What is this card game?

I played a card game with some friends long ago and don’t remember what it was called. It was for 4 or more players, you started with 2 decks 4 people, then added another deck for every 2 players. The game was played in 6 rounds and every round the objective got more difficult.

Deal 10 cards to every person. Put the rest of the cards face down in the middle and turn one over. On every turn a player must pick up (the face up or face down card) and discard (into the face up pile). The discard may be claimed by any other player, but the player whose turn is next has dibs on it. When you have all the required hands you “put them down”. When other players put down AND you have put down, you may put your extra cards onto either players hands. The object of the game is to get rid of all your cards (“go out”). When you go out, you still have to pick up and discard on that round. A player going out ends the round.

As far as I can remember the hands alternate between trips (3 of the same value card irregardless of suit; ie 3 Aces) and runs (sets of 4 consecutive cards of the same suit; ie 2, 3, 4, and 5 of clubs). The round 1 objective was to get 2 trips, round 2 was a trip and a run, until the last round which was 3 runs. Cards remaining in players hands are worth face value for numbered cards, 10 for JQK and 20 for A. Lowest score after all rounds wins. I don’t remember if Aces were high, low, or either (in runs).

Also, there were restrictions on how many times you could claim discards outside of your turn (which would give you an extra card). I think it was one claim for rounds 1 and 2, 2 claims for rounds 3 and 4, and 3 claims for rounds 5 and 6. If someone else claimed the same discard, whoever yelled first got it. And as I said, the person whose turn was next could deny and pick it up himself as part of his turn (no claim used).

It was a fun game that required more strategy as it went on. I played it with 10-12 people and it was a blast, but it was more strategic with 5-6 people. Has anyone else ever played it? What is it called?

I knew this as Michigan Rummy.

Too late to edit (for clarity): Starting the turn after you “put down”, you can get rid of your extra cards by adding them to any put down stack. For example, if someone (including you) has put down a run of 4, 5, 6, 7 of hearts, and you have a 3 or 8 of hearts you may add it to that stack. Stacks have no point value, only cards in hand are worth points at the end of the round. You can put down and go out in the same turn (I think).

I think this was a favorite if my three aunts. They called it, “Oh, Shit!”

Yes it’s rummy: http://www.rummy-games.com

My Dad’s side of the family like to play this for money. So when I visit this is how we often finish the evenings after the kids have been put to bed. We have some odd little family rules though, not sure if these are more widespread. For instance you can call for a re-deal and if everyone agrees then the money rolls over and the next game is worth double the cash. Of course, if someone doesn’t agree to a re-deal then they are showing strength and get watched very closely by everyone around the table.