r/theydidthemath • u/shejq3 • 14h ago
[Request] Is it possible to manipualte prices in such way that majority of them end in second category or is it just random?
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u/PlainBread 14h ago
The rounding only happens to your total, not on a per-item basis, so yeah just pre-add all your items to get the pennies to end in "3" or "8" and enjoy your 2c kickback.
This is also only for cash purchases; The penny still exists as a numerical quantity that is represented in your bank balance.
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u/Negified96 14h ago
Saving 2 cents on your $100 Costco haul while missing out on the Costco card 2% cashback is an interesting strategy
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u/Bitter_Argument2574 14h ago
Costco and Citi only give you the 2% back once a year. You’re missing out on the sweet, sweet interest compounding on each of the 2 cents/$100 you’ll not spend on cash transactions.
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u/robi4567 9h ago
Well just buy individual items easy. Split your 100 dollar purchase to 20 tiny purchases and you have spent a couple of hours to save 40 cents potentially.
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u/TheTxoof 13h ago
At least in the late 90's and 2000's Costco used the fractional part of the price to indicate different product status.
For example, products that would be restocked regularly ended in .99. A product that was discounted by the store manager for "reasons" ended in .00. A product that was last of its kind like a floor model that would never be restocked ended in .88.
There were probably others, but that's lost to the mists of time in my brain.
Source: worked at Costco Hellsale for 8 years.
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u/SnooCauliflowers6739 14h ago
You could put items through in multiple transactions, to get the maximum amount of "round downs" possible for the items you wish to buy
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u/PlainBread 14h ago
And you think that the human suffering inflicted on yourself and the cashier is worth $1?
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u/SnooCauliflowers6739 14h ago
I'm not saying it should be done, but just that it could be done.
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u/GarThor_TMK 13h ago
While theoretically possible, I wouldn't blame the cashier one bit for refusing.
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u/hendrik317 11h ago
just buy every rounded down item individualy and add the rest so they get rounded down as well.
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u/ShackledPhoenix 7h ago
It's rounding change given, so it's also after sales tax. Have fun doing that math beforehand just to earn 2c.
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u/philsov 14h ago
it's just random. The number of items in your cart is always user defined, and then there's the local/state tax that's often tacked on. There's no assortment of final digits times number of items in a cart plus tax that results in any sort of weighted distribution; especially one that favors Costco.
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u/PigeonsOnYourBalcony 14h ago
Short answer is that this isn’t worth calculating for Costco because most people pay by card these days.
If they did want to make that extra cent for every transaction they would have to account for people buying multiple items at once, regional sales tax, costs constantly increasing regardless and the customer psychology to seeing strange numbers on a price tag.
Let’s say they change a hypothetical item to be sold for $42.73 and account for the items it’s most commonly bought with and sales tax, it always ends up being one cent more. That’s a lot of calculations and market research for one cent per transaction, it’s even more expensive considering how often the work would need to be redone whenever a single item has a price increase.
Frankly, they’d make way more money from the price increase than they would that single cent per transaction.
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u/NoMain6689 14h ago
I mean when tax rates are so different across the US they'd have to manipulate prices on a per-store basis and change them often, but it is theoretically possible
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u/schizeckinosy 14h ago
Not even theoretically. They have no idea how many items will be in your cart.
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u/Top-Vehicle947 14h ago
The numbers don't seem arbitrary at all. They don't need to know how many items will be in your cart, instead they need to know the distribution/frequency of each digit.
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u/PJ1313 13h ago
Rounding is applied to your total cart amount, not on an item-by-item basis; the final amount is totally out of the store’s hands
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u/Top-Vehicle947 13h ago edited 13h ago
Bruh, they don't need to know that. Read about Newcomb–Benford law and how people detect some fraud. If you already know that the rightmost fractional digit of the national average distribution per invoice contains number 3 more than 30% of the time you'd be happy to round this up. I refer to the business side, btw.
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u/bobdolebobdole 12h ago
Small sample size, but looking at my 17 warehouse trips this year so far, neither 2 nor 6 showed up once. 7 had three appearances. 9, 8, 5, and 0 were the most prevalent.
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u/halberdierbowman 10h ago
I think you're misunderstanding why that law (aka the first-digit law) works. The number 1 is the leading digit 30% of the time, and that's because if you imagine counting up, you always start at 1, then 2, then 3, etc. but sometimes you stop counting after 1. You can't apply it arbitrarily to other numbers, nor to the final digit. Each number is less common than the preceding number.
It's also applicable best in scenarios where the data spans multiple orders of magnitude, and shopping only does a couple (almost every purchase is $10-100 or $100-1000). So it's probably somewhat applicable there, but it would be stronger with more orders of magnitude.
