*If you use a point-earning credit card and pay $3.95 for a $500 reload card, what is your cost per point? The answer may surprise you (it surprised me). *

If you find a store that allows you to buy reload cards with a credit card (see “Reader reload research“), you can essentially buy points for less than a penny each. Right? The math is simple: cost = $3.95. points earned (with a 1X card) = 504. Cost per point = .78 cents. It’s simple.

Not so fast…

I recently held an email conversation about this with the “Traveling Mileonaire” where he said:

In my mind it is always 2 cpm or so

If I go to CVS and buy 500$ VR and pay 4$ load to Bluebird I have a choice of 2 cards to do it with:

A) My SPG [where] I get 504 SPG=605 AA miles (or US etc etc) for 395c = 0.63 cpm

B) I use my 2% cash back Amex / Visa. I get 10$ cash back and spend 4$ for it (250% return). I am ahead by 6$

So by using option A, I am not only spending 4$ for fees, I am also losing 10$ I would have got back from the cash back card. So 504 SPG – 4$ = 10$-4$ or, 504 SPG = 10$ or 1000 SPG = 20$ = 2 cpm

So even when you go and buy VR at CVS, you are still paying 2 cpm in opportunity cost.

Traveling Mileonaire’s viewpoint is directly aligned with how I think about everyday credit card spend. In my 2011 post “The Cost of Credit Card Points” I essentially argued the same thing. I said that when buying things with a credit card you always have the choice of using a 2% cash back card instead. So, if you earn only 1 point per dollar with your credit card, you are essentially buying those points for 2 cents each since that is the amount of cash you are forfeiting. 2 cents per dollar is the opportunity cost of using a point earning credit card.

Despite my prior posts on the subject, I wasn’t convinced that this was the right way to think about reload cards. I replied with this:

I’m not sure that opportunity cost is the right measure here. If you go to a store and buy a box of cereal for $4, that’s the cost regardless of whether you could have spent your time making money mowing lawns instead. So, when I go to the store and buy [a reload card] for the purpose of buying points cheaply, I think that $3.95 is the cost regardless of what I could have done instead. I know this goes directly against things I’ve written in the past but there seems to be a difference (at least to me) when manufacturing spend vs. doing regular spend. Let me try to give an example (I’m sort of thinking “aloud” here):

If I use a credit card to buy dinner, then my goal is to get dinner. The choice of credit card is a choice of what type of rebate I want. If, on the other hand, my goal is to buy points, then I don’t really have any choice but to use the credit card that offers the points I want. So, I think you can choose to buy points at less than a penny each or to buy pennies (cash) at a cost of less than a penny each.

I’m still struggling with how best to think about all of this, but the above is my current position… I think 🙂

In my response, I essentially argued that the purpose of your purchase makes a difference to the cost. This is, in hindsight, complete nonsense. At the end of the day, your bank account and point balances will be the same regardless of the purpose of your purchase. Still, its hard to shake the thought that my 504 points cost only $3.95 so of course I’ve paid only .78 cents each. What’s the right answer? Is the cost .78 cents or 2 cents per point? That’s a big difference!

### The Monty Hall problem

The situation described above reminds me of the famous Monty Hall problem where the answer is counterintuitive. Wikipedia has the details:

[The Monty Hall problem] became famous as a question from a reader’s letter quoted in Marilyn vos Savant‘s “Ask Marilyn” column in

Parademagazine in 1990 (vos Savant 1990a):

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?Vos Savant’s response was that the contestant should switch to the other door. (vos Savant 1990a)

The argument relies on assumptions, explicit in extended solution descriptions given by Selvin (1975a) and by vos Savant (1991a), that the host always opens a different door from the door chosen by the player and always reveals a goat by this action—because he knows where the car is hidden. Leonard Mlodinow stated: “The Monty Hall problem is hard to grasp, because unless you think about it carefully, the role of the host goes unappreciated.” (Mlodinow 2008)

Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance. One way to see this is to notice that there is a 2/3 chance that the initial choice of the player is a door hiding a goat. When that is the case, the host is forced to open the other goat door, and the remaining closed door hides the car. “Switching” only fails to give the car when the player had initially picked the door hiding the car, which only happens one third of the time.

I expect that some readers will argue that the answer presented above is wrong, but it’s not. Before any decisions are made, the probability of the car being behind any given door is exactly 1 out of 3. *After* a door is selected and the host shows a different door to have a goat, the probability of the car being behind the remaining door (not the one you picked) is exactly 2 out of 3. Trust me (or write angry comments, if you prefer).

