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[Please correct me if I'm wrong]
For the rules of piraten kapern, see <b>[[Gamehelppiratenkapern|GameHelpPiratenKapern]]</b>


=Throwing 2 dice=
== Probabilities ==
*1 chance out of 36 (2.78%) to get 2 Skulls
 
*11 chances out of 36 (3.56%) to get AT LEAST 1 Skull
{{infoBoxes | title1=Binomial formula | body1=<b></b>
*25 chances out of 36 (69.44%) to get NO Skull
<u>  n!  </u> × pᵏ(1 − p)ⁿ⁻ᵏ
k!(n-k)!
 
n: number of trails (dice thrown)
k: number of successes (dice with a face value)
p: probability of success (of a die face value)
| title2=Example | body2=
Probability of throwing '''3'''{{whiteDie|=4}} with '''5''' dice:
<u>  5!  </u> × (⅙)³ × (1 − ⅙)⁵⁻³
3!(5-3)!
 
= <u> 5×4×3×2×1 </u> × (⅙)³ × (⅚)²
  3×2×1 × 2×1
 
= 10 × (⅙)³ × (⅚)²
≈ 0.0321 or 3.21%
}}
 
=== 2 dice ===
 
{|class="wikitable" style="width:auto;"
|+Probabilities of throwing X skulls with two six-sided dice
!In words
!In maths
!Percentage
|-
|Probability of no skulls
|P(X = 0) = (⅚)²
|≈ 69.4%
|-
|Probability of one skull
|P(X = 1) = 2 × (⅙) × (⅚)
|≈ 27.8%
|-
|Probability of two skulls
|P(X = 2) = (⅙)²
|≈ 2.78%
|}
 
=== 8 dice ===
 
{|class="wikitable" style="width:auto;"
|+Probabilities of throwing X skulls with eight six-sided dice
!In words
!In maths
!Percentage
|-
|Probability of no skulls
|P(X = 0) = (⅚)⁸
|≈ 23.3%
|-
|Probability of one skull
|P(X = 1) = 8 × (⅙) × (⅚)
|≈ 37.2%
|-
|Probability of two skulls
|P(X = 2) = 28 × (⅙)² × (⅚)⁶
|≈ 26.0%
|-
|Probability of three skulls
|P(X = 3) = 56 × (⅙)³ × (⅚)⁵
|≈ 10.4%
|-
|Probability of four skulls
|P(X = 4) = 70 × (⅙)⁴ × (⅚)⁴
|≈ 2.60%
|}
 
{|class="wikitable" style="width:auto;"
|+Probabilities of throwing X ''or more'' skulls with eight six-sided dice
!In words
!In maths
!Percentage
|-
|Probability of one ''or more'' skulls
|P(X ≥ 1)
= 1 − P(X = 0)
 
= 1 − (⅚)⁸
|≈ 76.7%
|-
|Probability of two ''or more'' skulls
|P(X ≥ 2)
= 1 − [ P(X = 0) + P(X = 1) ]
 
= 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ ]
|≈ 39.5%
|-
|Probability of three ''or more'' skulls
|P(X ≥ 3)
= 1 − [ P(X = 0) + P(X = 1) + P(X = 2) ]
 
= 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ + 28 × (⅙)² × (⅚)⁶ ]
|≈ 13.5%
|-
|Probability of four ''or more'' skulls
|P(X ≥ 4)
= 1 − [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ]
 
= 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ + 28 × (⅙)² × (⅚)⁶ + 56 × (⅙)³ × (⅚)⁵ ]
|≈ 3.07%
|}

Revision as of 20:57, 30 December 2021

For the rules of piraten kapern, see GameHelpPiratenKapern

Probabilities

Binomial formula
   n!    × pᵏ(1 − p)ⁿ⁻ᵏ
k!(n-k)!
n: number of trails (dice thrown)
k: number of successes (dice with a face value)
p: probability of success (of a die face value)
Example
Probability of throwing 3white die with 5 dice:
   5!    × (⅙)³ × (1 − ⅙)⁵⁻³
3!(5-3)!
=  5×4×3×2×1  × (⅙)³ × (⅚)²
  3×2×1 × 2×1
= 10 × (⅙)³ × (⅚)²
≈ 0.0321 or 3.21%

2 dice

Probabilities of throwing X skulls with two six-sided dice
In words In maths Percentage
Probability of no skulls P(X = 0) = (⅚)² ≈ 69.4%
Probability of one skull P(X = 1) = 2 × (⅙) × (⅚) ≈ 27.8%
Probability of two skulls P(X = 2) = (⅙)² ≈ 2.78%

8 dice

Probabilities of throwing X skulls with eight six-sided dice
In words In maths Percentage
Probability of no skulls P(X = 0) = (⅚)⁸ ≈ 23.3%
Probability of one skull P(X = 1) = 8 × (⅙) × (⅚)⁷ ≈ 37.2%
Probability of two skulls P(X = 2) = 28 × (⅙)² × (⅚)⁶ ≈ 26.0%
Probability of three skulls P(X = 3) = 56 × (⅙)³ × (⅚)⁵ ≈ 10.4%
Probability of four skulls P(X = 4) = 70 × (⅙)⁴ × (⅚)⁴ ≈ 2.60%
Probabilities of throwing X or more skulls with eight six-sided dice
In words In maths Percentage
Probability of one or more skulls P(X ≥ 1)

= 1 − P(X = 0)

= 1 − (⅚)⁸

≈ 76.7%
Probability of two or more skulls P(X ≥ 2)

= 1 − [ P(X = 0) + P(X = 1) ]

= 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ ]

≈ 39.5%
Probability of three or more skulls P(X ≥ 3)

= 1 − [ P(X = 0) + P(X = 1) + P(X = 2) ]

= 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ + 28 × (⅙)² × (⅚)⁶ ]

≈ 13.5%
Probability of four or more skulls P(X ≥ 4)

= 1 − [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ]

= 1 − [ (⅚)⁸ + 8 × (⅙) × (⅚)⁷ + 28 × (⅙)² × (⅚)⁶ + 56 × (⅙)³ × (⅚)⁵ ]

≈ 3.07%