Make all of your battles on spaces 3 and 6 where you get free support (1 extra dice). So immediately retreat to 3. Later when you have just 2 cards retreat all the way to 6 and get a full hand of 5 cards.

For some of the your lower cards, 10's and 11's for example can be used as 'take a chance fodder', for example if you have enemies 15, 16 then throw down the 10 in the hope for getting a 5 or 6 on the free die.

You can make a judgment call on whether you can go all in to annihilate the opponents and finish the game quicker by getting 12 in the graveyard, otherwise you will need to play conservatively by not always using your good cards. Use the 'take a chance fodder' tactic whenever possible.

Use the number of cards in the various piles to better understand your position and chances.

If you have a large difference of defence values, say 14 in 1st place, and a 22 in the 2nd slot. Use a small card (say 12) to initially get rid of the 14 in 1st place. Then say the next army comes in as a 21. So now there is 22 and 21 to attack, when you play your high value 20 card you will be doing so with maximum effect (taking out 2 large armies rather than just 1).

When deciding if to use dice, or to choose a 2nd die, remember that the expected value from a 6-sided die is 3.5. Therefore you assume that you can get a roll of 3 or better from each die. If you aren’t rolling to get a four or better occasionally, you’ll seldom win Thermopyles.