# Debating my 1.67 cents screwed up math

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In response to my recent post “Up to 1.67 cents per point value from ThankYou points,” some accused me of publishing junky and screwed up math.  I answered those accusations in the blog comments, but there’s more to the story…

When news first came out that the Citi Prestige card would allow 4th Night Free bookings online and with points, a blogger published a questionable conclusion.  Through the ThankYou portal you can now choose to pay with cash or with points.  If you do the latter, you’ll be charged 1 point for each penny of the cash price.  In other words, Prestige points are worth exactly 1 cent each towards hotels.  But this blogger compared the number of points required to the original hotel price before the 4th Night Free discount.  And he concluded that points were then worth up to 1.33 cents each.  I thought that was nuts.  It was 100% clear to me that the point value was straight up 1 cent per point.  If a total booking costs you \$300 after the 4th Night Free rebate, then the point price would be 30,000 points.  There’s no mystery there.  Prestige points are worth a penny each towards hotels.  Period.

I considered writing a rebuttal to this blogger’s post, but then I thought about the situation from a different perspective:

Imagine a couple where one has the Premier card (which offers 1.25 cents per point value for all travel, including hotels), and the other person has the Prestige card.  If this couple wanted to use points to pay for a four night stay, which card should they use?  The answer is the Prestige card.  Let’s take an example:

#### Example: 4 night hotel stay at \$100 per night (to keep things simple, no taxes)

• With the Premier card, the hotel stay would cost 40,000 / 1.25 = 32,000 points
• With the Prestige card, the hotel stay would cost 40,000 – 10,000 (4th night free) = 30,000 points

Conclusion: For 4 night stays, Prestige points are worth more than Premier points

In the above example, you’d clearly want to use the Prestige card to book the stay since the stay will cost fewer points that way.  Therefore, it seems that Prestige points are worth more than 1.25 cents each.  And so, 1.33 cents per point is reasonable.

### I was still not convinced

I was still not convinced that the Prestige offered 1.33 cents per point value, but the above thought process at least stopped me from writing up a rebuttal.  I still believed that if you value your ThankYou points at more than 1 cent per point, then you shouldn’t use those points to pay for Prestige 4th Night Free stays (regardless of whether you do so before or after the stay).

### Then I realized that you can do even better by pooling Premier and Prestige cards….

When you pool Citi ThankYou points from multiple cards, you automatically get the best redemption value.  So, a person with both the Prestige and Premier card would get both the Prestige 4th Night Free and the Premier 1.25 cents per point value towards hotels.  That’s cool, but I was left with the same confusion as before.  On the one hand, points are clearly worth exactly 1.25 cents each in this scenario.  On the other hand, pooled Prestige + Premier points are worth more towards a 4 night stay than other point programs where points are worth 1.5 cents each.  Let’s look at an example:

#### Example: 4 night hotel stay at \$100 per night (to keep things simple, no taxes)

• With Chase Sapphire Reserve (where points are worth 1.5 cents each towards travel), the hotel stay would cost 40,000 / 1.5 = 26,667 points
• With pooled Prestige and Premier cards, the hotel stay would cost 40,000 – 10,000 (4th Night Free) = 30,000 / 1.25 (Premier) = 24,000 points

In this example, ThankYou points are worth more than Sapphire Reserve points.  Sapphire Reserve points are worth 1.5 cents per point towards travel.  In this example, the pooled Prestige and Premier points are worth 1.67 cents each.

### I was still not convinced

Pooling points clearly leads to a way to spend fewer points for a 4 night stay.  It is counter-intuitive, though, to say that the points are worth 1.67 cents each.  After all, when it comes time to pay, you clearly get only 1.25 cents per point value compared to the cash price.  For this reason, in my previous post on this topic I added a section titled “Wait, isn’t the value really just 1.25 cents per point?”  I wrote and re-wrote that section several times.  In a way, today’s post is yet another re-write of that section.  But, I still mostly agree with what I wrote there:

Ultimately it depends on whether you compare the point price to the original hotel price or to the price after the 4th Night Free.  If you compare to the former, then your pooled points are worth up to 1.67 cents each.  If you compare to the latter, then they are worth exactly 1.25 cents each with the Premier card.

In other words, if you take it as a given that you are using the 4th Night Free benefit and you’re simply trying to decide whether to use points or pay with your Prestige card, then your points are worth 1.25 cents each with a pooled Premier card.

On the other hand, if you are trying to decide which points to use for a hotel stay, and if all paid price options are equal, the 1.6 to 1.67 per point value is accurate since you can’t use other point currencies to book 4th Night Free stays.

### More intuitive to think of it as a discount

In retrospect, I think that the entire topic is better understood in terms of discounts rather than point value.  When a card offers more than 1 cent per point value towards travel, that means that travel rewards cost fewer than 1 point per cent.  For example, with a card that offers just 1 cent per point value, a \$100 award would cost 10,000 points.  But with a card that offers 1.25 cents per point value, a \$100 award would cost 8,000 points.  That’s a 20% discount.

Via this approach, we get:

• Chase Sapphire Reserve: 33.33% pay with points discount towards travel rewards
• Citi Prestige: 4th Night Free = 25% discount for 4 night stays with no taxes, but no additional point discount
• Citi Premier: 20% pay with points discount towards travel rewards
• Pooled Prestige plus Premier: Prestige 25% discount combines with Premier 20% discount = 40% discount

I’m sure some readers will tell me why the above is wrongheaded, but to me it’s clear.  The Prestige card offers up to 25% off hotel stays.  And if you have a pooled Premier card, the Premier card offers an additional 20% discount that applies only if you pay with points.  Whether or not it’s a good idea to pay with points is a whole different story…

### The ultimate nail in the 1.67 cents per point coffin

I’m now convinced that when combining a discount or rebate (4th Night Free) with point values, we should discuss the combination as discounts rather than point values.  While I don’t think that my math or logic was wrong, I now think that I was wrong to describe the combined benefit as “up to 1.67 cents per point value.”

I still think that it is logically correct to say that the combination of the Premier and Prestige card can offer up to 1.67 cents per point value towards a hotel stay, but only until you take it as a given that the Prestige benefit will be used.  The problem is that it is not helpful to think of point values in that way.  Here’s an example of where it would be problematic to think of it this way: If you took the 1.67 cents thing at face value, you may excitedly sign up for both cards in order to get that value from 4 night stays. But then, once you decide to use the Prestige 4th Night Free benefit, the 25% discount becomes a given and the decision to use your ThankYou points comes down to whether or not you want to get 1.25 cents per point value from the Premier card.  And, at that point, you would say no because you believe that you can get up to 1.67 cents per point value!

I now think it is much better to say that it is possible to stack the Prestige 4th Night Free discount with the Premier 20% pay with points discount.  Whether you want to do the latter depends on whether you value your ThankYou points at or below 1.25 cents each, and whether you’re willing to accept the ThankYou portal’s online booking limitations (inability to apply promo codes, possibility that you won’t earn hotel points for your stay, etc.).