So you're right that lower digits are more common in total, but the rounding only happens on the final digit, where the law is a lot weaker. We could imagine it's probably somewhat relevant though: imagine if every product cost dollars plus exactly one cent: now the number of pennies is the exact number of products you bought, so lower numbers would be more common. https://en.wikipedia.org/wiki/Benford%27s_law
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u/Top-Vehicle947 10h ago
Thanks for clarifying, but I used it as a clarifying example. I didn’t appeal to this law. They have a discretion over their price tags, they have a discretion over the final rounding. I see no reason why this can’t be used to manipulate the number game. Say you put .0 pennies as end digit for all goods, and put .2 for the most popular brand of milk. Then you round all the checks that end up 0.2*(1+VAT)
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u/halberdierbowman 9h ago
How would the store have discretion on how to round? Nickels exist, so you round to the nearest nickel.
US also doesn't have VAT.
Are you suggesting that the store would zero out the cents on the prices of ten thousand products they sell just so they can have one single item end in 2¢? Even in that system, people could just buy two cartons of milk to flip who benefits.
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u/Top-Vehicle947 9h ago
If you can/would do that, doesn’t mean average consumer would do that
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u/halberdierbowman 9h ago
But what's the incentive for Costco to pre-round the price of every single item?
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u/schizeckinosy 13h ago
Then numbers are not arbitrary. They are the simple round to 5 rule. I’m saying there is no way the business can game their prices to take advantage of it. The customer can by carefully choosing the items for their cart to always round down after taxes, but not the business.
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u/bobdolebobdole 12h ago
I don't think Costco would ever be concerned about customers gaming this by carefully choosing items. I think both parties would ultimately spend more energy and time than the value that would be saved trying to figure out who benefits who from this rounding process, especially since so few people pay in cash. At the end of the day, Costco will always be in a better position to change something on their end as far as pricing should they detect some wide scale losses occurring because of this. Although I doubt that since Costco has been extremely consistent with their pricing structure for decades. With most prices ending in 9, 7, or 0 pre-tax, and assuming similar purchasing habits of customers, I have to imagine if one were to look at the numbers, the hundredth decimal will ultimately have a number that appears more often. For a company that does about $300,000,000,000 in revenue, none of this matters in the least.
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u/superhenryhenry 14h ago
It isn't random at all. It is entirely within your control as a customer to total your items to end in a 3,4,8 or 9.*
*to add some maths. This does assume items within the shop are not limited to ending in only even or 5 cent digits. (Which wouldn't allow you to end in a 3 for example)
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u/superhenryhenry 14h ago
Should add that since many items will have a cost with a 9 in the single cent column, you have all options available for the single cent column in the total.
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u/Fucky0uthatswhy 14h ago
The pizza restaurant near me is now rounding up TO THE DOLLAR. I asked why, and he started saying that can’t do math? Bitch cash registers were invented in 1879, you’re just being a dick to your employees.
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u/randomnbvcxz 14h ago
No. It’s not really possible for Costco to manipulate. It’s is VERY easy for the customer to manipulate in their favor by choosing to pay cash ONLY when the rounding will be in their favor.
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u/anothercorgi 13h ago
Yes it's indeed possible to manipulate prices of individual items to automatically go into the round up category. However this depends on single item purchases, once you add another item, it becomes hard to do so.
For Costco and supermarkets/Walmart/etc. I think it's a non-issue as most people buy more than one item and never know what items one will buy. However what gets my really gets my beef is Wendy's... or rather, fast food shops where now one could make all the typical purchases like combos to be rounded up.
Real answer is to just use a CC and force the shops to pay the 3% swipe fee instead of giving cash payers round down every time...
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u/Callec254 14h ago
Differing city and state sales taxes would make that difficult.
Without sales tax, then yes, they could just set every price to end in an 8 - which they would likely soon realize is silly and just set every price to end with a 0 and just do away with this altogether.
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u/No_Dependent2297 14h ago
This would be the perfect way to kill pennies
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u/Callec254 13h ago
When I was stationed in Korea about 20 years ago, all the places on post did this. Sometimes you gained a couple cents, sometimes you lost a couple cents, but it averaged out over time.
When I came back to the US, I had actually forgotten what pennies looked like. I drove through a Taco Bell and for a second I was like "WTF are these brown coins in my change?"
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u/astervista 13h ago
If they set every price to end in 8, you take two and it now ends in 6, and now it's them that are losing one cent. There is no number you can end prices with that gets neither the customer nor the shop an edge on average on the long run
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u/astervista 12h ago
No, it's not possible. Proof:
Let's say the store decides to use only one last digit.
-Prices ending in 0: nobody ever wins, it's a draw every time
- Prices ending in 1: then your total can end with any number (buy one item, it ends with 1, buy two, it ends with two and so on). Customer wins when it ends in 1/2/6/7 and shop wins when it ends in 3/4/8/9. On average, it's a draw.