The important take away from above, is that the right answer changes once action is taken and extra information is revealed.

### Back to reload cards

The comparison of the cost of points via reload cards to the Monty Hall problem is imperfect, but I do think there is some similarity. After lots of thought about it, here is (I think) the counterintuitive solution to Frequent Miler’s Reload Card problem:

- When deciding between doing nothing at all or buying a reload card with a credit card that earns 1 point per dollar, then the cost
*is*.78 cents per point. *After deciding*to buy a reload card, you can choose to stick with your 1X point earning card or switch to a 2% cash back card. If you stick with the 1X card, then that decision costs you 2 cents per point.

The interesting thing about this solution is to note that the costs are *not additive*. That is, it doesn’t cost a total of 2.78 cents per point to use a 1X card. It either costs .78 cents or 2 cents per point depending upon how you think about it.

### The solution, in practice

There are two important decisions to make regarding reload cards: 1. Should you buy them at all? and 2. Which credit card should you use?

With the first question, you need to decide first whether it is worth your time and likely frustration when things don’t go as easily as expected. If this is your hobby and so don’t mind spending the time, then I think it is reasonable to use the .78 cents calculation as a rough way to decide whether or not to do this at all.

Once you’re committed to buying reload cards, it makes sense to decide which credit card is best to use. In the post “Questioning Delta loyalty” I showed how I compared my spend with Delta credit cards to the same spend with 2% cash back cards and decided ultimately that I would get more travel value from the Delta cards. Thanks to high spend bonuses with the Delta cards, I earn approximately 1.5 miles per dollar. I determined that, for me, it was worth giving up 2 cents per dollar to get 1.5 Delta miles per dollar.

### Conclusion

When deciding whether or not to buy reload cards to earn points, the cost per point is easy to calculate. Once the decision has been made, though, it is important to consider the opportunity cost of choosing one credit card over another. For example, buying Starwood points for .78 cents each is a great deal, but is it a *better* deal than earning a profit by using a 2% cash back card? For you, the answer may be yes, but keep in mind that *that* answer is costing you more than .78 cents per point.

## Leave a Reply

94 Comments on "The true cost of reload points"

Another argument for the VR’s is that I can apply for more credit cards because now I have a way to meet the minimum spend. I used to apply for 1-2 cc’s every 6 months due to this issue. Recently, I just applied and received 5 cc’s with a total minimum spend of $15k in 3-6 months. So I value the VR’s a bit more since it allows me to get the 50k bonuses from the cc’s.

If you thought about everything in terms of opportunity cost, there would be very little you could afford.

Opportunity cost is useful as a comparison tool only, not as a means of account.

It is true that you could be getting 2% cashback instead of 1 point, but the value of 1 point may very well be greater than 2 cents. Also, getting $6 doesn’t get me out in the morning, getting a first class trip for free after x number of trips to CVS does.

Thanks for the post, as always.

Another monkey –

Signup bonuses. If I’m using VRs to fulfill bonus spend, The $3000 I spend is suddenly worth, say, 50k AA miles instead of 3024 of them. My cpm drops to .04.

Or, my value for the purchase jumps to $800 (assuming 1.6 cpm value) as opposed to the $60.48 I would have made with a 2% card.

If you’re constantly thinking about how much greener the grass could have been, you’ll never be happy.

While I dont disagree with FMs article. I have to say sometimes you can get lost in discussions about how much it costs to earn. So I agree with Anon, I have a card that earns 4% and another earning 6.33% and I still from time to time spend on other cards like Ink or Sapphire just to earn UR pts.

I don’t have a cash back credit card so this dilemma does not affect me. 😉

to beat the dead horse……

If you are using manufactured spend solely as a perpetual point machine notwithstanding CC sign up bonuses then the conversation is a valid one. The CC sign up bonuses are the major selling point to why we are all here. Sure I could go try the UR mall and generate 11 UR per dollar and make a small profit but that is not a guaranteed return and my capital outlay is considerably higher. The reload is a guaranteed point return on a cash loss.

Why wouldn’t one use the Club Carlson Biz card for 5x points?

The thing with opportuniy costs is that you have to be consistent. The cash card also has an opportunity cost (ie. the best return you could have gotten elsewhere).

Don’t act like the 2% is without cost if you are doing it this way.

