<p>Each die contains six faces: bow, bow with star, cheese, sword with star, sword with shield, and sword with shield &amp; star.</p>
<p>Melee attacks hit with unblocked sword symbols (any). Ranged attacks hit with unblocked bow symbols (any). Defenders may block with any shield symbols. See <a href="https://media.plaidhatgames.com/old_images/games/mice-and-mystics/mmrulebook.pdf" rel="nofollow noreferrer">Rulebook</a>, page 11.</p>
<h3>Probability of a Melee Hit</h3>
<p><strong>Probability of a Melee hit</strong> given the number of dice for each side.<br />
<sub>Sample probability of success with <em>n</em> = 50,000</sub></p>
<div class="s-table-container"><table class="s-table">
<thead>
<tr>
<th>Attack \ Defend</th>
<th>0</th>
<th>1</th>
<th>2</th>
<th>3</th>
<th>4</th>
<th>5</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>0.50</td>
<td>0.33</td>
<td>0.22</td>
<td>0.15</td>
<td>0.10</td>
<td>0.07</td>
</tr>
<tr>
<td>2</td>
<td>0.75</td>
<td>0.59</td>
<td>0.44</td>
<td>0.34</td>
<td>0.25</td>
<td>0.18</td>
</tr>
<tr>
<td>3</td>
<td>0.87</td>
<td>0.75</td>
<td>0.63</td>
<td>0.51</td>
<td>0.41</td>
<td>0.32</td>
</tr>
<tr>
<td>4</td>
<td>0.94</td>
<td>0.85</td>
<td>0.76</td>
<td>0.66</td>
<td>0.56</td>
<td>0.46</td>
</tr>
<tr>
<td>5</td>
<td>0.97</td>
<td>0.92</td>
<td>0.85</td>
<td>0.77</td>
<td>0.68</td>
<td>0.59</td>
</tr>
</tbody>
</table></div>
<h3>Probability of a Ranged Hit</h3>
<p><strong>Probability of a Ranged hit</strong> given the number of dice for each side.<br />
<sub>Sample probability of success with <em>n</em> = 50,000</sub></p>
<div class="s-table-container"><table class="s-table">
<thead>
<tr>
<th>Attack \ Defend</th>
<th>0</th>
<th>1</th>
<th>2</th>
<th>3</th>
<th>4</th>
<th>5</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>0.33</td>
<td>0.22</td>
<td>0.15</td>
<td>0.10</td>
<td>0.07</td>
<td>0.04</td>
</tr>
<tr>
<td>2</td>
<td>0.55</td>
<td>0.41</td>
<td>0.30</td>
<td>0.21</td>
<td>0.15</td>
<td>0.11</td>
</tr>
<tr>
<td>3</td>
<td>0.71</td>
<td>0.55</td>
<td>0.43</td>
<td>0.34</td>
<td>0.25</td>
<td>0.19</td>
</tr>
<tr>
<td>4</td>
<td>0.80</td>
<td>0.67</td>
<td>0.55</td>
<td>0.45</td>
<td>0.35</td>
<td>0.28</td>
</tr>
<tr>
<td>5</td>
<td>0.87</td>
<td>0.76</td>
<td>0.65</td>
<td>0.55</td>
<td>0.45</td>
<td>0.37</td>
</tr>
</tbody>
</table></div>
<p>Of course these tables do not include any modifiers that deal extra damage based on the star symbol, but the code below can be easily modified to most game situations.</p>
<hr />
<p><strong>Julia code</strong></p>
<pre><code>using Statistics

# Setup
dice_face = [&quot;bow&quot;, &quot;bow/s&quot;, &quot;cheese&quot;, &quot;sword/s&quot;, &quot;sword/shield&quot;, &quot;sword/shield/s&quot;]
dice_movement = [2, 1, 1, 2, 3, 3]
rollh = n -&gt; rand(1:6, n)

# Probability of Hit
Num_Trials = 50000

Num_A_range = 1:5
Num_D_range = 0:5
pHit_Melee = zeros(length(Num_A_range), length(Num_D_range))
pHit_Ranged = zeros(length(Num_A_range), length(Num_D_range))

for (ii, Num_A) in enumerate(Num_A_range)
    for (jj, Num_D) in enumerate(Num_D_range)
        Hit_Melee = zeros(Num_Trials)
        Hit_Ranged = zeros(Num_Trials)

        for kk in 1:Num_Trials
            Akk = rollh(Num_A)
            Dkk = Num_D &gt; 0 ? rollh(Num_D) : zeros(Int, Num_A)

            Num_Meleekk = sum(Akk .&gt;= 4)
            Num_Ranged = sum(Akk .&lt;= 2)
            Num_Blockk = sum(Dkk .&gt;= 5)

