Dice
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.
| #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% |
| #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% |