Winning. Have you ever wondered about just how many games must your team win to know, guaranteed, it has won a certain number of consecutive games? This is, not likely to have won a certain number of consecutive games. But actual consecutive wins . Thinking a bit combinatorially we can determine this with a simple formula. Notation: n = number of games in a season r = number of consecutive wins desired Let n/r = m R k . That is m is the integer divisor of n by r , which is 0, 1, 2,…, and k is the remainder, 0 ,1,…, r -1. For example 53/5 = 10 R 3, or 21/6 = 3 R 3. Then we have the minimum number of games that must be won to guarantee r consecutive wins W sometime during a season is given by W = m ( r -1) + k + 1 In the table below, we give some examples for various sports.Of course, when r = 2, that value is the next highest number greater than half the number of games when n is even. Number of games played Run of consecutive w
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