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

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.

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

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%

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