# Winning Probability

This is the one feature of the app that I think you will find helpful in determining whether you should engage in a battle with another player. The figure below shows the probability when 10 attacker engages in a battle with 10 defender.

The top section shows the probability of the attacker and the defender winning if they fight until one side loses. This happens when either the attacker is down to one army, or when the defender has lost all its armies.

The bottom section shows the probability distribution of each outcome. For example, there is a **0.7%** chance that the attacker will win without losing a single army. The most likely outcome appears to be the case where the attacker will win with four armies remaining, with a probability of **9.6%**.&#x20;

![](https://4242518636-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FbmdmbU3dBI3jtn0HjZvs%2Fuploads%2FwWoeWBCyrU5soiY3EP1M%2FSimulator%20Screenshot%20-%20iPhone%2014%20Pro%20-%202023-08-12%20at%2023.09.09.png?alt=media\&token=4addf3e1-3e9f-499c-a7a6-e74ae4bcc251)

The probabiliy calculation assumes the attacker and the defender will always use the maximum number of dice. The attacker will always use three dice if he or she has four or more troops, and the defender will always use two dice if he or she has two ore more troops.&#x20;

The probability table is also smart enough to account for the modification of dice's values! For example, if the defender is fortified (+1 to all dice), the defender is pretty much guaranteed to win!

![](https://4242518636-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FbmdmbU3dBI3jtn0HjZvs%2Fuploads%2Fy92xrlXUlUCdhMwy9LFQ%2FSimulator%20Screenshot%20-%20iPhone%2014%20Pro%20-%202023-08-12%20at%2023.19.20.png?alt=media\&token=3cbe6734-ab98-4c00-92d6-e8798588dbc0)
