Strategy Tips: Dice Rolling

I'm still working on Game 1, Part 2, please be patient.
Let me take a minute to discuss an interesting part of Risk strategy: chance.
Now, how can something like chance be part of your strategy? In the game of Risk there are many things that rely on chance. You cannot control them, but there are several things that you can at least attempt to predict. The focus here is to manipulate the chance into working for you, not against you. Be an informed player... know everything there is to know about the game. One of the most useful things to know is the chances you have of winning a battle.
I found a fun little website that calculates the probability of winning a battle based on how many armies (mods in our case) each player has. This calculator is based on classic Risk, though, which means it does not take into consideration 8-sided dice, but it is still very useful to know the basic probabilities. Also, the calculator assumes that each player always rolls with the maximum amount of dice allowed for each roll.
Here's the link for the calculator itself: http://bartell.org/risk/riskodds.shtml
Here's a chart. The numbers in the center represent the chance (by percent) that the attacker will win:

                           Defender Mods
           1   2   3   4   5   6   7   8   9 10 11 12 13
       -------------------------------------------------
     1 |   0   0   0   0   0   0   0   0   0  0  0  0  0
     2 |  42  11   3   1   0   0   0   0   0  0  0  0  0
     3 |  75  36  21   9   5   2   1   0   0  0  0  0  0
     4 |  92  66  47  31  21  13   8   5   3  2  1  1  0
     5 |  97  79  64  48  36  25  18  12   9  6  4  3  2
     6 |  99  89  77  64  51  40  30  22  16 12  8  6  4
     7 | 100  93  86  74  64  52  42  33  26 19 15 11  8
     8 | 100  97  91  83  74  64  54  45  36 29 22 17 13
     9 | 100  98  95  89  82  73  64  55  46 38 31 25 20
    10 | 100  99  97  93  87  81  73  65  56 48 40 33 27
    11 | 100  99  98  95  92  86  80  72  65 57 49 42 35
Attak12 | 100 100  99  97  94  91  85  79  72 65 58 51 43
Mods 13 | 100 100  99  98  96  93  90  84  79 72 66 58 52
    14 | 100 100 100  99  98  96  93  89  84 79 72 66 59
    15 | 100 100 100  99  98  97  95  92  88 83 78 72 67
    16 | 100 100 100 100  99  98  96  94  91 88 83 78 73
    17 | 100 100 100 100  99  99  98  96  94 91 87 83 78
    18 | 100 100 100 100 100  99  98  97  95 93 90 87 83
    19 | 100 100 100 100 100  99  99  98  97 95 93 90 87
    20 | 100 100 100 100 100 100  99  99  98 97 95 92 89

As you can see by the chart... in a battle between an even number of mods (4 on 4, 8 on 8, etc.) the attacker has a chance of winning above 50% once the battle reaches 12 on 12 or higher.
Also, the attacker usually only needs to have 1 more mod than the defender to top a 50% chance in battles where the defender has less than 12.
What all of this means for me is that the defender does not necessarily have the superior advantage that I had once thought. The fact that the defender wins in the event of a tie helps alot, but the fact that the attacker gets 3 dice also helps. According to this calculator, the odds are very even. So, when playing our version of Risk, you will need to rely on only 2 things (asside from cards) to give you an advantage when in battle: superior numbers and 8-sided dice.
Remember... 8-sided dice come from commanders and bases. So, if you want to defend a territory well, get a base or a diplomat there... and if you want to successfully take over others' land, get the appropriate offensive commander (remember the Nuke Commander works everywhere). If the statistics are correct, the 8-sided dice should be an integral part of your strategy.