It's said that kaioken x2 increases the power level by 2. And it's also said that the regular kaioken increases the strenght. Then, how much does the regular kaioken increase the power level?
When Goku learns the Kaio-ken, he is told it will temporarily double his power level at the cost of draining him and potentially injuring him. But when he uses the Kaio-ken x2 against Vegeta, it also doubles his power. It could just be that Goku is saying x2 for the audience, especially since he breaks out the x3 moments later. Or it could be that there is some other improvement in the Kaio-ken x2 versus the base version (i.e. it is safer or more efficient).