Results of simulated Risk fights

results.txt

Documentation :

Defenders strategies :
- 0 : always roll 2 dice
- 1 : roll one die if the sum of the best two attacker dice is >= 8
- 1.n : roll one die if the sum of the best two attacker dice is >= n
- 2 : like 1 but if there are only 2 defender units remaining always roll 2 dice
- 3 : like 2 but if the attacker has only 3 or fewer units remaining always throw 2 dice

Winning rate is the probability of an attacker victory

Units : describes the army size : attacker units number vs defender units number

Attackers remaining : average number of attacker unit remaining across sample_size simulations (loss included)

Defenders remaining : average number of defender unit remaining across sample_size simulations (loss included)

Sample size : the number of times a fight has been simulated to get these average numbers

Fights were all simulated until the defender had no unit left or the attacker had only one unit left


Data :

Units : 12 vs 8
Winning rate : 0.79
Attackers remaining : 5.71
Defenders remaining : 0.65
Defenders strategy : 0
Sample size : 10_000_000


Units : 12 vs 8
Winning rate : 0.77
Attackers remaining : 5.42
Defenders remaining : 0.70
Defenders strategy : 1
Sample size : 10_000_000


Units : 12 vs 8
Winning rate : 0.77
Attackers remaining : 5.35
Defenders remaining : 0.71
Defenders strategy : 2
Sample size : 10_000_000


Units : 12 vs 8
Winning rate : 0.77
Attackers remaining : 5.36
Defenders remaining : 0.70
Defenders strategy : 3
Sample size : 10_000_000


Units : 12 vs 8
Winning rate : 0.73
Attackers remaining : 5.01
Defenders remaining : 0.85
Defenders strategy : 1.9
Sample size : 10_000_000


Units : 12 vs 8
Winning rate : 0.84
Attackers remaining : 6.12
Defenders remaining : 0.46
Defenders strategy : 1.7
Sample size : 10_000_000


Units : 12 vs 12
Winning rate : 0.51
Attackers remaining : 3.41
Defenders remaining : 2.33
Defenders strategy : 0
Sample size : 10_000_000


Units : 12 vs 12
Winning rate : 0.45
Attackers remaining : 3.05
Defenders remaining : 2.57
Defenders strategy : 1
Sample size : 10_000_000


Units : 8 vs 2
Winning rate : 0.97
Attackers remaining : 6.55
Defenders remaining : 0.04
Defenders strategy : 1
Sample size : 10_000_000


Units : 8 vs 2
Winning rate : 0.97
Attackers remaining : 6.46
Defenders remaining : 0.05
Defenders strategy : 2
Sample size : 10_000_000


Units : 8 vs 2
Winning rate : 0.97
Attackers remaining : 6.46
Defenders remaining : 0.05
Defenders strategy : 3
Sample size : 10_000_000


Units : 8 vs 4
Winning rate : 0.83
Attackers remaining : 4.93
Defenders remaining : 0.37
Defenders strategy : 0
Sample size : 10_000_000


Units : 8 vs 4
Winning rate : 0.83
Attackers remaining : 4.84
Defenders remaining : 0.38
Defenders strategy : 1
Sample size : 10_000_000


Units : 8 vs 4
Winning rate : 0.82
Attackers remaining : 4.78
Defenders remaining : 0.38
Defenders strategy : 3
Sample size : 10_000_000


Units : 5 vs 3
Winning rate : 0.64
Attackers remaining : 2.92
Defenders remaining : 0.76
Defenders strategy : 0
Sample size : 10_000_000


Units : 5 vs 3
Winning rate : 0.62
Attackers remaining : 2.82
Defenders remaining : 0.78
Defenders strategy : 1
Sample size : 10_000_000