Thank you for a detailed feddback!
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I'm used to Risk where reinforcement happens before your turn not after it, not sure what a difference it makes in game play though!
I'm going to continue the experiments with gameplay and I'll see what if put dealing cards before the attack phase.
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so I just ordered them high -> low every time then attacked
As for me I used almost the same tactics but with some modifications: I put the smallest card that is higher than the enemies top card on the top of my deck. Otherwise I put my smallest card there. e.g. I'll arrange the deck of 2, 3, 4, 5, 6, 7 as [5, 7, 6, 4, 3, 2] if enemy has 4 on the top of his deck, and as [2,7,6,5,4,3] if the top enemy's card is 10.
Well, I'm sure, after multiplayer implemented the new tactics will appear.
As for the current game rules, they are the result of such consequence:
1. I wanted to make the analogue of DiceWars with cards instead of the dice.
2. I chose the rules of card game called "p'yanitsa" ("a drunk man") to determine the battle outcome. In this game the deck is divided evenly among the players. Then they simultaneously open their top cards. The card with the highest vallue wins and its owner takes all the open cards to the bottom of his deck. This step continues until in game stays a single player - a winner.
Recently I googled out that the rules have much common to the rules of card game War.
3. But in the "drunk man" game aces are almost invincible, that's why I included the "loss of one point after the victory" concept. So, an army will suffer from attrition aven after several victorious battles. Besides, the defeated card is not inprisoned, it just vanishes.
Indeed, according to these rules there'll be multiple cards of the same value and suit. And, really, as I start to think about it, they must not necessarily be the cards, they can be symbols of soldiers with different abilities.
BTW, one of the sources of inspiration was the cards army from "Alice in the Wonderland", there were also multiple identical cards. I was adviced to implement Alice-style animation to the game, i.e. draw a card-shaped soldiers and animate battles in that way. Perhaps, with the help of my friends, who are good at drawing I'll be able to do this.
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I'm not sure what happens when a smaller NUMBER of cards attack a larger number, the animations don't entirely make it clear.
In that case some cards from the smaller stack can go to battle for several times.
Here's the example of the battle
[10, 9, 2] attack [7,6,5,6,7]
From the top of both stacks cards a taken, and then the higher card wins (if tie, the defender wins). Then, the defeated card vanishes, and the winner card looses 1 point and goes to the bottom of the stack. Battle stops when one stack looses 50% of its initial quantity.
In the given example the battle will go in such way:
[10, 9, 2] vs [7, 6, 5, 6, 7]
10 vs. 7 -> 10 wins, turns to 9 and goes to the bottom of the attacking deck.
[9, 2, 9] vs. [6, 5, 6, 7]
9 vs. 6 -> 9 wins and turns to 8
[2, 9, 8] vs. [5, 6, 7]
2 vs. 5 -> 5 wins and turns to 4
[9, 8] vs. [6, 7, 4]
9 vs. 6 -> 9 wins and turns to 8.
So, the defeated stack of [7, 4] retreats if it has anywhere to retreat, otherwise vanishes. The victorious stack of [8,8] leaves its bottom card in the province, from where the attack was started, and is moved to the conquered province.
Now I think of another variant of battle animation, which will let the player see the outcome of all the melees within the battle, perhaps, it will be more informative than the current animation.
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I played the Barbarian invasion scenario and because the reinforcement is at the end of the turn you get hit by 4 teams and then have to attack from there before getting reinforcements.
This one, together with The Fall of Empire are my favourite random map scenarios

Yes, in Barbarian invasion the start is tough, but later, when the invaders start the war between each other the players gets a chance to re-claim the land.
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My girlfriend loves these types of games and played through it and could see the potential. Again she commented on the restriction that hidden cards mean ordering cards doesn't have a huge impact on strategy, also noted lack of indication that your turn is over that was confusing to get started with.
And did you try hotseat game? (just set Human controller for two or more players in the Game Start screen).
Thank you very much again. I'll continue gameplay experiments, usability enhancement, and later on a multiplayer is planned.