Guides

First of all, egg drops are rare and too low to calculate. You can, however, influence the odds in your favor.

Start by looking at Maki's Coli Drop Guide.

Per the guide, eggs drop in all but venues and are dropped only by the monster with the same element as the egg. You'll want to fight in the venue with the fewest number of neutral monsters. As of November 4, 2018:

If you're looking for a specific element of unhatched egg check Georgieanna's Coliseum Element Odds Guide to see which venues have the highest encounter rate for the element you're looking for.

By spending my grinding time in venues that I can 1-shot Eliminate everything or have easy bosses I've been able to bring my average up to 3-5 eggs per month. As a warning I typically spend at least a couple hours a day every day doing this.

Leveling exalts and buying eggs from luckier people in the AH is much, much faster.

Update 12/12/18 with new info based on FR changing egg drops so that they drop from every elemental monster.

Wow. I guess I have a lot to do before my dragons are in a level high enough to battle in those venues. This thread was pretty helpful anyways. Thx for doing this!

@mizta According to the elemental guide I linked to in my first post the current venue with the lowest chance and fewest number of neutral monsters is the Sandswept Delta. Additionally you might want to use an [item=tincture of dissolution] to reset the stats of your coli team to help you battle faster. Eeveedream's [url= http://www1.flightrising.com/forums/gde/2217190]Sedona Guide[/url] has great stats for a team without Eliminate.