Magic Intuition:Probability - Revision history

Oleksandr at 14:03, 25 September 2019

2019-09-25T14:03:35Z

Oleksandr at 14:03, 25 September 2019

2019-09-25T14:03:23Z

Oleksandr at 14:03, 25 September 2019

2019-09-25T14:03:13Z

Oleksandr: Marked this version for translation

2019-01-23T10:39:39Z

Marked this version for translation

Oleksandr at 10:39, 23 January 2019

2019-01-23T10:39:08Z

Oleksandr at 10:35, 23 January 2019

2019-01-23T10:35:49Z

Oleksandr at 10:33, 23 January 2019

2019-01-23T10:33:52Z

Oleksandr: Created page with " '''Probability''' is the measure of the likelihood of getting no less than certain amount of right answers out of total number of trials. It is quanti..."

2019-01-23T10:32:49Z

Created page with "<languages/> <translate> '''Probability''' is the measure of the likelihood of getting no less than certain amount of right answers out of total number of trials. It is quanti..."

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'''Probability''' is the measure of the likelihood of getting no less than certain amount of right answers out of total number of trials. It is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). It is calculated in different ways for different types of games.

# For Forex, Dice, Soccer and Space games we use Bernoulli formula, as in each round probability to get the true answer doesn\'t depend on the previous rounds results: 
<tt>Pn(k) = Cnk * pk * qn-k;</tt> 
where <tt>p</tt> - probability to guess right in every single round.
For example, for Forex it is 1/2, for Dice - 1/6, and Space - 1/2 (easy), 2/5 (medium), 1/3 (hard) 
<tt>q = 1 - p</tt> 
Probability to guess no less than <tt>k</tt> times in <tt>n</tt> rounds: 
<tt>Probability = Pn(n) + Pn(n-1) + … + Pn(k);</tt>

# For Sector game conditional probability rule is used. Here probability describes how likely is to reach the round <tt>k</tt> with <tt>t</tt> attempts for each round: 
<tt>Probability = t/ν1 * t/ν2 * … * t/νk;</tt> 
where <tt>νk</tt> - number of sectors in round k.

# For Color and Suit games we apply conditional probability rule together with the rule of the sum of probabilities. We assume that player chooses the most probable variant every round.
Here probability shows how likely it is to guess correct no less than <tt>k</tt> times with <tt>n</tt> cards in the shuffled deck, using such strategy. 

