Should You Enter Book Award Contests?

​Should you enter the Book Award game?
It is about as difficult for a self-published author to get noticed as it is to undertake a mission to colonize Mars.  Two of the most common ways to gain attention for your work is through book reviews or book contests.  Here’s the rub – the self-published author must pay a fee to enter the contest.  Everybody has their hand out to help a self-published author; the problem is they expect you to put money in their hand to help.
I subscribe to the Writer’s Digest because they have a number of interesting articles every month on the craft of writing and the business of writing.  They have supported self-published authors for years.  In fact, they run a self-published author contest annually and this is their 25th year.   The prizes include:
One Grand Prize for $8000 and a feature article in their magazine and a trip to their annual convention
First Prize in a Category $1000 (there are 8 categories) and other promotional items
Total cash prizes $16,000
Sounds alluring.
But WAIT.  The entrance fee for a book is $99 plus the cost of your book plus shipping.  In my case it would cost me about $121 to enter this contest.  There is a potential to win only one of two prizes – the Grand Prize or the Category Prize.
Los Vegas is required to inform you of the odds of a winning a game when you gamble.  I think that all book competitions should inform entrants on how many submissions they receive each year.  With that information you could roughly calculate your odds of winning.  For example, if 9451 people enter the literary fiction category – my odds would be 1 in 9451 or 0.0001.  For the grand prize let’s say 23,801 submit entries so my odds would be 1 in 23,801 or 0.00004.
Of course, self-published authors must invest in themselves.  I accept that.  I compare the cost of entering a contest to how many books I would need to sell just to break even.  In my example, above, I would need to sell between 8-9 books to break even.  The problem is, just entering the contest doesn’t gain me anything, I would need to win in order to get enough promotion to sell those 8-9 books, then you need to look hard at the odds of winning.
I’ve researched and was unable to learn how many submissions there are each year so it’s impossible to determine your odds of winning.
There is something that doesn’t settle right with me for any award that I have to pay for to receive.  A rational analysis indicates it’s not a good investment for a self-published author.