<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, 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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