Quote Originally Posted by Pelion
You have just (almost) described crazy pineapple. In that game you start with three hole cards and discard one on the flop.
I was a at a casino in Calgary once playing Pineapple like this. But they also opened up another table with a variation of Pineapple where you decide on the river which hole card to toss. I thought the latter was called Crazy Pineapple but I must be wrong.