Who has the advantage in Risk: Attacker or Defender?

  • Thread starter adrianopolis
  • Start date
  • Tags
    Game
In summary, the article discusses how to calculate the expected value of a game, using a Monte Carlo simulation.
  • #1
adrianopolis
10
0
In risk, the attacking party rolls 3 die and the top two numbers of the 3 die rolled get put up against 2 die rolled by the defender. If the die are equal then the defender wins. For example if the offender rolls 5 5 2 and the defender rolls 4 3, then 2 defender men die. If the offender rolls 5 5 2 and the defender rolls 5 4 then they trade kills because when die are equal the defender wins.
If offender rolls 5 5 2 and the defender rolls 6 6 the defender wins. Who has the advantage? Attacking or defending? What is the comparative advantage?
 
Physics news on Phys.org
  • #2
Start with die in the singular and dice in the plural.
 
  • #3
Here's one way to approach it.
Break it into four cases from defender's perspective:
++ win on both
+- win on high dice, lose on low
-+ etc.
--

Case ++:
For each defender roll, count attacker possibilities:
6+6: 63
6+5: 53+3.1.52 (attacker rolls no 6s or one 6)
6+4: 43+3.2.42 (attacker rolls no 5s nor 6s, or just one such)
:
6+1: 13+3.5.12 (attacker rolls nothing above 1 or just one such)
(remember to count all above except 6+6 twice)
5+5: 53
etc.
Summing, we get sum for r = 1 to 6 for each of:
r3, 2r3(6-r), 6r2(6-r) = -2r4+7r3+36r2
Sum the series to r and plug in r=6.

Similarly, for case +-:
6+5: 13+3.12.5
6+4: 23+3.22.4
etc.
 
  • #4
haruspex said:
Here's one way to approach it.
Break it into four cases from defender's perspective:
++ win on both
+- win on high dice, lose on low
-+ etc.
--

Case ++:
For each defender roll, count attacker possibilities:
6+6: 63
6+5: 53+3.1.52 (attacker rolls no 6s or one 6)
6+4: 43+3.2.42 (attacker rolls no 5s nor 6s, or just one such)
:
6+1: 13+3.5.12 (attacker rolls nothing above 1 or just one such)
(remember to count all above except 6+6 twice)
5+5: 53
etc.
Summing, we get sum for r = 1 to 6 for each of:
r3, 2r3(6-r), 6r2(6-r) = -2r4+7r3+36r2
Sum the series to r and plug in r=6.

Similarly, for case +-:
6+5: 13+3.12.5
6+4: 23+3.22.4
etc.

Thanks man. I'm a little confused by what for example 3.1.5^2 means but thanks for the help
 

1. What are the odds of winning in the game Risk?

The odds of winning in the game Risk vary depending on several factors, including the number of players, the size of the board, and the players' strategies. Generally, the odds range from 15-25% for each player.

2. How does the game calculate the odds of winning?

The game calculates the odds based on a combination of dice rolls and card bonuses. Each player has a set number of dice to roll during battles, and the higher number of dice rolled, the better the odds of winning. Additionally, certain cards can provide bonuses that increase a player's odds of winning.

3. Can the odds be manipulated in the game?

No, the odds in the game Risk cannot be manipulated. They are based on random dice rolls and card draws, making the game fair for all players.

4. Are there any strategies to increase the odds of winning in Risk?

While there is no guaranteed strategy to win in Risk, there are some tips that can help increase your odds. These include focusing on controlling continents, establishing strong defensive positions, and knowing when to attack and when to hold back.

5. Are the odds different for each battle in the game?

Yes, the odds can vary for each battle in the game Risk. This is because the number of dice rolled and any card bonuses can change with each battle, affecting the overall odds of winning. Additionally, the players' strategies and decisions can also impact the odds in each battle.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
2K
Replies
1
Views
453
Replies
2
Views
4K
  • Set Theory, Logic, Probability, Statistics
2
Replies
41
Views
3K
  • Precalculus Mathematics Homework Help
2
Replies
53
Views
5K
  • Set Theory, Logic, Probability, Statistics
Replies
10
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
Back
Top