<tt>Probability = p1/ζn + … + pt/ζn;</tt> 
where <tt>pt</tt> - probability to win within the certain order of cards (t) in the deck 
<tt>ζn = n! / ((n / 2)! * (n / 2)!)</tt> - all possible card orders of this deck (permutations of n cards with repetitions).
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 #:<tt><b>ζ<sub><small>n</small></sub> = n! / ((n / 2)! * (n / 2)!)</b></tt> - all possible card orders of this deck (permutations of n cards with repetitions).
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 #:<tt><b>ζ<sub><small>n</small></sub> = n! / ((n / 2)! * (n / 2)!)</b></tt> - all possible card orders of this deck (permutations of n cards with repetitions).
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 #:<tt><b>ζ<sub><small>n</small></sub> = n! / ((n / 2)! * (n / 2)!)</b></tt> - all possible card orders of this deck (permutations of n cards with repetitions).
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@@ Line 3: / Line 3: @@
 '''Probability''' is the measure of the likelihood of getting no less than certain amount of right answers out of total number of trials. It is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). It is calculated in different ways for different types of games.
-# For Forex, Dice, Soccer and Space games we use Bernoulli formula, as in each round probability to get the true answer doesn\'t depend on the previous rounds results:
+# For Forex, Dice, Soccer and Space games we use [https://ru.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0_%D0%91%D0%B5%D1%80%D0%BD%D1%83%D0%BB%D0%BB%D0%B8 Bernoulli formula], as in each round probability to get the true answer doesn't depend on the previous rounds results:
-:<tt><b>P<sub><small>n</small></sub>(k) = C<sub><small>n</small></sub><sup><small>k</small></sup> * p<sup><small>k</small></sup> * q<sup><small>n-k</small></sup>;</b></tt>
+#:<tt><b>P<sub><small>n</small></sub>(k) = C<sub><small>n</small></sub><sup><small>k</small></sup> * p<sup><small>k</small></sup> * q<sup><small>n-k</small></sup>;</b></tt>
-:where <tt><b>p</b></tt> - probability to guess right in every single round.
+#:where <tt><b>p</b></tt> - probability to guess right in every single round.
-:For example, for Forex it is 1/2, for Dice - 1/6, and Space - 1/2 (easy), 2/5 (medium), 1/3 (hard)
+#:For example, for Forex it is 1/2, for Dice - 1/6, and Space - 1/2 (easy), 2/5 (medium), 1/3 (hard)
-:<tt><b>q = 1 - p</b></tt>
+#:<tt><b>q = 1 - p</b></tt>
-:Probability to guess no less than <tt><b>k</b></tt> times in <tt><b>n</b></tt> rounds:<br/>
+#:Probability to guess no less than <tt><b>k</b></tt> times in <tt><b>n</b></tt> rounds:<br/>
-:<tt><b>Probability = P<sub><small>n</small></sub>(n) + P<sub><small>n</small></sub>(n-1) + &#8230; + P<sub><small>n</small></sub>(k);</tt></b>
+#:<tt><b>Probability = P<sub><small>n</small></sub>(n) + P<sub><small>n</small></sub>(n-1) + &#8230; + P<sub><small>n</small></sub>(k);</tt></b>
 # For Sector game conditional probability rule is used. Here probability describes how likely is to reach the round <tt><b>k</b></tt> with <tt><b>t</b></tt> attempts for each round:
-# For Sector game conditional probability rule is used. Here probability describes how likely is to reach the round <tt><b>k</b></tt> with <tt><b>t</b></tt> attempts for each round:<br/>
+#:<tt><b>Probability = t/ν<sub><small>1</small></sub> * t/ν<sub><small>2</small></sub> * &#8230; * t/ν<sub><small>k</small></sub>;</b></tt>
-<tt><b>Probability = t/ν<sub><small>1</small></sub> * t/ν<sub><small>2</small></sub> * &#8230; * t/ν<sub><small>k</small></sub>;</b></tt><br/>
+#:where <tt><b>ν<sub><small>k</small></sub></b></tt> - number of sectors in round k.
-where <tt><b>ν<sub><small>k</small></sub></b></tt> - number of sectors in round k.
+# For Color and Suit games we apply conditional probability rule together with the rule of the sum of probabilities. We assume that player chooses the most probable variant every round. Here probability shows how likely it is to guess correct no less than <tt><b>k</b></tt> times with <tt><b>n</b></tt> cards in the shuffled deck, using such strategy.
+#:<tt><b>Probability = p<sub><small>1</small></sub>/ζ<sub><small>n</small></sub> + &#8230; + p<sub><small>t</small></sub>/ζ<sub><small>n</small></sub>;</b></tt><br/>
-# For Color and Suit games we apply conditional probability rule together with the rule of the sum of probabilities. We assume that player chooses the most probable variant every round.
+#:where <tt><b>p<sub><small>t</small></sub></b></tt> - probability to win within the certain order of cards (t) in the deck
-Here probability shows how likely it is to guess correct no less than <tt><b>k</b></tt> times with <tt><b>n</b></tt> cards in the shuffled deck, using such strategy.<br/>
+#:<tt><b>ζ<sub><small>n</small></sub> = n! / ((n / 2)! * (n / 2)!)</b></tt> - all possible card orders of this deck (permutations of n cards with repetitions).
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@@ Line 4: / Line 4: @@
 # For Forex, Dice, Soccer and Space games we use Bernoulli formula, as in each round probability to get the true answer doesn\'t depend on the previous rounds results:
-<tt><b>P<sub><small>n</small></sub>(k) = C<sub><small>n</small></sub><sup><small>k</small></sup> * p<sup><small>k</small></sup> * q<sup><small>n-k</small></sup>;</b></tt>
+:<tt><b>P<sub><small>n</small></sub>(k) = C<sub><small>n</small></sub><sup><small>k</small></sup> * p<sup><small>k</small></sup> * q<sup><small>n-k</small></sup>;</b></tt>
-where <tt><b>p</b></tt> - probability to guess right in every single round.
+:where <tt><b>p</b></tt> - probability to guess right in every single round.
-For example, for Forex it is 1/2, for Dice - 1/6, and Space - 1/2 (easy), 2/5 (medium), 1/3 (hard) <br/>
+:For example, for Forex it is 1/2, for Dice - 1/6, and Space - 1/2 (easy), 2/5 (medium), 1/3 (hard)
-<tt><b>q = 1 - p</b></tt>
+:<tt><b>q = 1 - p</b></tt>
-Probability to guess no less than <tt><b>k</b></tt> times in <tt><b>n</b></tt> rounds:<br/>
+:Probability to guess no less than <tt><b>k</b></tt> times in <tt><b>n</b></tt> rounds:<br/>
-<tt><b>Probability = P<sub><small>n</small></sub>(n) + P<sub><small>n</small></sub>(n-1) + &#8230; + P<sub><small>n</small></sub>(k);</tt></b>
+:<tt><b>Probability = P<sub><small>n</small></sub>(n) + P<sub><small>n</small></sub>(n-1) + &#8230; + P<sub><small>n</small></sub>(k);</tt></b>
 # For Sector game conditional probability rule is used. Here probability describes how likely is to reach the round <tt><b>k</b></tt> with <tt><b>t</b></tt> attempts for each round:<br/>