This is a variation of the Piggy game which you might like to try. In this version of the game there is no penalty whatsoever attached to throwing a six but a double one takes the whole score you have accumulated down to zero. When only one of the dice comes up as a one your turn ends and you score zero for that particular turn.
To have the best chance of winning this game should you use the same strategy as for Piggy Sixes?
What is the expected score at a single throw in each of the versions?
You might like to look up the mathematical analysis and optimal strategy for the game of Pig on Durango Bill's website.