*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.

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[…] you use a mileage card instead of a cash back you are buying miles slowly at 2 cpm. http://boardingarea.com/frequentmile…reload-points/ __________________ Fix US http://www.azag.gov/consumer/complaintform.html Avoid CHASE. Aim for […]

Cole, I like your example. If you pick one card from a 52 card deck, then at least 50 of the 51 remaining cards will not be the Ace of Spades. The dealer, knowing the cards, just shows you those 50 cards.

Monty Hall initially seems so simple and it is amazing how strong the human impulse is to think 50-50. I’m surprised casinos haven’t used this to their advantage.

Consider a casino game based on Monty Hall (but where a player cannot switch). This leverages the player’s false belief that their odds are improving as the game progresses.

There a 10 doors. Behind one door is a magic ball, the other 9 doors are empty. The player makes an initial guess of which door has the magic ball. One by one, the remaining empty doors are opened. As each one is opened, the player gets more and more excited s/he could win – its looking better and better for me! Once there are two doors left, the player is given the option to bet on their door with 5:1 odds. The player thinks There are only two doors left, there is a 50-50 chance the magic ball is behind my door – and I get 5:1 odds?!! Heck yea! I’ll bet the farm on that! The player actually has a 1:10 chance and the casino would make a fortune.

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

I’m a math teacher and tried to explain the Monty Hall problem to a group of sophomores my first year teaching. It was a disaster.

I think an example that might help is to try to pick the Ace of Spades (the car) from a 52 card deck. Once you’ve made your pick, the all knowing host reveals 50 of the remaining 51 cards and none of those are the ace of spades. You’re left with your card and the card leftover by the host’s actions. Do you want to switch?

Of course. It’s not 50-50. You only had a 1/52 chance of being right originally.

I also like the explanation to ignore what the host does and consider choosing between 1 door/card and the other two doors/51 cards.

Lemma: It is not true that points should be taxable as they don’t have intrinsic value – most points expire and subject to devaluation as they are technically not owned by you but by the operator of the program. In fact ALL frequent program (miles, hotel points) state EXPLICITLY that points have no value. And in fact Citibank stopped issuing 1099 after being criticized for that.

Cash and other financial derivatives on the other had has nominal value and there is no way to argue that it is not a profit. May be you can wiggle your way as a “income from hobby” but not for amounts that most people manufacture spend. If it is worth getting the cash back (>$1000 per year) there is no way to argue that this is non taxable profit.

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.

What this article (and many posters) misses is that when you are getting 2% cash back that represents ~ 1% profit that is actually taxable.

Normally cash back is not taxable since in most cases it is like a rebate on a regular purchase but not in this case. It will be extremely easy for IRS to show that you are making $6.05 profit on each VR purchase so you should consider your tax bracket. And I am willing to bet that people engaging in manufactured spending are much more likely to get audited than general public. So for me personally 1.25 AA points wins easily not even considering that 30,000 spending on SPG card gives you gold status.

Lemma,

awesome analysis. FM should repost using this.

A lot of incorrect reasoning in these comments, I think somewhat motivated by the idea that earning free travel is fun while earning a modest cash profit is less exciting.

Opportunity cost is indeed important, but the opportunity cost is different for different people. The way this would be put in a microeconomics 101 class is: rational people think at the margin. That means you aren’t concerned with the value of the best redemption you ever got with SPG (or whatever program), you are concerned with the value of the redemption another 504 points would go towards. Because if you didn’t buy that VR, you would still have gotten that best redemption ever (or even the average redemption), just not the marginal one that you would have to give up. (This is why, as FM has pointed out, UR points are so valuable – they can be transferred to top off an account where they will have very high marginal value.) Likewise whether FM’s scenario #1 (cost = 0.79 cents) or scenario #2 (cost = 2 cents) is correct for you depends on your situation. What are YOU giving up by buying that VR on your SPG Amex? For some people it is 2 cents, for others it is 0.79 cents.

If you aren’t manufacturing spending at all, you can put your spending (ignoring issues like merchants that don’t accept Amex) on whatever CC you like without fear of shutdown. So CC spending ability is not a limited resource and the cost of $1 of spending on SPG Amex is at least 2 cents (maybe higher if you have the JCB Marukai card, buy Amex GC, etc.) because you could have put that $1 of spending on another card. FM is implicitly applying this principle when he says 2 cents should be used rather than a higher value because the 2% is unlimited and unrestricted, but you can buy $5k worth of Amex GC every 14 days on a 2% card through TCB. Some people might not manufacture that much spending anyway, so Amex GC might be effectively unlimited for them, making the true cost of points higher than 2 cents.

Now let’s consider someone who only manufactures a little bit of spend, say $5k/mo of VR they can load to BB. Unless they have a low CL they can still probably put that 5k in addition to their normal spending for the month on one card, especially if they make multiple payments during a cycle. So we are still in FM’s scenario #2 where the cost is 2+ cents per point. If you value SPG points at 1.5 cents each, you might say you are still ahead if you buy VR and pay 0.79 cents. True, but you could have been more ahead if you had used the Priceline Visa instead. If you think that’s not very worth it to use the 2% card for such a small profit, well you were willing to do it for a smaller profit (unless the SPG points are worth more than 2 cents to you, and they might be).

But now suppose you are a heavier hitter, I won’t give any specific numbers because how much you have to do to fall into this category is highly variable but suppose you manufacture enough spending so that you have to spread it around multiple credit cards in order to not get shut down. Then, you might already be doing as much as you feel comfortable on the 2% card (and it’s wise to go for the long run benefits by playing it safe). So, your cost might only be the 0.79 cents if the SPG Amex was the only card you felt comfortable putting that extra $503.95 of spend on. This is the only way FM’s scenario #1 is correct.

On the other hand, as I pointed out, the value of the first SPG point earned from CC spending is higher than the value of the last. If you are earning sign-up bonuses or getting a category bonus buying VR on a miles/points card, then it’s probably better to earn that bonus than get the 2% CB. FM has discussed the proper way to value points before but it depends on what YOU would buy with them (at the margin!). As with valuing miles and points, this is a situation where you have to think for yourself about your own circumstances.

@ 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 🙂

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.

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).

[…] 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 […]

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

[…] 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 […]