Sunday, September 30, 2012

Analyzing the DubLi Xpress Gift Card Auction

Go to and click on the "Play Video" link for the Xpress auction.

The video describes a type of reverse auction in which you can buy "Gift Cards". Gift cards are vouchers worth a certain amount ($100, $200, etc.) from many different stores such as: Amazon, Disney, Starbucks and Macys.

It is even possible to purchase a Gift Card from Mastercard or American Express, in which case (I assume) the money is available on your credit card and can be used to purchase anything you like.

The Gift Cards are guaranteed to be sold at a discount because of the nature of the reverse auction.

As the video explains, there are a limited number of cards on auction, and potentially thousands of bidders for each card at any one time. You see the type of card being auctioned, for example: $100 Amazon Gift Card, but you do not see the current price when you enter the auction. Instead you have 2 buttons: "Show Price" and "Buy Now!".

A click on "Show Price" reveals the current price. Each time someone does this, the price goes down 20c. Anyone who is happy with the price can click on "Buy Now!" to purchase the card at the current price (but you must click at least once on "Show Price).

Each click on "Show Price" costs you one DubLi Credit. DubLi Credits have to be purchased beforehand, and cost 80c each.

Sound like a good deal? After all, in some cases you can get a 50% reduction for the cost of one credit (80c). Apparently thousands of people think so.

But, as we examine things a bit closer, a different picture arises. The problem is the, so-called, house advantage, which can be shown to be 75%. Compare this to American Roulette which has a house advantage of 5.26%.

To understand this, the first thing you have to know is that the Xpress auction is a game of chance. Your bets are the credits you spend, and when you click "Buy Now!", you win if your click is in before any of the other players trying to "win" the card. So, if 1000 people are bidding for a card, your chances of winning are 1 to 1000, assuming everyone uses the optimal strategy (more about this later).

Now if you have a chance of 1 in 1000 of winning, then to be absolutely fair, the payout should be 1000 to 1 (for betting $1 you should get $1000 if you win). But, this is never the case because then a Casino could never earn anything. The difference in odds to payout is called the house advantage. It means that, in the long run, this is the Casino's "sales margin", and since every Casino has expenses, everyone understands that this is necessary to make gambling a viable business.

But what about a house advantage of 75%?

Consider the following:

You walk into a casino and look over in amazement at the roulette table. Gathered around it are literally thousands of people, all madly placing bets in what looks something like a gold rush! You realize you must be missing some massive winning streak, and run over to join in!

You are about place a bet, but when you see the Roulette wheel you are shocked. Instead of the usual two green numbers, 0 and 00, the wheel has whopping 108 green numbers on it! The man next to you places a bet on red, and you ask him what the payout is. He looks baffled and says: "Red and black, pays 2 to 1 of course..."

What you are witnessing is a house advantage of 75%. Now, would you place a bet?

Well the scene described above is similar to what is happening at DubLi. From the illustration it is clear that a house advantage of 75% is so high that people would normally never place a bet. So the only reason I can think that people are playing is because they cannot see the wheel!

But how do we get the 75%?

Firstly, let me explain how to calculate the house advantage. You take the "fair" payout and subtract the actual payout, and then multiply this by the odds.

For example, in the case of the Roulette wheel with 28 numbers (18 black, 18 red, and 2 green), a fair payout is 38 to 1, because the odds are 1 to 38 (1/38). The actual payout is 36 to 1, so the difference is 2 (38/1 - 36/1). Now we multiply this by the odds and the result is 2/38 which is equal to 5.26%.

This reflects the fact that there are 2 ways of creating a house advantage: increase the odds with the same payout (which is what is done in roulette, where the odds are increased by adding green numbers but the payout remains the same, i.e. as if the green number were not on the wheel), or you can keep the same odds, and decrease the payout (this is what DubLi does).

So to figure out the house advantage for DubLi, we need to know the odds, and the actual payout.

