Optimal “First Batting” Strategy

Description

We want to find the optimal strategy employed by a team batting first. The assumptions are stated as follows:

At any point of time only 1 batsmen is playing.

Let (b; w) denote the state, where b is the balls left, and w is the wickets left.

There are 5 possible shots, i.e., trying to score A = f1; 2; 3; 4; 6g. These shots are associated with the risk of getting out, and it varies from batsmen to batsmen. The top batsman w = 1 has the following probabilities of getting out p^out_min = f0:01; 0:02; 0:03; 0:1; 0:3g, where the i^th entry is for the i^th action. The last batsman (i.e., w = 10 pair) has the following

out pout		=	0:1; 0:2; 0:3; 0:5; 0:7			g	. If there are w wickets in hand,
probabilities of gettingout	max		fout	out	(a)		out	(a)) ((w 1)=9)
then use the formula p	(w; a) = pmax			(a) + (pmin		pmax

Compute the Best-Score(b,w) and Best-Shot(b,w), for all b = 1; : : : ; 300 and w =

0;1;:::;10.