $20. Once you get into it, it's just as easy to do, and slightly faster.
Most of this mess can be avoided by pricing things sensibly. Any price can be adjusted so that the after tax price (if tax is applicable) is a nice round number. Of course, due to rounding this sometimes breaks down on multiple item purchases, but anyone with half a brain can notice which price combinations result in bad totals and adjust the underlying prices to compensate. Or you can just take advantage of the "give a penny, take a penny" method to avoid dealing with units under five cents. You know, round in the customer's favor.
Just be glad it's not the problem they have in Japan where a $2 item costs 240 yen and a monthly rent on an apartment can be in the hundreds of thousands. Their yen is worth less than a penny, but it's the base unit in which they count monetary value. It's like expressing every price in cents.
Don't get me started (Score:5, Insightful)
It doesn't matter what the denomination is. As long as change has to be made, some patrons will receive the wrong change.
Lots of cashiers don't know how to make change. Many have been trained to do it wrong. The most common error is the cashier puts the large bill the customer just handed them into the drawer before giving the customer change and watching them count it. There used to be a little slot between the plastic guard and the metal cash register enclosure that was perfect for temporarily storing that large bill in customer sight. When the customer looks at you after counting his money, pause to see whether he questions it, then put the large bill in the drawer and close it.
Adding this momentary delay before putting the customer's large bill in the drawer and closing it, protects the cashier and the customer from being short changed.
I've seen managers put large bills in the drawer before I counted my change. One gave me change for $10 instead of change for a $20. I'm a creature of habit. When I hand a cashier a large bill, I always say, "outta twenty" or whatever the bill is. I'm sure I did that with this one. But she'd already put the bill in the drawer and insisted upon a recount of the drawer and by the time she did, my food was cold. That is not the way to do things. When I pointed out her mistake, she lost her temper. Then I lost mine.
I was trained on older cash registers to do things this way by a store manager who was very particular about this. He's been in business for more than 30 years and says he's never had a dispute with a customer over incorrect change. Way back then, you had to actually count the coin change. Many of the newer cash registers do this for you. I wonder how many of today's cashiers could make change in their heads.
What's my point? Most point of sale problems concerning change making are due to lack of skill and/or poor training of the cashier. Using more efficient denominations or pricing items to the nearest buck won't fix this.
Re:Pet peeve (Score:1, Insightful)
Re:Yeah Right... (Score:3, Insightful)
Re:Instead... (Score:3, Insightful)
Du Pont also has a posted speed limit of 19 instead of 20 on their plants for several reasons. One of the top reasons being that at 20, a majority of people will drive any speed in the 20's. At 19, amazingly, they will not drive above 20.
People familiar with Du Pont will also remind me that 19 sticks in your head better than 20 because it is an odd number to see on a limit sign -- so you will adhere to it because you are more concious about it.
What I find interesting, though, are the people that think the
Re:Yeah Right... (Score:2, Insightful)
Re:5?! -Interesting +Utter Crap (Score:3, Insightful)
It says that the practice didn't start catching on until the 1920s, when merchants would under-price things at
So there must be a *lot* of suckers out there today...
Re:I hate math... (Score:3, Insightful)
Have you been to a McDonald's recently? Them, donut shops, and any other minimum wage job tends to have a lot of "Tide me over through high school" students working for them who can't figure out change with or without a "Change due" amount in front of them.
This is making two very large assumptions;
Sadly, in many cases neither of the above conditions can be relied upon, so we get kids (and adults) who don't understand how to make regular change (ie; with a single bill of a denomination larger than the order total), letalone convenient change (ie; a 20 and a single for an 11 dollar order), and get confused and often attempt to hand back the extraneous currency.
You make it sound as if there's a course. I'd go so far as to say most cashiers are taught the specifics of the cash register at hand and are left to figure things out on their own. Stores / restaurants don't tend to spend time instructing 6.85'ers what is thought to be common knowledge (how to count, how to change a $20, how to combine small coins to make the change an even amount, etc.). In the cases where such skills are taught, many teenagers exhibit stereotypical symptoms and ignore the lessons because, hey, they know it all anyways.
Re:I hate math... (Score:3, Insightful)
That doesn't take into account taxes which almost always mess up the totals. Besides.. If you're going to be dishonest, then why not just keep a cache of pennies on top of the till?
The actual answer is apparently marketing: They definitely do studies on these things.
$4.99 is less than $5.00. The fact that it's only infinessimally smaller doesn't quite register on the harried consumer's mind. People seem to think in round things to the nearest 5, because
$4.97 will often seem like more than $4.99. I'm guessing that it's internally converted to more than $4.95.
$*98 is generally almost as good as *99, bur it seems to make some people stop and think.
Similarly *95 works as good as *99. I'm guessing that it works because it's one 'chunk' down (the chunk being $.05, now rather than $.01). My guess as to the reason why *.99 is used more more often than *.95 is that $.04/unit adds up over a million boxes without adding enough sales to make it worthwhile.
Re:Instead...Japan, the land of confusion (Score:4, Insightful)
Life gets more complicated when coming originally from Germany, where VAT is always included in the advertized price (for end-users, not for businesses) and going to Japan, where 5% tax is mostly added. About 90% of all times I need to add 5% at the cashier. In the other cases I don't need to. Now that makes calculation the price to pay complicated.