def daysToWin(netspaceFraction, confidence = 0.95, challengesPerDay = 4608):
    losingProbability = 1 - netspaceFraction
    challengesToWin = math.log(1 - confidence, losingProbability)
    return challengesToWin / challengesPerDay

def earningsPerYear(xchValue_USD, netspaceFraction, confidence = 0.95, challengesPerDay = 4608, xchPerWin = 2):
    xchPerDay = xchPerWin / daysToWin(netspaceFraction, confidence, challengesPerDay)
    dailyUSD = xchValue_USD * xchPerDay
    return dailyUSD * 365