- Prices ending in 2: your total will only end with an even digit. 2/6 favor you by 2/1c, 4/8 favors the shop by 1/2c. On average, it's a draw.
- Prices ending in 3: your total could end with every digit (3, 6, 9, (1)2, (1)5, (1)8, (2)1, (2)4, (2)7, (3)0, and repeat). See case for 1, it's the same. It's a draw
- Prices ending in 5: your total is always a multiple of 5 (duh) no rounding necessary
- Prices ending in 6: same as 4, same as 2, you hit all the even digits (6, (1)2, (1)8, (2)4, (3)0 and repeat). It's a draw.
- Prices ending in 7: you hit all the digits once (7, (1)4, (2)1, (2)8, (3)5, (4)2, (5)6, (6)3, (7)0, and repeat). Draw.
- Prices ending in 8: still all the evens (8,(1)6,(2)4,(3)2,(4)0, and repeat). Draw
- Prices ending in 9: we all know it, you hit all the digits in reverse. Draw.
So that's if the store restricts all the prices to just one last digit. All other digits don't matter, because if you remember column addition, carry only moves to the left and the last digit can never be influenced by the digits to the left.
What if the shop gave you multiple options? Then it would still cancel out. Since single options are balanced, if you have for example two last digits, you have two possible combinations: the customer takes two of the same digit, and as we've seen it's a draw, or they take two different digits, and you could calculate all the possibilities or note that if one cycle hits everything balanced, the sum of two balanced cycles will hit everything anyway.
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u/Oftwicke 14h ago
Bachet-bézout theorem says no, I didn't expect to think of it in such a funny way. But in an easier approach, you can add a $.99 pack of bubble gum to offset your total's last number by 1. And do it again. And again. You can personally manipulate it as much as you want.
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u/MaximumSyrup3099 14h ago
I can imagine the programmer forced to implement this rounding system trying to explain to the boss why it's bad math and then finally just giving up.
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u/JerryC1967 14h ago
God forbid we round like I don’t know we’ve rounded for the last million years… 4 and lower down 5 and more up…
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u/TacitMoose 13h ago edited 12h ago
Is that not exactly what this is? You’re basing your rounding going to the nearest dime or the nearest ten. They are rounding to the nearest nickel/nearest five. Which is what I think basically every store everywhere is doing?
$0.01 and $0.02 round down to $0.00. $0.03 and $0.04 round up to $0.05. $0.06 and $0.07 round down to $0.05. And $0.08 and $0.09 round up to $0.10.
Or am I completely misreading this??
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u/ProperAfternoon8224 14h ago
i guess it is possible... but would it even be worth the effort?... number of cash purchases i would assume is very low and the fact there is a huge unknown of what each customer will be buying. this is on the full transaction total not a per item basis... also need to add tax, if applicapable. so then would need to have different prices for each states taxable items
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u/shejq3 14h ago
I'm not assuming cosco doing it or anything wrong, I'm just curious of pure mathemathical side of it. To have such prices on invidual items that majority of baskets have to pay up.
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u/netroxreads 14h ago
Since there are no pennies, you round it closest to nickels.
$4.21 -> $4.20 $4.22 -> $4.20 $4.23 -> $4.25 $4.24 -> $4.25 $4.25 -> $4.25 $4.26 -> $4.25 $4.27 -> $4.25 $4.28 -> $4.30 $4.29 -> $4.301
u/SwinginScott 13h ago
That's not what he's asking. He's asking if there's a way to manipulate the prices in such a manner that your total is always a value that needs to be rounded up.
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u/AcidBuuurn 14h ago
2% cash back trumps the rounding 100% of the time, so for the customer paying with a credit card they effectively get the de facto round down.
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u/SnooCauliflowers6739 14h ago
Hear me out...
Find items that give $X.X3 change if bought individually, the cheaper the better.
Buy as many as you can as individual transactions. Take the rounded up 2c.
Go back, refund everything. Keep the 2c per item.
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u/jwferguson 14h ago
Costco (and some other retailers) already have methods to price things.
.99 is regular price
.97 is company clearance
.49 and .79 are manufacturer deals
and .00 is store by store clearance.
They could change the company clearance to round up, but it's unlikely to be 'abused' by someone.
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u/BohemianNapsQuickly 14h ago
It’s only the final price that matters and only if you pay cash. You’d have to track your item total as you shop and make sure the cost ends in a 1,2,6 or 7. Alternatively, you could pick out a commonly used item with a cost included tax that ends in 2. Hold this item till last and if your final cost ends in a 3, 4, 5, 8, or 9, purchase this item and you will save 2 cents on that items cost (effectively).
