The Bidding Traveler blog

We’ve recently released some revisions to the site based on feedback from users that we’d like to tell you about.

The first is that we’ve made it much easier to see a list of hotels for a given area.  You’ll notice on the homepage, once you select a city where we have information, you’ll have a “Just Looking” option.

That will bring you to a new page we call the “research” page where you can clearly see the hotels you might end up winning.  We’ve also displayed the retail price next to these hotels so you can see how much money you save from Priceline bidding.

There’s another feature that’s somewhat related to this research page.  Users have long asked us for a method to add their own past Priceline bids to the site.  Previously, we had been collecting these through email and through regular usage of the site.  But we’ve introduced the “My Trips” page where you can add your past history, and we’ll even calculate the approximate savings off the retail price for you.

The best part about this is that you don’t have to provide your email address or sign up for an account.  We’ve always hated this aspect about other sites that force you through a cumbersome signup process and then smack you on the hand for writing your posts a certain way.  Try it out and you’ll be pleasantly surprised.

You can also personalize your account by giving it a name, after which point it’ll show up in the search results.

We’ve posted in the past about determining the optimal bidding strategy for Priceline.  In that post, we talked specifically about maximizing the number of bids you had at your disposal.  But that presents an interesting quandary.  Just because you have 20 or so bids at your disposal, does that necessarily mean you’ll have the patience to actually run through them all on Priceline?

When we originally designed the ability to execute these bids on Priceline, we assumed that most people would only have the patience for a few bids.  So, given a particular bidding range, we generated strategies which had a good balance of good bid increments and not having to do too many bids.  For example, here’s what the default strategy is, starting at $100 and ending at $115:

The problem was, we kept receiving email from really hardcore, patient bidders who were telling us: “I know I have more bids to use, why are you only offering so few?”  I guess a lot of you guys out there really do want the best price.. to the dollar.. and are willing to increment very slowly until you get it.

So, on that note, we’ve made a minor change to the bidding strategy generator that will let you past the default strategy.  For that $100-$115 bid, you’ll now be able to generate a strategy like this:

It’s important to understand that this isn’t the default option, and you’ll have to change the dropdown if you’re a patient person and want to do a lot of bidding.  Also, this expanded strategy is only available in the manual bidding path (AutoBid will always use the default bidding strategy).

It’s been a while since we’ve done a blog post, mainly because we’ve been busy writing some new features for the site which we’d like to share with you today. They’ll make it easier for you to get that elusive hotel at a great price.

The first improvement is that in the manual bid path we have begun to collect counteroffer information. A counteroffer occurs when Priceline denies your bid, but then suggests a “one-time opportunity” (one time, sure..) .. you can retry a bid immediately if you raise your offer price to a certain amount. This is called a counteroffer because if you agree to their terms your bid is sure to succeed.

Unfortunately, the counteroffer amount is almost always a significant margin away from the optimal price. Still, it provides useful information because it represents a price that you can be sure you will get a hotel. The information itself has been the subject of some lively debate at Flyertalk.

You’ll notice if you do a bid manually on our site now, you’ll see a screen like this:

Additionally, we’ve begun to surface the information we have for this in the map screen itself.

This will provide invaluable information as to how much you should bid for on your Priceline hotel.

Finally, we’ve extended another feature that has existed for our AutoBid users for quite some time. However, if you’re been bidding manually, you’ve probably had your own share of failed bids where you don’t end up winning. We’re now pleased to offer you the option to get emailed the first time another site user ends up winning a hotel with similar criteria to yours.

Bidding for a hotel on Priceline actually has some pretty interesting mathematical properties that can potentially get you a better price. In this post, I’ll cover them. A quick note before you read on though.. (especially if you hate math!).. this is purely an academic post, since we’ve got a handy site to do these computations for you and get you a great deal on Priceline!

