Home Page |
Shareware |
Movies |
US Constitution |
Tractates |
Risk page |
Feedback |

**Risk Player's Cheat Sheet**

For a complete explanation of these notes, see Section 3 of the Risk FAQ page created by Owen Lyne.

For other Risk resources see The Risk Page

My Shareware Page also has 2 versions of Risk to download.

**CHANCES OF OUTCOMES FROM ONE ROLE**

| ||||||

3 Dice | Att. Lose 2: 29.26% (2275/7776) Def Lose 2: 37.17% (2890/7776) 1 and 1 : 33.58% (2611/7776) | Att. Lose 1: 34.03% (441/1296) Def. Lose 1:65.97% (855/1296) | ||||

2 Dice | Att Lose 2: 44.83% (581/1296) Def lose 2: 22.76% (295/1296) Each lose 1: 32.41% (420/1296) | Att lose 1: 42.13% (91/216) Def lose 1: 57.87% (125/216) | ||||

1 Die | Att lose 1: 74.54% (161/216) Def lose 1: 25.46% (55/216) | Att lose 1: 58.33% (21/36) Def lose 1: 41.67% (15/36) |

**EXPECTED LOSSES EACH ROUND:**

If the attacker rolls 3 and the defender rolls two average losses will be:

Attacker: 0.921 Defender: 1.079 Estimate: 5/6

If the defender can see the attacker's roll before choosing how many dice to roll, and then rolls 2 only if the attaker's second die is below 4 (as is reccomended):

Attacker: 1.001 Defender: 0.999 Estimate: Slight attacker's advantage

**LOSSES TO TAKE A TERRITORY:**

Assuming: Attacker rolls 3 and defender rolls two dice until s/he only has one army left:

Average Losses=0.8534144 N - 0.2213413 (1 - (-0.525359)^N)

where n=number of defending armies.

**Note:** The final part of this formula (-(0.525359)^N) will be negative or positive depending on whether N is odd or even, there is a slight advantage to having an even number of armies defending a territory.

1 Defending army: Expect loosing 0.5 armies.

2 Defending armies: Expect loosing 1.5 armies.

3 Defending armies: Expect loosing 2.3 armies.

Each additional army: estimated loss from each army decreases toward 0.8545 (about 5/6).

**Policy Reccomendation**: To avoid anihilation have two armies on each teritory, and pile the rest into one teritory.

**If defender can choose how many dice to roll after attacker has rolled** and rolls two only if attacker's second die is less than 4:

1.0010293 N - 0.3891440 + 0.6147449 * (-0.1563182)^N

Note: since last part of statement decreases more rapidly, even/odd advantage is less. Still advantageous to keep 2 armies in each territory in order to avoid anihilation.

**ARMIES NEEDED TO ANIHILATE ENEMIES**

Assumptions: always rolling three dice and not splitting up your armies to follow two sents of armies.

**Expect to loose**: 5/6N+7/9T+1/18D-1/9S where

N=Defending armies T=Teritories D=Teritories w/2 armies S=Territories w/1 armies

**Policy Recomendation:** Take this number plus three extra so you will always will be rolling 3 dice. Add some more for safe keeping.

**When defender sees attacker's roll before deciding how many to roll: **Take this number of armies: N+3/5T-1/10S+3

**CHANCES OF RISK CARD FORMING SETS**

By number of Jokers accounted for

0 Jokers 1 Jokers 2 Jokers

3 Cards 42.28% 38.06% 33.41%

4 Cards 81.70% 79.87% 77.80%

5 Cards 100% 100% 100%

Chances of forming a set with your fourth risk card when the first 3 did not formulate a set:

With 0 Jokers accounted for: 68.29%

With 1 Joker accounted for: 67.5%

With 2 Jokers accounted for: 66.7%

**
**

Home Page |
Shareware |
Movies |
US Constitution |
Tractates |
Risk page |
Feedback |

people have accessed my pages since since 6:15 PM On 4/12/96 not including reloads

This Counter Provided Free By Digits.com