We start by assuming that we have N DubLi members (you have to have a VIP membership subscription to be able to take part in an Xpress Auction) auctioning the same card. Now when calculating the house advantage we always assume that all players use the optimal strategy (if they don't, things just get worse!).

If all members are using the optimal strategy, then they are also using the same strategy, which in turn means that the odds of any member winning the card are the same as any other. So the odds of any member winning are simply 1 to N, in this case.

Now let us assume that the number of clicks on the "Show Price" button, before the card is won, is M. This means that the price of the card is reduced by M x 20 (20M) cents before it is purchased. So 20M cents is the amount the winning member actually wins (because he has to pay for the rest of the card).

Since all members are using the same strategy we can assume that all members will click the "Show Price" button the same number of times, on average, before they press the "Buy Now!" button. This means that each member pressed the "Show Price" button M/N times (M divided by N), including the winner. This means the winner is "in" for M/N x 80 (80M/N) cents. So we now know the payout. On a bet of 80M/N cents, DubLi pays out 20M cents, which means the payout is 20M to 80M/N, or (20M) / (80M/N) to 1 which is N/4 to 1, after simplification.

So the house advantage is: N/1 (fair payout at odds of 1:N) minus (N/4)/1 (actual payout) multiplied by 1/N (the odds).

And, (N/1 - (N/4)/1) x 1/N = (4N/4 - N/4)/N = (3N/4)/N = 3/4 = 75% QED!

Is this the same as a Roulette wheel with 108 green numbers? Lets check:

A Roulette wheel with 108 green numbers has a total of 144 numbers (18 black, 18 red, and 108 green), so a fair payout is 144 to 1. The actual payout is 36 to 1 so the difference is 144 - 36 = 108. The odds are 1 to 144, which we multiply by the payout difference to get 108/144 = 75%.

Now if that was all, that would be certainly be bad enough, but it gets worse!

Imagine a Casino that does not convert your chips to cash at the end of the day, but instead gives you a voucher for Starbucks! And imagine a Casino that does not let you place a bet until you have signed up for a monthly membership fee!

Well that's DubLi ... enjoy!


Anonymous said...

Great analysis, but you need to add a couple of facts to make it factual.
1.- The subscription you buy, pays you back in full and more your credits. The 80c cost calculation, you need to drop to about 60c.
2.- The gift cards cash you win is actually deposited into a debit card, where you can take your money out. So, this is the same as cashing your chips in a casino.
3.- Almost all gift cards are discounted at least $2, or more. On average - really you have to check to see - DubLi gives back almost, if not all or more, of the money it receives in the gift card auctions.
I suggest you check the website, run the numbers again and repost. It would be interesting to see if it is really more fair the way they've changed it. You actually would wonder, if they make any money with these changes.

Paul McCullagh said...

Indeed, these facts would make the Gift Card Auction much more fair, maybe even a "good deal".

So it is very strange that DubLi has no information about this on their Web-site. Surely DubLi is doing itself no service by not mentioning these facts on the Web-site.

As I mentioned in my analysis, I am going simply by the information supplied by the Web-site.

On the web-site there is no mention of the points you listed.

In particular, there is no information on the Web-site that the "Gift Cards" you auction are like a Casino chips (i.e. you win cash). This makes a big difference, of course!

There is also no mention of a discount of at least $2 per card. This is even more significant, and changes the calculation considerably.

According to the Web-site, credits cost 80c (Dollars). I believe on the European site they cost 60 EUR cents.

So, while all you say may be true, why doesn't DubLi make this additional information official (any link or reference to such information would be welcome)?

If DubLi actually offers a good product, then I will be more than willing to re-do the calculations to prove it.

But, I would require an official statement to this effect. Anything else would mean they can change the rules anytime they like!

And it all comes down to the rules in the end. Every casino game has rules. Because players know the rules they are able to calculate the risk and the reward.

This is what I have done, going by the rules that DubLi has published for their Auction.

If DubLi has not published all the rules, and that make them look bad, then that's a problem they need to solve..