Many numerical identities are proved applying clever but informal combinatorial arguments. A way of proving these identities by a formal representation that closely follows these arguments is presented. Operationals, ...
详细信息
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary ...
详细信息
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given score. We use these findings to investigate the dependence of these quantities on the different parameters involved (number of points needed to win a set, number of consecutive serves, etc.), with particular focus on the rule change imposed in 2001 by the International Table Tennis Federation (ITTF). Finally, we briefly indicate how our results can lead to more efficient estimation techniques of individual players' abilities.
暂无评论