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2015 Kurschak Competition
1
1
Part of
2015 Kurschak Competition
Problems
(1)
Fencing, probability of winning
Source: Kürschák 2015, problem 1
10/7/2016
In fencing, you win a round if you are the first to reach
15
15
15
points. Suppose that when
A
A
A
plays against
B
B
B
, at any point during the round,
A
A
A
scores the next point with probability
p
p
p
and
B
B
B
scores the next point with probability
q
=
1
−
p
q=1-p
q
=
1
−
p
. (However, they never can both score a point at the same time.)Suppose that in this round,
A
A
A
already has
14
−
k
14-k
14
−
k
points, and
B
B
B
has
14
−
ℓ
14-\ell
14
−
ℓ
(where
0
≤
k
,
ℓ
≤
14
0\le k,\ell\le 14
0
≤
k
,
ℓ
≤
14
). By how much will the probability that
A
A
A
wins the round increase if
A
A
A
scores the next point?
probability
combinatorics