Dice game strategy

Question

So, I have to find a solution to this seemingly simple dice game, but I am not sure if my answer is the right one. The game goes as follows:

There are two dice which each have a different color. You predict the outcome of both dice and throw them. If:

1. you correctly predict both numbers on both dice, you get 10 points;
2. you predict the correct numbers, but they are the wrong color, you get 5 points;
3. you only predict one color and number correctly, you get 2 points.

What is the best strategy to choose the numbers?

My logic is that I look at which numbers summed up show up most frequently and then try to predict them, since every game is independent and the last outcome doesn't say anything about the next one. Since 7 has a 16.6% probability to show up, try with combinations like $1-6$, $2-5$, $3-4$, $4-3$, $5-2$, $6-1$. Is there a better way to go about it?

EDIT: Forgot to add, only the highest points are paid out. So if you predict $(1,1)$ and get that, you would get 10 points and not 5 or 2, or all of them.