Yesterday, we posted an example on how to generate a Priceline bidding strategy for San Diego using BidSmartForHotels.com. At the time of creating that example, Priceline offered 12 areas in San Diego that did not have 4-star deluxe hotel bidding. For our purposes, those 12 areas are considered free rebid areas because they are areas that we can add to our bid allowing us to bid again for a 4-star deluxe hotel. Since we were bidding for a 4-star deluxe hotel, we know that we can not win a hotel in the free rebid areas.
For our strategy generator, the expert strategy generation mode will always generate the maximum number of bids possible and for San Diego that was an incredible 4096 bids! How did 12 free rebid zones lead to such an incredible number of possible bids? In this article, we will look at the math behind Priceline bidding. We will utilize Google’s calculator feature to apply some basic combinatoric mathematics to the problem.
Remember, a free rebid area is any bidding area within a given city that only offers hotels at lower star levels than our desired star level. If we are bidding for a 4-Star Deluxe hotel, a free rebid area can offer 1-Star Economy, 2-Star Moderate, 2 1/2-Star Moderate-Plus, 3-Star Upscale, and/or 3 1/2-Star Upscale-Plus hotels. The free rebid areas cannot offer 4-Star Deluxe, Resort, and/or 5-Star Luxury hotels.
When we ask what is the maximum number of bids that a given number of free rebid areas allow, what we are really asking is how many unique combinations (where order is irrelevant) can we create from the rebid areas. For example, if we have 1 free rebid area, we know that we can vote for our desired area by itself which is 1 bid and that there is only 1 choice after that and that is to add the free rebid for an additional bid. It’s pretty clear that the maximum number of bids when there is only 1 free rebid area is simply 2.
But what if there are 3 free rebid areas? How do we determine the number of distinct combinations that can be created? It helps if we break it down into the following questions: 1) How many distinct groups of 1 free rebid area are there?; 2) How many distinct groups of 2 free rebid areas are there?; and 3) How many distinct groups of 3 free rebid areas are there? We breakdown the problem into a set of smaller problems.
In discrete mathematics and specifically combinatorics, the number of ways that K things can be selected from N things is typically represented as “N choose K”. This is known as the binomial coefficient. The unique number of ways that we can group 3 free rebid areas is represented by the following equation: (3 choose 1) + (3 choose 2) + (3 choose 3). Adding back in the original single area bid, the maximum number of bids that we can make with 3 free rebid areas is represented by the following: 1 + (3 choose 1) + (3 choose 2) + (3 choose 3) = 1 + 3 + 3 + 1 = 8. So, when there are 3 free rebid areas, we can have up to a maximum of 8 bids on Priceline.
Luckily for us, Google’s calculator functionality will calculate (N choose K) for us. Simply enter, any valid (N choose K) expression such as (5 choose 2) into Google. Google returns the correct answer of 10 to us. How cool!
By using Google, we can easily create the following table that shows how maximum bids increase along with free rebid areas:
It doesn’t take many free rebid areas before we have a large number of bids that we can make. And after we reach 4 rebid areas, it’s likely that we will find the Advanced or Simple Strategy Generation modes sufficient.
Hopefully, you found this short explanation interesting, and remember that bidding for the maximum star level available in a city will typically lead to the most free rebid areas and the most bids any any of the stretgy modes available at BidSmartForHotels.com. Happy Bidding!
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