Magic Intuition:Probability/en

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.

1. 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:

   P_n(k) = C_n^k * p^k * q^n-k;

   where p - 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)

   q = 1 - p

   Probability to guess no less than k times in n rounds:
   

   Probability = P_n(n) + P_n(n-1) + … + P_n(k);

2. For Sector game conditional probability rule is used. Here probability describes how likely is to reach the round k with t attempts for each round:

   Probability = t/ν₁ * t/ν₂ * … * t/ν_k;

   where ν_k - number of sectors in round k.

3. 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 k times with n cards in the shuffled deck, using such strategy.

   Probability = p₁/ζ_n + … + p_t/ζ_n;
   

   where p_t - probability to win within the certain order of cards (t) in the deck

   ζ_n = n! / ((n / 2)! * (n / 2)!) - all possible card orders of this deck (permutations of n cards with repetitions).