            Hit_Melee[kk] = Num_Meleekk &gt; Num_Blockk
            Hit_Ranged[kk] = Num_Ranged &gt; Num_Blockk
        end

        pHit_Melee[ii, jj] = mean(Hit_Melee)
        pHit_Ranged[ii, jj] = mean(Hit_Ranged)
    end
end

pHit_Melee
pHit_Ranged
</code></pre>

CC BY-SA 4.0
2024-12-30T21:59:43.390Z
2024-12-30T21:59:43.390Z
SecretAgentMan
<p>When playing <strong>Mice and Mystics</strong>, one is often faced with deciding which enemy minion to attack based on a mouse's battle and the minions' defense values which can vary widely based on the character, equipment, and minion. Melee and ranged attacks clearly have different likelihoods based on the dice.</p>
<p><strong>What are the chances of successfully landing at least one hit during an attack?</strong></p>
<p><a href="https://i.sstatic.net/wj8CLRIY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wj8CLRIY.png" alt="Picture of action dice for Mice and Mystics." /></a></p>

<dice><statistics><mice-and-mystics>
What are the chances of a successful hit in Mice and Mystics?
SecretAgentMan
# What are the chances of a successful hit in Mice and Mystics?

(Asked by: username_0 on 2024-12-30)

When playing **Mice and Mystics**, one is often faced with deciding which enemy minion to attack based on a mouse's battle and the minions' defense values which can vary widely based on the character, equipment, and minion. Melee and ranged attacks clearly have different likelihoods based on the dice.

**What are the chances of successfully landing at least one hit during an attack?**

[![Picture of action dice for Mice and Mystics.](https://i.sstatic.net/wj8CLRIY.png)](https://i.sstatic.net/wj8CLRIY.png)

**Tags:** dice, statistics, mice-and-mystics


---

## 1 answers

### Answer by username_0 on 2024-12-30. Score: 0

Each die contains six faces: bow, bow with star, cheese, sword with star, sword with shield, and sword with shield & star.

Melee attacks hit with unblocked sword symbols (any). Ranged attacks hit with unblocked bow symbols (any). Defenders may block with any shield symbols. See [Rulebook](https://media.plaidhatgames.com/old_images/games/mice-and-mystics/mmrulebook.pdf), page 11.

### Probability of a Melee Hit

**Probability of a Melee hit** given the number of dice for each side.  
Sample probability of success with *n* = 50,000

| Attack \ Defend | 0 | 1 | 2 | 3 | 4 | 5 |
| --- | --- | --- | --- | --- | --- | --- |
| 1 | 0.50 | 0.33 | 0.22 | 0.15 | 0.10 | 0.07 |
| 2 | 0.75 | 0.59 | 0.44 | 0.34 | 0.25 | 0.18 |
| 3 | 0.87 | 0.75 | 0.63 | 0.51 | 0.41 | 0.32 |
| 4 | 0.94 | 0.85 | 0.76 | 0.66 | 0.56 | 0.46 |
| 5 | 0.97 | 0.92 | 0.85 | 0.77 | 0.68 | 0.59 |

### Probability of a Ranged Hit

**Probability of a Ranged hit** given the number of dice for each side.  
Sample probability of success with *n* = 50,000

| Attack \ Defend | 0 | 1 | 2 | 3 | 4 | 5 |
| --- | --- | --- | --- | --- | --- | --- |
| 1 | 0.33 | 0.22 | 0.15 | 0.10 | 0.07 | 0.04 |
| 2 | 0.55 | 0.41 | 0.30 | 0.21 | 0.15 | 0.11 |
| 3 | 0.71 | 0.55 | 0.43 | 0.34 | 0.25 | 0.19 |
| 4 | 0.80 | 0.67 | 0.55 | 0.45 | 0.35 | 0.28 |
| 5 | 0.87 | 0.76 | 0.65 | 0.55 | 0.45 | 0.37 |

Of course these tables do not include any modifiers that deal extra damage based on the star symbol, but the code below can be easily modified to most game situations.

---

**Julia code**

```
using Statistics

# Setup
dice_face = ["bow", "bow/s", "cheese", "sword/s", "sword/shield", "sword/shield/s"]
dice_movement = [2, 1, 1, 2, 3, 3]
rollh = n -> rand(1:6, n)

# Probability of Hit
Num_Trials = 50000

Num_A_range = 1:5
Num_D_range = 0:5
pHit_Melee = zeros(length(Num_A_range), length(Num_D_range))
pHit_Ranged = zeros(length(Num_A_range), length(Num_D_range))

for (ii, Num_A) in enumerate(Num_A_range)
    for (jj, Num_D) in enumerate(Num_D_range)
        Hit_Melee = zeros(Num_Trials)
        Hit_Ranged = zeros(Num_Trials)

        for kk in 1:Num_Trials
            Akk = rollh(Num_A)
            Dkk = Num_D > 0 ? rollh(Num_D) : zeros(Int, Num_A)

            Num_Meleekk = sum(Akk .>= 4)
            Num_Ranged = sum(Akk .<= 2)
            Num_Blockk = sum(Dkk .>= 5)

            Hit_Melee[kk] = Num_Meleekk > Num_Blockk
            Hit_Ranged[kk] = Num_Ranged > Num_Blockk
        end

        pHit_Melee[ii, jj] = mean(Hit_Melee)
        pHit_Ranged[ii, jj] = mean(Hit_Ranged)
    end
end

pHit_Melee
pHit_Ranged

```


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