As said before, be sure to factor in all benefits of using the non-cash credit card (be it initial spend or other level that gets you something – bonus points, status, companion ticket or whatever).

The benfits of the best card are then an opportuniy cost of the cash reawrd card.

You are basically asking, Do you value starpoints at or above 2cpm? If you do, then buy VR with your starwood card. If not, buy VR with a 2% cashback card. Which would also be true on any purchase whatsoever. If you don’t value starpoints above 2cpm why would you have the card outside of the sign up bonus (or starwood hotel purchases)?

Enjoyed the article but you are way overthinking a simple question about the value of starpoints.

My question is how to dispose of reload cards. My wife and I both have a Bluebird, but there do not seem to be other good options. Any input?

I think you missed one key concept of opportunity cost.

It only applies if you are facing a consumption limit.

If you can buy unlimited reload cards (or as many as you want to consume) then there is no opportunity cost.

But, if you are like me, and have 1 BB, then I am limited to $5,0000 in reload cards.

For what it is worth, I buy reload cards with my cash back card unless there is a bonus I am chasing.

This is very simple from a manufactured spending standpoint. Rule 1, You want a gOod relationship with the bank. Don’t spend too much on one card and spread out your spending. Thus all point wil cost 0.79 cents. The opportunity cost you’re describing does not exist. You’re making sure that the opportunity to use the CC is still there in the future.

Too bad you can’t get vanilla @ OD anymore, this conversation would never have happened.

I would first equate 504 SPG points at 2.2 cents a point.. so that would equal $11.08 – $3.95, which equals $7.13 profit.

Using my Barclaycard arrival 2X on all purchases, I would then equate 1108 Barclaycard points subtract $3.95, which also equals $7.13 profit.

I value both these options the same. Therefore, there is no opportunity cost when comparing these two options. However, if you value SPG points less than 2.2 cents per point, there would be an opportunity cost.

What do you think?

Once the door is opened, the game is new. The new probabilities are 1/2 and 1/2.

what bosstom said, with emphasis on the fact that you are neglecting the different values of the two types of currencies you are receiving.

@Matt B, @Dan…The Wikipedia link that FM provided has all of the details about the Monty Hall problem and why the optimal strategy is to switch rooms. This is a classic problem that is discussed in any course that covers conditional probability.

@Matt B, @Dan…If you still don’t believe the explanation, play it yourself a bunch of times with one of the many simulations available online such as this one: http://math.ucsd.edu/~crypto/Monty/monty.html

Wow, lots of comments, so I’ll try to address them via the theme rather than one by one…

Along the lines of the signup bonus argument, you are also not accounting for spend on cards that have a calendar year bonus. I just earned the TT ticket for the Chase BA card from VRs, but ALSO got the Avios points. Not sure how to value that but it’s certainly >0.

@dan — There is a 1/3 chance that the car is behind the curtain you picked and 2/3 chance it is behind one of the others. That is still true after one goat is exposed. Therefore, after one goat is exposed, there is a 1/3 chance that the car is behind the curtain you originally picked and 2/3 chance it is behind the remaining curtain.

@DBest — The TT ticket is worth about 5 cents in my book. The taxes and fees are a huge rip-off.

To follow on to FM’s Excel suggestion, use one of the many online simulations available after a quick search for “Monty Hall problem simulation”

Great post FrequentMiler. I distinctly remember studying the goat and car prize in statistics class in college. I think it was Applied Probability course or something very similar to it. Ah the good times.

Opportunity cost: All I’m saying is that you have a choice between points or cash back. Regardless of whether you agree that opportunity cost is a good way of thinking about things here, at the end of the day you’ll either end up with a bunch of points or a bunch of cash. I think it is important to decide which you prefer. Even if your opportunity is unlimited (which it isn’t), you are still making a choice and the choice will leave you with more cash or more points.

Sign-up bonuses (and other bonuses): If you are working towards a sign-up bonus (or other type of spend bonus), then the math changes because you no longer compare to 1X. For example, if you’ll get 30K points for 5K of spend, then you would end up with 35K points (30K bonus plus the 5K points you would normally get). In this case, you are earning 7X for your purchases up to $5K. Most point systems will easily give you better value at 7X than 2% cash (although, with some hotel programs that’s not necessarily the case).

Dan, the game is only new if they randomly re-position the goat after the door was opened. Only then would it be a 50-50 chance.

Has anyone ever watched “Deal or No Deal”? If so, is it to the contestant’s advantage to switch briefcases before the final opening? My family has disagreed on this for years.

