Aiki probabilities

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====== Aiki probabilities ======

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The following table conveys the statistics for rolling the Cleromancer's [[cleromancer#Aiki]] ability. Aiki is calculated in the following manner:

>The attacker rolls only the dice portion of their offensive formula, dropping all other bonuses. For each successful hit, the defender must match the die face in order to successfully defend against the attack. A match can be made by rolling the same face, or by rolling the opposite face (1|6, 2|5, 3|4). If the attacker rolls no successful hits, the defender wins

The chart below dictates the defender's chance of successfully blocking an attack by using Aiki

|  ^  Defender has\\ 6d6  ^  \\ 7d6  ^  \\ 8d6  ^  \\ 9d6  ^  \\ 10d6  ^  \\ 11d6  ^  \\ 12d6  ^ 
^  Attacker has\\ 6d6  |  57%  |  66%  |  75%  |  81%  |  86%  |  89%  |  92%  |
^  7d6  |  48%  |  59%  |  68%  |  75%  |  81%  |  85%  |  89%  |
^  8d6  |  39%  |  51%  |  60%  |  69%  |  75%  |  81%  |  85%  |
^  9d6  |  32%  |  43%  |  53%  |  63%  |  69%  |  76%  |  82%  |
^  10d6  |  25%  |  35%  |  45%  |  56%  |  63%  |  71%  |  77%  |
^  11d6  |  19%  |  29%  |  38%  |  48%  |  58%  |  65%  |  72%  |
^  12d6  |  14%  |  23%  |  32%  |  42%  |  51%  |  60%  |  68%  |

**Note**: These numbers were calculated by running 12,000 simulations per matchup, and are therefore only and approximation. To stress this point, the percentages have been rounded to the nearest whole number


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**Example**

The attacker has an offensive formula of 7d6+5. The defending Cleromancer is using Aiki, which has not been improved and therefore has a defensive formula of 6d6. The attacker rolls 7d6 and gets [6,6,4,3,3,2,1]. This is three successful "hits" from the [6,6,4] rolled. The cleromancer defensively rolls 6d6 and gets [6,5,3,2,2,1]. The cleromancer is successful in neutralizing the attack with the following pairs: (6,6) (6,1) (4,3)

Statistically in a matchup where the attacker has 7d6 and the cleromancer has 6d6, the odds of the cleromancer defending the attack are 48%, from the table above
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