# Star Wars Risk Odds

I did a bunch of number crunching to figure out odds with different rolls in Risk Reinvented. But Star Wars Risk – The Original Trilogy also has some rule variations that change the odds of the typical Risk battles. When Rebels attack the Empire’s bases the Empire can defend with 8-sided dice instead of 6-sided dice. Using all the same analysis as last time and figuring out every possible combination of dice thrown by the attacker and defender, it turns out that on average the attacker would need 162 troops to successfully attack a base with 100 defending troops, rolling the dice 132 times. Actually you would need 3 more than that so that you have 3 troops to move in, plus one more to leave on the attacking country. And the luck of the dice could change that profoundly.

Star Wars Risk also allows players to buy ships that help the troops on any given country (“planet” for Star Wars Risk). There are three types of ships: fighters, bombers, and capital class ships. Fighters prevent a player from rolling a 1 with one of their dice, though you can get multiple fighters to affect up to three dice. If a 1 is rolled, you just roll it again until it isn’t a 1. I thought there would be no way to model that, but I think you can just say the die rolls go from 2 to 6. With one fighter for defense, the attacker will lose 105 troops before defeating 100 defenders. With two fighters on defense, the attacker loses 130 troops. With one fighter on each side, the attacker has the advantage, losing 93 troops to the defender’s 100. Since the 6-sided die has essentially become a 5-sided, a tie is more likely which works to the defender’s advantage, therefore these odds are closer to 50-50 than if no fighters are involved. When the attacker has a fighter, he will lose only 76 troops. With two fighters, the attacker loses 68 troops.

Another type of ship is a bomber which adds 1 to the highest die. Again you can get up to 3 bombers (though realistically this is a very hard thing to do, and is pointless since you only use the two highest dice rolls). This is similar to the airfields of Risk Reinvented where if you add 1 to the highest defensive die, the attackers will lose 126 troops taking over. Add another bomber to the defense, and the attacker’s losses increase to 189 troops. On offense, adding one to the highest attack rolls means the attackers will only lose 51 troops defeating 100 defensive troops, while 2 bombers will reduce the number of losses to only 38. If each side has 1 bomber, they will cancel each other out exactly and the attacker will lose 85 troops, the same as if neither side had a bomber.

The hardest type of ship to buy is a capital class ship which allows you to replace a 6-sided die with an 8-sided die. On defense, this is similar to the Empire’s bases. So what I found was that on defense, one 8-sided die means the attacker will lose 119 troops to defeat a planet with 100 defenders compared with losing only 85 troops when using all 6-sided dice. With two 8-sided dice, 162 attackers will be lost. On offense with 1 8-sided die, the attacker will lose 60 troops against 100 defenders. With 2 8-sided dice, the attacker loses only 43 troops. And using 3 8-sided dice the number drops further to only 32 losses. If each side has one 8-sided die, the attacker will lose 87 troops, which is 2 more than if neither had an 8-sided. It seems like the odds should be more in favor of the attacker since there will be fewer ties, but since half of the defense dice are 8-sided and only one-third of the attackers are 8-sided, I think this works to the favor of the defense. If 3 8-sided dice go against 1 6-sided and 1 8-sided, the attacker can expect to lose 51 troops. And if all 5 dice are 8-sided, then the attacker will lose 76 troops in defeating 100 defenders.

Conclusion: Bombers are better than Capital Ships and on offense are better than two Fighters.

Attacking Troops Defending
3 Capital 32 Normal
2 Bombers 38 Normal
2 Capital 43 Normal
3 Capital 51 1 Capital
1 Bomber 51 Normal
1 Capital 60 Normal
2 Fighters 68 Normal
3 Capital 76 2 Capital
1 Fighter 76 Normal
Normal 85 Normal
1 Bomber 85 1 Bomber
1 Capital 87 1 Capital
1 Fighter 93 1 Fighter
Normal 105 1 Fighter
Normal 119 1 Capital
Normal 126 1 Bomber
Normal 130 2 Fighters
Normal 162 2 Capital
Normal 189 2 Bombers

To calculate odds on your own, use the Risk Odds Calculator program.

## One thought on “Star Wars Risk Odds”

1. I thought the Fighter, which replaces a 1 with another roll, could be modeled by saying that die could only roll 2 through 6. That works with one die, but if you’re rolling two dice the Fighter will replace a 1 on either die with another roll. The only way to roll a 1 with one Fighter is to roll two 1’s and only replace one of them. So you can only get a 1 every 36 rolls. If you have 2 Fighters then you can never roll a 1, so you can model 2 Fighters with 2 dice of 2 through 6. I could maybe model 1 Fighter by counting each roll 5 times, but dividing any roll with 1 5 ways (2, 3, 4, 5, and 6). So I have to think about that some.