It may be impossible to know the number of contestants precisely. However, you may have a good idea whether you're talking about 10 competitors or 100, especially if entries are posted over time. If you don't have any idea, then you should probably not enter.
Similarly, if you cannot estimate the quality of the field (or your own skill), you should probably not enter a contest based on quality.
The opportunity cost is a factor. However, if the chance of winning is 10%, and the prize is $500, it still makes sense to enter instead of doing a $25 commission, unless you need a guaranteed return.
It may be impossible to know the number of contestants precisely. However, you may have a good idea whether you're talking about 10 competitors or 100, especially if entries are posted over time. If you don't have any idea, then you should probably not enter.
Similarly, if you cannot estimate the quality of the field (or your own skill), you should probably not enter a contest based on quality.
The opportunity cost is a factor. However, if the chance of winning is 10%, and the prize is $500, it still makes sense to enter instead of doing a $25 commission, unless you need a guaranteed return.