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The probabilities to win in a classical risk battle.

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Welcome to the stadistics of risk!

The probabilities to win in a classical battle in the board game: risk.

Rules for the battle

Compare the highest die each of are rolled. If the attackers is higher, the defender loses one army from the territory under attack. But if the defender's die is higher than the attacker, he loses one army from the territory.

The attacker will roll 3 dice. He must have at least one more army in the territory than the number of dice is rolling, in the case he has 3 armies, he will play with 2 dice. The defender will roll 2 dice. Likewise, he must have at least 2 armies on the territory under attack, if he have only 1 then he plays with 1 die.

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risk_visual.py

Screenshot

risk_data.py

Attacking units Defending units Winner Winning probability
3 3 defender 59'85%
5 5 defender 55'98%
8 8 defender 50'51%
10 10 attacker 52'54 %
100 100 attacker 81'34 %
75 80 attacker 66'71%
100 110 attacker 62'88%
100 120 defender 59'05%

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The probabilities to win in a classical risk battle.

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