## Dice

This page contains a description and the distributions of the different dice options.

## Normal dice

The algorithm chooses a random number between 1 and 6 for each die.

### Statistics

Defender loses two: 37.17% of the time.
Each loses one: 33.58% of the time.
Attacker loses two: 29.26% of the time.

## Balanced dice

Playing with this dice setting approximately doubles the chance of both sides losing one army when rolling 3 vs 2 dice.

The algorithm uses a 130 sided die and two 6 sided dice for the attacker, and two 28 sided dice for the defender. For non 3 vs 2 dice situations (like attacking a territory with only 1 troop on it) the normal dice are used.

### Statistics

Defender loses two: 20.36% of the time.
Each loses one: 67.40% of the time.
Attacker loses two: 12.24% of the time.

## Results from an experiment

The above statistics are the theory. We ran some experiments with our dice to get the practical numbers. As expected, with only a few rolls you get some weird outliers, and the more rolls you do, the closer you get to the expected outcomes.

Below are the results from 02 oktober 2019.

Results for a 3 vs 2 dice battle
#Rolls Description Normal dice Balanced dice
10 Kill 2 troops 3/10 = 30% 2/10 = 20%
Kill 1, lose 1 6/10 = 60% 8/10 = 80%
Lose 2 troops 1/10 = 10% 0/10 = 0%
100 Kill 2 troops 41/100 = 41% 18/100 = 18%
Kill 1, lose 1 30/100 = 30% 74/100 = 74%
Lose 2 troops 29/100 = 29% 8/100 = 8%
1000 Kill 2 troops 359/1k = 35.9% 184/1k = 18.4%
Kill 1, lose 1 332/1k = 33.2% 692/1k = 69.2%
Lose 2 troops 309/1k = 30.9% 124/1k = 12.4%
100000 Kill 2 troops 36998/100k = 37% 20260/100k = 20.26%
Kill 1, lose 1 33445/100k = 33.45% 67432/100k = 67.43%
Lose 2 troops 29557/100k = 29.56% 12308/100k = 12.31%
Results for a 3 vs 1 dice battle
#Rolls Description Normal dice Balanced dice
10 Win 7/10 = 70% 5/10 = 50%
Lose 3/10 = 30% 5/10 = 50%
100 Win 58/100 = 58% 73/100 = 73%
Lose 42/100 = 42% 27/100 = 27%
1000 Win 657/1k = 65.7% 673/1k = 67.3%
Lose 343/1k = 34.3% 327/1k = 32.7%
100000 Win 66236/100k = 66.24% 65895/100k = 65.9%
Lose 33764/100k = 33.76% 34105/100k = 34.11%