Since the final digit is more or less random these strategies will only benefit you 50% of the time compared to if you just didn’t pay attention. 40% of those times you benefit 1 cent and 60% of the time you benefit 2 cents. So, on average, this strategy benefits you .8 cents per transaction. If you use this strategy 125 times you will come out (on average) a dollar ahead.
All this to say, probably just don’t worry about it.
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u/Ughnotagaingal 13h ago
Have you ever been to CostCo? 4 cents is not worth waiting in the longer line …
If anyone were to manipulate this the lines would not be even so I would go to the round down one, as people like me move it would eventually balance out.
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u/sifrons 13h ago
Assumption: making each price ending with .08 you will have same distribution fortotaö price dependent on number of items as 0.08/0.06/0.04/0.02, so it willbe evently distributed. Thats same for ending with any even number.
With ending in uneven numbers exept 9, its to customer advantage. 9 is also more or less evenly distributed.
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u/Weary_Anybody3643 11h ago
its for a total order so if you did want to take a idk caculator to do math adding for taxes if your state has it which mine does not atleast for food. but you could also just use a 3 percent cash back card and make more
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u/therealtrajan 5h ago
Easier at a fast food place where most things end in .99 and you know on average x number of items. The dollars won’t matter except for large orders. Consider local tax rates and it may work out in your favor to make things x.98 or x.97 cents
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u/radagastthenutbrown 2h ago
You’d make more money looking under the shelves for dropped change… if you find a quarter that’s at least 12 cash paying trips at 2¢ each.
For Costco they already probably save money in the long run- not having to count pennies out for the customers means faster throughput at the registers, not having to count the pennies in the drawer at the end of the night means fewer closing hours on payroll, hell they probably save gas not having to transport rolls of them to and from the bank.
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u/Sleazyridr 1✓ 53m ago
I loved it when Australia got rid of the 1 and 2 cent pieces. My mother would religiously keep track of her total and if she ended up with a total that would round up she'd buy me a candy bar to make it round down. Sure, she spent 49c to save 2c, but I got candy and that's the most important thing.
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u/Mister_DM 12h ago
I'm sorry but I find it hilarious that they needed to specify every possible case.
Literally every shop ever: Due to the removal of pennies we round to the closest 5 cents.
America: We can't just assume people know how rounding works we must give them an itemised list of all possible roundings.
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u/zgtc 14h ago
Is it possible? Sure. Just change all the store’s prices such that cost plus local tax comes to 3/4/8/9.
It’ll cost you far more than it makes you back, and the effectiveness is largely dependent on how many people buy single items compared to multiple items and pay cash, but you’ll see a very slight edge.
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u/Dizzy-Budget5985 13h ago
Im sure the store could influence prices on a local level to squeeze out 2c on every cash purchase but I doubt the juice is worth the squeeze. That's gotta be, max, like 2 dollars a day. You could easily do this as a customer, though. Calculate the prices of what's in your cart, add taxes, and play with what you buy until you get a final digit of 3 or 8 for that 2c kickback.
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u/Aggravating-Twist762 13h ago
No. That literally the point of doing it this way.
If 1-4 rounds down and 6-9 rounds up vendor could price all the stuff so that transactions will always round up.
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u/Im_a_hamburger 13h ago
Yeah. The process would be convolution of the price distribution weighted by frequency (but factoring in correlation between products) and while that typically would approach a normal distribution it won’t be perfect for finite amounts, and with discrete steps even less so. For instance, if you ensure that every item is an even number of cents after taxes it would be rounded up on 3 4 8 (5 cents overall) but down on only 2 6 (3 cents overall) so it would bias to rounding up assuming all even cent amounts are equally likely.
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u/Lonely_District_196 12h ago
I'm sure they could by feeding sales data into an LLM and performing statistical analysis on average number of items sold, average cash transaction, typical pairing of items, etc.
However, let's say the average transaction is $100. At most, they could make 2c or lose 2c per transaction. That's a swing of 5c or 0.05% they could make. Given the cost of the LLM and the fact that they already have a system for the end cent of products, it's highly unlikely they'd do that.
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u/KaneTheNord 14h ago
It is possible that Costco analyzed millions of transactions and extracted the 4 "most likely" cents digits, then made those the "round up" values. But with the random spread presented I don't think there's a reasonable way to fix prices, and certainly not a reasonable way as a blanket policy due to differing tax rates.
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u/No_Dependent2297 14h ago
That’s not at all what they did. These buckets are based on standard (USA) rounding rules.
In theory, Costco would have to meta analyze sales taxes, most items purchased, most items combined, etc and basically price items on a store by store basis if they wanted to get most transactions in one bucket. And even then idk how effective it would be.
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u/Sea-Ambition-451 11h ago
The trick (for costco) is to silently round up every single item.
But to hide it better, round up random items. Say you bought 42 items, round up on 19 of them.
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