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Adversarial Bifurcation

​
number of propositional variables
3
4
new game
choose in order
a
¬a
b
¬b
c
¬c
6
3
8
7
2
4
5
1
This Demonstration shows a two-person game between you and an imaginary adversary. A move consists of choosing
x
or
¬x
in order through
a
,
b
,
c
,
d
. Each such choice eliminates (shown by shading) all corresponding numbers in the bottom row.
The game starts at the root with no number eliminated. You get first move. You may choose
a
or
¬a
, then
b
or
¬b
, and so on. Before making a move, you first must ask your adversary whether he wants to choose (unless he has already chosen twice in a row). If he does not, you can choose. Your aim is to get as high a number as possible. The aim of your adversary is that you get as small a number as possible. Without an adversary, you can play for both sides.
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