This works if the user ends up with 3% more balance than what he started with and do you think it is possible to do for 349 consecutive days?

In math we can derive lot of things but you need to understand the practical nuances that feels negligible but will make a huge difference at the end results and especially the whole strategy is build with the compunding effect so assume one bad day at 100th day and lost 50% of your balance then you need another 50 more days to make it up and one bad day will just keep ruining from this strategy to work.
If the gambler play the game and end up with 3% additional with the initial capital.They will think the money he had raised for the used time is not acceptable.So he again start to trade minimum 2x of the initial capital to satisfy his own soul.But the problem in this game was it may end with 2-3times of the capital or the loss will get away all the holding into the loss.So it was better to end with the 3% and back to the game again with the same capital.In this the gambler will not loss the holding money in gambling loss.