There's a game that uses 6 dices

When playing you will be provided with six dice which the computer randomly rolls for you. Your goal is to achieve the highest score possible (24), or at least to beat the other three players.

1. During the course of the game, you must "keep" a 4 and 1 to "qualify." This means that if you don't qualify.

2. You must score at least one higher than all three of your opponents to have it considered a win.

3. You must keep at least 1 dice after each roll (dice numbers range from one to six (1-6)

So far the highest win ratio I've gotten is 1/5, this is by collecting the qualifers first, (1 and 4) and then picking multibles of 6 dices, if there is no 6 dice I pick highest dice number.

Could anyone work out the best play method to get the best win ratio, preferabally 1/3 by calculating the odds of when the best time to pick the qualifers or other dices to get a higher score.

E.g. would it be better to take the qualifers first, or maybe wait until I get a few dice first, to get a higher score.