The rules are simple as is the game but there are lots of details. You play with two decks, deal 3 cards on the first hand and threes are wild (along with the jokers). In the next hand you deal 4 cards and the fours are wild. When you get to Jacks being wild, the deal is 11 cards; Queens 12 and Kings 13. Some people play with 14 cards to make the Ace wild but you can run out of cards if you're playing with six people or more. (If you play with more than 6 people you might want to add a third deck of cards.)
There are many variations to the rules of 313. Click here to find the most generic set on John McLeod's pagat.com website. (John will not allow us to post the rules here.) With these in mind you can make changes and customize your own version. Some of those variations are listed at the end. Thanks to Leah Mathis for submitting this very comprehensive overview of 313.
I've done some research and found that the game known as "313” doesn't have much of an internet presence except for the Pagat website where so many card games can be found. Sometimes you will find it as "313 Rummy." Other web pages featuring the game "313":
This is a blog post from "StChristoper" in which he touts the game as being for 3 people and his rules are just a little different. Click here for his website. It hasn't been active for 2 years or more.
"Suite 101" is a website that seems to catalog of lot of useful information, bearing in mind that "useful" is in the eye of the beholder. Here Robin Lewis posted another version of 313 in which you can play your cards on others once they have been put down. Not sure if you can put those cards down before going out or not. (Wasn't clear in the instructions.) Robin seems to be a little more active as her post was updated in March of this year.
Last but not least, there is an online version by the name of "Rummy 313" but it is only for Android users (3.2 and later) and is $1.99. There are no plans to write this program for iOS or PC users.
Anyone who wants to contribute another site please let us know.