Remember the rules for bidding for a hotel on Priceline? If your win gets rejected, you need to either add an area that you’re willing to stay in, or drop the star level of the hotel you’re looking for, if you want to bid again. Otherwise you have to wait 24 hours.

Let’s talk about about that first part, adding an area that you’re willing to stay in. If you’re interested in staying in more than 1 area, it makes sense to order your bids strategically so you can bid again without waiting 24 hours. Let’s take a very simple case. Say you want to stay in Las Vegas, and you’re interested in both the “Las Vegas Strip North” and “Las Vegas Strip Vicinity South” zones. For simplicity, I’m going to name these zones A and B. Let’s say you are NOT interested in staying anywhere else — it has to be one of these two areas.

So, should you start a bid and select these two zones? Well, no. If your bid was rejected, you would have to wait 24 hours, because you wouldn’t be able to add any more zones that you were willing to stay in. (A and B would already be used up!). Instead, you should do it this way:

A   - bid 1
  B - bid 1
A B - bid 2

See what we did? We bid for zone A first (individually), then zone B (individually), at a particular price, which we called “bid 1.” If both those fail, you can then do another bid with both zones together at a slightly higher price, because you have added zones to a prior bid.

The more zones you select, the better your options are. Let’s take a slightly more complicated example where you were willing to to stay in 3 zones. The optimal bidding pattern would be:

A     - bid 1
  B   - bid 1
    C - bid 1
A B   - bid 2
A   C - bid 2
A B C - bid 3

Cool! 3 bids. That’s a lot better than just the one bid you would have gotten had you started with all three zones (A B C). If you notice, we start with single-zone bids first (”singles”), then move to “doubles”, then finally, the “triple”, because you have to always be adding zones you can stay in. In other words, mathematically, you can’t bid a subset of a bid you’ve already submitted.

Ok, let’s take it up a notch. These computations are pretty easy. What happens if you’re willing to stay in 5 zones? Well, initially, you would just run through each of the 5 zones individually, the “singles”. Nothing too exciting here.

A         - bid 1
  B       - bid 1
    C     - bid 1
      D   - bid 1
        E - bid 1

It gets slightly more interesting when you have 2 zones you need to select from the 5 you’re willing to stay in, the “doubles.” Here are all the combinations:

A B       
A   C     
A     D   
A       E 
  B C     
  B   D   
  B     E 
    C D   
    C   E 
      D E 

Ok, remember, we’re willing to stay in any of the zones, from A to E, so each bid amount you’re doing needs to cover all the zones, right? So, you actually have to order these combinations in such a way that each zone, A to E, gets a bid. For 5 zones, these so-called “doubles” aren’t too hard to optimally order. If you look at the combinations I’ve posted, I bet you can find the optimal solution after thinking about it for a bit.

A     D   - bid 2
A       E - bid 2
  B C     - bid 2

  B   D   - bid 3
  B     E - bid 3
A   C     - bid 3

A B       - bid 4
    C D   - bid 4
    C   E - bid 4

      D E (unused)

There you go. We managed 3 bids out of these doubles. If we add that to the bid we got from the singles, that’s 4 bids so far!

Ok, ready for a challenge? With 5 zones, these are the possible “triples”… where we bid on 3 out of the 5 neighborhoods.

A B C     
A   C D   
A     D E 
A B   D   
A B     E 
A   C D   
A   C   E 
A     D E 
  B C D   
  B C   E 
  B   D E 
    C D E 

Alright, here’s a challenge for you. You need to order these combinations in such a way that zones A to E all get a bid. In other words, you need to maximize the number of “complete sets” here, where a complete set means that all zones, A to E, are covered. How many complete sets do you think you can make? It’s probably pretty easy to make 3. You just have to go in the exact order that I listed the combinations in.

A B C     - bid 5
A   C D   - bid 5
A     D E - bid 5

A B   D   - bid 6
A B     E - bid 6
A   C D   - bid 6

A   C   E - bid 7
A     D E - bid 7
  B C D   - bid 7

  B C   E (unused!)
  B   D E (unused!)
    C D E (unused!)

