Which cards to play first
Choosing which cards to play is important. Cards which match another number in your hand are a priority to play. This is because the more variety of numbers in your hand that you have, the more types of dice rolls there are that will benefit you. A different priority is to play the most difficult numbers from your hand. For example, you probably know that when someone rolls two six-sided dice, the least common outcomes are 2 and 12. The same principle applies here. In Cardiceo, the least common dice rolls are 15, 14, and 13, due to the unequal size of the three dice. Out of the 384 possible dice rolls, the number of ways to attain each is as follows:
1: 153 (39.8%)
2: 172 (44.7%)
3: 190 (49.4%)
4: 211 (54.9%)
5: 158 (41.1%)
6: 167 (43.4%)
7: 174 (45.3%)
8: 183 (47.6%)
9: 150 (39.0%)
10: 145 (37.7%)
11: 139 (36.1%)
12: 132 (34.3%)
13: 92 (23.9%)
14: 81 (21.0%)
15: 69 (17.9%)
Thus, the card numbers are, in order from easiest to hardest: 4 3 8 7 2 6 5 1 9 10 11 12 13 14 15. 13, 14, and 15 are dramatically more difficult because they cannot be attained without the cooperation of the twelve-sided die, while 4 and 3 are the easiest because they can be rolled singly on any die or as a sum of any two or three dice. Because it cannot be made via addition, 1 is harder to attain than any of the numbers from 2 through 8 (but still easier than any of the numbers from 9 through 15).
Which die to use
Which die you choose to use affects the next player's options.
Remember, that unused die are "locked" and the next player can't roll them. If you have a choice of more than one die with the same value, keep this in mind. For instance, if you had a 3 on all dice, and you have a 3 card, then use the 4 sided die. This locks the 8 and 12 sided die to a value of 3 for the next player, and they can only roll the 4 sided die you used. The maximum total that they can get will be 10, and only if they manage to get a 4 on the 4 sided die.