It is common for two teams or two players to play a game in which the first one to win a majority of the initially determined number of matches wins the championship. We will explore the probabilistic conditions under...It is common for two teams or two players to play a game in which the first one to win a majority of the initially determined number of matches wins the championship. We will explore the probabilistic conditions under which a team (or player) that is considered weak may win the championship over a team (or player) that is considered strong, or a game may go all the way to the end, creating excitement among fans. It is unlikely to occur if the initially estimated probability remains constant when the weaker one wins each game against the stronger one. The purpose of this study is to identify probabilistically what conditions are necessary to increase the probability of such an outcome. We examine probabilistically by quantifying momentum gains to see if momentum gains by a weaker team (or player) winning a series of games would increase the likelihood of such an outcome occurring. If the weaker one gains momentum by winning a series of games and the probability of winning the next game is greater than the initial probability, we can see that such a result will occur in this study. Especially when the number of games is limited to seven, the initial probability that a weaker one will beat a stronger one in each game must be 0.35 or higher in order to win the championship and excite the fans by having the game go all the way to the end.展开更多
文摘It is common for two teams or two players to play a game in which the first one to win a majority of the initially determined number of matches wins the championship. We will explore the probabilistic conditions under which a team (or player) that is considered weak may win the championship over a team (or player) that is considered strong, or a game may go all the way to the end, creating excitement among fans. It is unlikely to occur if the initially estimated probability remains constant when the weaker one wins each game against the stronger one. The purpose of this study is to identify probabilistically what conditions are necessary to increase the probability of such an outcome. We examine probabilistically by quantifying momentum gains to see if momentum gains by a weaker team (or player) winning a series of games would increase the likelihood of such an outcome occurring. If the weaker one gains momentum by winning a series of games and the probability of winning the next game is greater than the initial probability, we can see that such a result will occur in this study. Especially when the number of games is limited to seven, the initial probability that a weaker one will beat a stronger one in each game must be 0.35 or higher in order to win the championship and excite the fans by having the game go all the way to the end.
