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## Battle calculations

Battle calculations
There are two calculations to find who the winner is in each battle round. Units with ambush value have a chance to ambush the enemy and kill him before entering a fight.When the ambush hit or missed that unit won't get another ambush chance until the next time you attack with that unit.The ambush chance is a percentage chance to success. Some units have a higher chance to ambush.If two units enter fight and both succeed with their ambush roll the ambush fail and the normal battle will start.

When a unit is ambushed it will die instantly regardless of HP.

After the ambush dice is rolled the normal battle dice will start.Only a few units can ambush others, but some units give the whole army a chance to ambush an enemy.

A battle is played out in a set of rounds where dices are thrown to discern the winner.

Both units roll a 100 sided dice.If a unit roll its battle value or less its a hit and if it roll more than its battle it's a miss.If both units hit the dices are rolled again. If both units miss the dices are rolled again.If one unit hit and the other miss the unit that missed will take a hit.

Only two units fight at a time. It's still better to attack with as many units as possible because units are healed after a battle.

If a unit with a bonus that apply to the entire army dies the bonus is still applied though the rest of the battle.

All bonuses that apply to the entire army such as leadership/chaos, morale/fear are summed. When calculating the army bonus only the highest modifier of each type apply. If there are two units with +5 morale the result is +5 morale, not +10.A units battle value is capped at 75.

Battles on water
Units that have transformed into boat mode will have their battle value capped depending on which boat they sail in.The galleon allow battle values up to 45, the galley up to 25 the djonk up to 15. Units that have not transformed into a ship function just as normal. A hero that have not converted to ship also function as normal. All bonuses are applied as normal,the only difference is that boat units are capped.If a hero is still in his hero form and all ships and flying armies die or leave him on water he will drown at the end of the turn of theplayer who own the hero. If you kill all enemy units in an army except the hero the player with the hero have a chance to save his hero from drowning if hecan get a boat or flying army there before the end of his turn.

Example calculation
**Since this example was written the dice has changed to 100 sides but the same logic still apply.**

Here is a example how to calculate the chance to win a battle between a unit with STR 7 and a unit with STR 5.

Unit 1, STR 5, Chance to hit 25% (5/20) (with 20 sided dice)
Unit 2, STR 7, Chance to hit 35% (7/20) (with 20 sided dice)

One battle round
Unit 1 hits: 0.25 * 0.65 = 16.25%
Unit 2 hits: 0.75*0.35 = 26.25%
Any other outcome will result in the dices are thrown again.

Probability for a hit after eventual re rolls:
26.25 / (26.25+16.25) = 61.8% for unit 2
16.25 / (26.25+16.25) = 38.2 % for unit 1

A battle that start with both unit having full HP can have this outcome:
Hit for unit 1, Hit for unit 1 (0.382 * 0.382 = 14.6%) Winner unit 1
Hit for unit 1, Hit for unit 2, Hit for unit 1 (0.382 * 0.618 * 0.382 = 9%) Winner unit 1
Hit for unit 1, Hit for unit 2, Hit for unit 2 (0.382 * 0.618 * 0.618 = 14.6%) Winner unit 2

Hit for unit 2, Hit for unit 2 (0.618 * 0.618 = 38.2 %) Winner unit 2
Hit for unit 2, Hit for unit 1, Hit for unit 2 (0.618 * 0.382 * 0.618 = 14.6%) Winner unit 2
Hit for unit 2, Hit for unit 1, Hit for unit 1 (0.618 * 0.382 * 0.382 = 9%) Winner unit 1

Probability for unit 2 is the winner: 14.6% + 38.2 % + 14.6% = 67.4%
Probability for unit 1 is the winner: 14.6% + 9% + 9% = 32.6%