*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 ðŸ™‚

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 actionâ€”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.