before starting I want to tell that the most important thing in the game is to be flexible and not to stick to one strategy if you see that it’s not so good in your case.
start a game and save it the first turn. Then go and explore the map a little. After that evaluate the situation and build your strategy and eventually choose a proper race if map permits it.
on some maps that are hard to play, I have the habit of starting several times, till I get an advantage: resources that I need near my castle (when they are random), starting with a strong army, a good hero at the tavern, a good artifact near me, weak guards at mines, etc.
then you must choose your goal: for example if you play a small map you probably won’t build the last dwelling so if you are with knights or barbarians, gathering crystals won’t be a concern. Your strategy is definitely different when you want to build your strongest unit.
buy one more hero the first day (possible in 90% of cases). Here are the reasons:
look for creature dwellings near your castle. If there are some, you’re lucky. You’ll need them like air in the beginning
go for the money very fast. You can leave some resources that will be collected later by another hero. In the beginning you need money, wood and ore for development
build the constructions that bring money money (town hall, city hall, etc) as fast as you can. But if you found many treasures and you have enough money, you can try to rush and build some powerful creatures that can help you to get a big advantage in the beginning or even win the map (e.g: rocs, trolls, minotaurs, druids, champions, vampires)
build fortifications only if necessary. Most of the time if you have a very aggressive strategy (like my case here) the opponent will never get to your starting castle. That’s why I don’t keep defending armies in my castle. Use the extra money for other things. If I see that somebody is approaching I usually manage to do something in that time. The offense is the best defense. There were very, very little cases when I failed. If you want to win fast you have to risk a little
in the beginning (or if you don’t have enough money) buy only the creatures you use. For example: after you’ve build vampires it’s very wise to buy them all very fast and not to invest in zombies & mummies. Usually on a small map with vampires, skeletons, and a good hero that knows animate dead you don’t have problems with winning.
don’t build more then level 1 mage guild (2 when required for other buildings, e.g. Dragon Cave). I know that this seems strange, but most of the time you won’t return with your main hero to the castle, especially if you want to make a good score. And you’ll learn spells from AI’s castles.
conquer as many castles as you can in the beginning and develop them only to produce money, because you won’t be able to defend them very well. Concentrate on your main castle to build the last dwellings. Then, if you have the money you can upgrade secondary castles that are the same as your starting race. Otherwise it’s not worth investing gold & resources. You’d better buy creatures from enemy’s conquered castles.
try to build important creature dwellings (last 2 grades) by day 7, to benefit from the weekly growth. Calculate from the beginning of the week what you can do max (e.g. an important building in day 7) and what resources you need and then do all you can to achieve the goal
build a marketplace and use it with confidence. It helped me a lot in some situations
sometimes is better to sacrifice the mage guild for a creature building (especially if you play with Knights or Barbarians)
try to attack AI in day 1 if you have your move before his, so he can’t buy the extra troops. Otherwise, attack him in day 7. If you play red you’ll always be first and day 1 will always come first for you. This is very important. I have situation when I bought the 1’st day armies and after this attacked the enemy with great advantage
use heroes to transport armies from one to another and finally to your main hero. Your hero will only fight and gather some resources that you need immediately. The rest is the job of the 2nd hero. Usually on week 2 I have enough money and build some of the important creatures. If I don’t manage to come with the 2nd hero to take the army from the castle, I hire another hero.
here are my preferences about how many heroes I buy according to the map size (but remember to be flexible): for small maps I have minimum 2, for medium 3 - 4, and for large ones usually 4, but I’ll buy as many as I need. I do that because I like to explore a lot and do it fast. When I played h3 I won most of the maps (against human opponent) because I expanded very fast and in very short time I reached the maximum of 8 heroes (on xl maps). So having many heroes is kind of a habit.
in some cases (warlocks&wizards) you can buy only 6’th level units. Black Dragons and Titans are very strong and you won’t need other units to win against AI. Your chances to succeed with this strategy increase if you have a good hero. With human opponents strategy is different.
in Pocket Heroes you can buy heroes only according to the castle type, so if there are more players that have the same beginning race as yours you should buy as fast as you can the heroes or you could end up with nothing to buy
timing is everything as some times you manage to take with your last step a treasure or mine that you’ll need. And this can cost you building or not a dwelling in the 7’th day of the week.
If you think that some monster will beat you save the game and give it a try. Some time your prognostic is worst then the real fact.
try to find as fast as you can the ultimate artifact. Usually is in the middle of the puzzle map and if you have experience you’ll find it very easy. If you play against AI then save before you dig, so in the end you’ll get it from the first time. When against human opponent bring there more heroes: at least 2. This is a great advantage and you must have it very fast. Here is another thing, but I considered a cheat. You play a map and you discover eventually that the artifact is near your castle. Restart the map and go from the beginning and dig the Artifact. Of course you must still have your initial save.