private double GetExpectedPrizeExcludingSomeVowelsAndConsonants(ILotteryTicket ticket)
{
uint numExcludedConsonants = Constants.NumberOfConsonants - (ticket.NumberOfGivenCharacters - NumberOfGivenVowels);
uint numExcludedVowels = Constants.NumberOfVowels - NumberOfGivenVowels;
List <double> prizes = new List <double>();
List <double> excludedWords = new List <double>();
double totalExcludedWords = 0;
foreach (var vCombo in Vowels.GetCombinations(numExcludedVowels))
{
var givenVowels = Constants.Vowels.Except(vCombo);
foreach (var cCombo in Consonants.GetCombinations(numExcludedConsonants))
{
var givenConsonants = Constants.Consonants.Except(cCombo);
var allGivenChars = givenVowels.Concat(givenConsonants);
var allExcludedChars = vCombo.Concat(cCombo);
double prize = ticket.GetPrize(allGivenChars);
uint numExcludedWords = ticket.Crossword.CountExcludedWords(allExcludedChars);
prizes.Add(prize);
excludedWords.Add(numExcludedWords);
totalExcludedWords += numExcludedWords;
}
}
return(CalculateExpectedPrize(prizes, excludedWords, totalExcludedWords));
}
public double GetExpectedPrize(ILotteryTicket ticket)
{
double expectedPrize = 0;
double probability = 1.0 / Combinatorics.GetNumberOfCombinations(
Constants.AlphabetSize, ticket.NumberOfGivenCharacters);
foreach (var combo in Alphabet.GetCombinations(ticket.NumberOfGivenCharacters))
{
double prize = ticket.GetPrize(combo);
expectedPrize += prize * probability;
}
return(expectedPrize);
}
public double GetExpectedPrize(ILotteryTicket ticket)
{
if (ticket.NumberOfGivenCharacters == 0)
{
return(0);
}
else if (ticket.NumberOfGivenCharacters == Constants.AlphabetSize)
{
return(ticket.MaxPrize);
}
uint numExcludedCharacters = Constants.AlphabetSize - ticket.NumberOfGivenCharacters;
List <double> prizes = new List <double>();
List <double> excludedWords = new List <double>();
double totalExcludedWords = 0;
// For each combination, compute the number of words excluded by the combination and
// store its prize.
foreach (var combo in Alphabet.GetCombinations(numExcludedCharacters))
{
var givenCharacters = Constants.Alphabet.Except(combo);
double prize = ticket.GetPrize(givenCharacters);
uint numExcludedWords = ticket.Crossword.CountExcludedWords(combo);
prizes.Add(prize);
excludedWords.Add(numExcludedWords);
totalExcludedWords += numExcludedWords;
}
// Compute the expected prize
double expectedPrize = 0;
for (int i = 0; i < excludedWords.Count; ++i)
{
expectedPrize += prizes[i] * (excludedWords[i] / totalExcludedWords);
}
return(expectedPrize);
}