You have to answer the question of what are you going to do with your miles before you answer the 2 cent question. As I am only using them for Hyatt international premium awards and First Class awards the value is dramatically more than 2 cents……..so for me that exercise is a no brainer………..a more difficult decision is whether to chase Hilton diamond with manufactured spend verses building UR points……

@FM

Right, so a useful comparison (make sure you know what you are giving up), but not accurate at all to say that your cost of acquiring points is 2cpm.

I think your blog is one of the best out there for being the most technical (and I’d almost even call your approach empirical), but I think the fewer economics theories involved, the better (this is a good heuristic for life in general as well) 🙂

Here is another way to look at the door scenario.

If you pick Door 1, you have a 2/3 chance of being wrong, then a 100% chance of being right if you switch. (Overall probability of switching to win = 2/3 X 1/1 = 2/3).

If you pick Door 1, you have a 1/3 chance of being right, then a 100% chance of being wrong if you switch. (Overall probability of switching to lose = 1/3 X 1/1 = 1/3).

Math gets so confusing. Thats why salesmen use it all the time. If I am buying a reload card then I am buying points. There should not be an opportunity to buy cash. (I have cash and want points) It’s different then if you are buying dinner or a TV.

FM, being a west coaster I’m a bit late to the discussion. In the Monty Hall scenario, wouldn’t your odds be 1 out of 2 in the 2nd round? The door with the goat is now removed from the equation – you have 2 doors and one has a car.

@Matt – I was typing when your post went up…thank you for squaring me on the 2/3.

Putting this in the context of manufactured spend and VR cards is irrelevant. It’s actually a simple comparison between SPG and a 2% type card. If you would choose a 2% card for VR, you should choose 2% card for all spending (non bonus categories of course).

A simpler article would be: Is SPG card better than a 2% card for non bonused spending.

There’s a very simple answer to the dilemma. Why not both? (Okay, that’s a question, but cue the cheering crowd anyway)

I have an amount of spend that I’m comfortable manufacturing on any given card and I allocate my VR purchases accordingly. Some go onto a 2% card, some go onto Club Carlson, and some go onto a *wood or equivalent. Putting all that spend onto any one card raises the potential for scrutiny that I just don’t want.

I think in terms of what I am using the points or cash back for.

For example: 90,000 SPG = 110,000 AA miles (80,000 SPG = 100,000 AA + 10,000 SPG = 10,000 AA).

or $1800 on Arrival card.

To use on Cathay from North America to SE Asia in business would cost $6000+ in May 2014. To me the SPG point is giving me more value than the cash back, even factoring in the ~25,000 miles I would have earned using the cash (I don’t have status or using special route bonus).

Another viewpoint:

Let’s say that you choose your door (out of 3). Then, without showing what’s behind any of the doors, Monty says you can stick with your first choice or you can have both of the two other doors. I think most everyone would then take the two doors collectively.

This is pretty spooky. I just did a post awhile back , saying pretty much the same thing, although not quite so eloquently.Is mine a Frequent Miler for dummies blog?

If you do go for the miles, you had better at least be getting redemption value of .02 or better long-term, or you’re just fooling yourself. Most people (read- people who don’t read blogs like this) are going to be better off with the straight 2% rebate.

I agree with Ed on acquisition cost and redemption value. I’ve always looked at points this way. The circular discussion around value of mile or point doesn’t help me as points are arbitrage.

When I calc my cost of points for mfg spend, I only look at out of pocket costs. That’s why I don’t manufacture spend unless there is a decent spread between what I pay for points and what I get in return (award).

62 comments on this already…

You are driving me SANE !!!

Ack, you really shouldn’t have posted the Monty Hall problem in the same post. Now you have people who don’t understand statistics as confused as those who can’t see they are buying SPG for 2 cents (minimum). I recall discussing this topic with you ~3 months ago and concluding a 2% card was probably the best proxy for measuring opportunity cost because using a 2% card isn’t a capped or limited opportunity (unlike juicing spend with AMEX GCs and higher X cards).

Folks, the easiest way to validate the Monty Hall problem is play the game yourself (do this before posting a question)! Have a friend hide a penny under 1 of 3 cups. Guess which cup has the penny, then ask the friend to show you which of the other 2 cups doesn’t have the penny. You will see very quickly that 2/3 of the time the penny will be under the cup they didn’t show you.

It seems to me that you cannot assign the value of forgone cash back, because you did not forgo it.

