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 poutmin = f0:01; 0:02; 0:03; 0:1; 0:3g, where the ith entry is for the ith 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.