Hmm, we got 3 bids from 3 complete sets, but 3 combinations at the end got wasted, because there aren’t anymore A’s left to use. We should have been able to squeeze more than 3 bids out of this. Isn’t there be a more optimal way to order the combinations? As you humor me and do this little exercise, just think how about how much mental effort you’re expending to solve the puzzle. Can you get 4 complete sets? How long did it take you?

Well, guess what? The optimal solution actually has 5 complete sets.

A B     E - bid 5
    C D E - bid 5

  B C D   - bid 6
A   C   E - bid 6

A     D E - bid 7
A B C     - bid 7

  B   D E - bid 8
A   C D   - bid 8

  B C   E - bid 9
A B   D   - bid 9

A   C D   (unused)
A     D E (unused)

This little exercise I just took you through is known in computer science as a packing problem. The reason why it’s called a packing problem is because you’re trying to “pack” differently shaped pieces into a single set, a complete set, minimizing the waste. As you can see, we had a lot of waste in the trivial 3-complete-set solution, and by re-ordering, we managed to get 5. Packing problems are among the more difficult problems in computer science because finding the optimal solution can take computers an extremely long time. Think about how much time you spent trying to do this 5-zone solution, and how long you think it would take you to do a 10-zone solution! That’s a lot of work to save money on a Priceline hotel, don’t you think?

But wait, it can get even crazier. Much has been written on the Internet about “free rebids” on Priceline. A free rebid occurs when you add a zone that doesn’t have hotels at the star level you are looking for. For example, if you want a 5-star hotel in Vegas, the “Las Vegas Airport” zone counts as a free rebid, because it doesn’t contain any 5-star hotels. Therefore, you can add it and bid again, knowing that you will not win a hotel in the free rebid zone, because there is nothing to win.

Now, can you recall everything we’ve talked about regarding bid ordering so far? The same thing applies to the free rebid zones. They themselves can get ordered optimally, and each combination of free rebid zones can be permuted with the optimal ordering of your regular bidding zones! Maybe it’s probably easier if I just showed you. Let’s say we had our standard five zones, A-E again, and two free rebid zones, Y and Z.

A B     E         - bid 5
    C D E         - bid 5

  B C D           - bid 6
A   C   E         - bid 6

A     D E         - bid 7
A B C             - bid 7

  B   D E         - bid 8
A   C D           - bid 8

  B C   E         - bid 9
A B   D           - bid 9

A B     E    +Y   - bid 10
    C D E    +Y   - bid 10

  B C D      +Y   - bid 11
A   C   E    +Y   - bid 11

A     D E    +Y   - bid 12
A B C        +Y   - bid 12

  B   D E    +Y   - bid 13
A   C D      +Y   - bid 13

  B C   E    +Y   - bid 14
A B   D      +Y   - bid 14

A B     E    +  Z - bid 15
    C D E    +  Z - bid 15

  B C D      +  Z - bid 16
A   C   E    +  Z - bid 16

A     D E    +  Z - bid 17
A B C        +  Z - bid 17

  B   D E    +  Z - bid 18
A   C D      +  Z - bid 18

  B C   E    +  Z - bid 19
A B   D      +  Z - bid 19

A B     E    +Y Z - bid 20
    C D E    +Y Z - bid 20

  B C D      +Y Z - bid 21
A   C   E    +Y Z - bid 21

A     D E    +Y Z - bid 22
A B C        +Y Z - bid 22

  B   D E    +Y Z - bid 23
A   C D      +Y Z - bid 23

  B C   E    +Y Z - bid 24
A B   D      +Y Z - bid 24

Wow, 24 bids. And that’s just doing the “triples” within our selections of 5 zones that we’re willing to stay in. We didn’t even cover the “quadruples”.. I’ll leave that as an exercise to the reader. In the meantime, come check out the other cool stuff we’ve built at the Bidding Traveler!