First, you chose to manufacture points, not cash.

Second, manufacturing points does not stop you from also manufacturing cash back.

You’re really just begging the question of what is better to manufacture.

I find it interesting to see that different explanations for the Monty Hall problem appeal to different people. That is, the explanation that makes the solution most clear to me, might not be the one that works best for you. I think that’s true also for the acquisition cost vs opportunity cost discussion. Everyone has their own way of thinking of it that makes sense to them. Nothing wrong with that.

After the door is opened revealing a goat, the odds now change. The odds with 2 remaining closed doors is now exactly 50/50. It no longer matters what the original odds were with 3 unknown doors. After opening one door it is now only relevant that there are 2 unknown doors, 50/50.

When the Monty Hall problem was published in 1990, over 90% of the public disagreed with the 2/3 answer. The author received thousands of letters that she was wrong (including over 1,000 letters from people with PhDs). Mathematicians constructed computer simulations and, sure enough, the answer is 2/3. There was one famous mathematician who refused to accept the 2/3 until he watched the computer simulation.

Eric: your rational is by far the most common. It was my initial reasoning as well. Yet, incorrect. The 2/3 solution is counter-intuitive and difficult to grasp.

“After a door is selected and the host shows a different door to have a goat, the probability of the car being behind the remaining door (not the one you picked) is exactly 2 out of 3.”

So, it’s not a goat — it’s Schrodinger’s cat behind the other door!

Oh, wow, has there been a response to this question…..and I know the original version of the issue was 1 or 2 percent type cards. But for me it is about 3 things:

1 – clearing the minimum spending thresholds for new card bonuses quickly and easily.

2 – topping off one account or another

3 – nailing tons of point on Club Carlson system and then using the points for redeeming at expensive hotels all over the world, as well as SPG card, and Barclays card at 2%. One needs free hotels when one travels.

If you continue to believe the odds are 50/50, please come see me. We’ll run the game. I will wager $100 against your $90. We can repeat the wager until you are convinced.

I agree exactly with FM’s reasoning. I travel 8 months of the year and can only manufacture gift card spend when in the USA, so my limit is $20K per year on BB and $12K via AP. I calculate the opportunity cost on every spending decision I make.

The problem with the Monte Hall problem is that it never existed. If you ever watched the show,Monte did not give the contestant the choice to switch doors on the final big door prize. You picked your door and you were stuck with it. Same with the new Let’s Make a Deal. Use a different metaphor for that example of chance.

[…] thoughts again over at Frequent Miler with “The true cost of reload points“. Let me say how I see this. 9 $500 Vanilla Reload cards cost $36 (rounded $4 times 9). This […]

Anyone suggesting that VRs cost 2cpp has their head where the sun don’t shine.

[…] Frequent Miler’s post yesterday, he states that the opportunity cost of using an AMEX SPG card to buy a Vanilla Reload card is 2 […]

I go down the opportunity cost rabbit hole when I’m dealing with limited points resources. For example: let’s say that someone buys Visa gift cards with a PIN for $4.95. That’s about 1cpp at $500.

I can use liquidate that card on Amazon Payments for free. Or I can take it to Walmart and buy a money order for 70¢. Because my Amazon Payment usage is limited, I can move that $500 spending to another non-PIN card, all it costs me is an additional 70¢ (and trip to WalMart).

Btw, the crux of the Monty Hall problem is that you want your first choice to be wrong (a goat). If there are 2 goats and 1 car, you have a 2/3 chance of having it wrong. By showing where the other goat is, you are given a “free pass” to change to the car.

If you don’t swap, then you are dependent on having chosen the car first — 1/3 chance.

@ Matt in response 43 – thanks, this explanation made it click for me.

FrequentMiler – based on the number of responses, perhaps you should throw out a brain teaser every few weeks to stretch everyone’s brains beyond the world of miles and points 🙂

Lemma,

awesome analysis. FM should repost using this.

xcg001: Theoretically, if profits from manufactured spending are taxable, then the points are taxable at their fair market value. The fact that it’s difficult to measure their value doesn’t stop Citibank et al. from sending a 1099 in non-CC situations where they give miles (bonus miles for opening a bank account). It seems to me like either it’s taxable or not regardless of whether it’s cash or points, like in situations where you would be sent a 1099. I’m not a CPA nor a lawyer so consult one about your taxes.

Thanks, everyone, for contributing your thoughts, opinions, and suggestions for how to think about this stuff. I love it!

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