Today, I played Pokémon Omega Ruby for a bit over three hours. Out of curiosity, I looked at how many eggs other people had to hatch before they got a shiny Pokémon. A few said that it took around 1,000 eggs before they hatched a shiny. As my total for one Pokémon so far is over 700 non-shiny Pokémon hatched so far, I have a fair way to go before I reach 1,000 (I hope I hatch a shiny soon though). I don't care if it takes me 5,000 eggs before I get a shiny, I am getting at least one shiny Pokémon from this challenge even if it lasts for longer than a week.
I am aware that if I hatch 683 eggs, none of them are guaranteed to be shiny. However, there is a 63% (0.63) chance of hatching at least one shiny from these 683 eggs. This %chance was obtained from this online calculator (note you may need to divide 1/683 on a real calculator in order for the website to use it). Without boring or confusing you with the mathematics behind it, the calculation (or formula) this online calculator uses is called binomial probability and the website I have provided gives an easy to understand explanation in the FAQ section. Note: This would be useful for calculating the chance of obtaining a shiny with any hatching method (I would not use it for Dexnav shiny hunting and anything similar).
Below are the chances of obtaining at least one shiny from the number of eggs I have mentioned in this post.
700 eggs hatched =64% (0.64) chance
1,000 eggs hatched = 77% (0.77) chance
5,000 eggs hatched = 99-100% (0.99-1) chance (note: The online calculator mentioned does not like numbers above 1,000, so be careful with this).
The point I am making with these probabilities/chances is that there is no guarantee that a shiny will be hatched using the Masuda method but with perseverance, it should happen sometime.