MathDB

On a board there is a regular polygon

A_1A_2\ldots A_{99}.

Ana and Barbu alternatively occupy empty vertices of the polygon and write down triangles on a list: Ana only writes obtuse triangles, while Barbu only writes acute ones.
At the first turn, Ana chooses three vertices

X,Y

and

Z

and writes down

\triangle XYZ.

Then, Barbu chooses two of

X,Y

and

Z,

for example

X

and

Y

, and an unchosen vertex

T

, and writes down

\triangle XYT.

The game goes on and at each turn, the player must choose a new vertex

R

and write down

\triangle PQR

, where

P

is the last vertex chosen by the other player, and

Q

is one of the other vertices of the last triangle written down by the other player.
If one player cannot perform a move, then the other one wins. If both people play optimally, determine who has a winning strategy.

Problem Statement