Sim
Players: Two
Players alternately join dots on a hexagon; the first player who competes a triangle in their own colour loses.
Description
First draw a board consisting of six dots arranged in a hexagon, with each dot connected to every other dot by a line:

The players take turns colouring an uncoloured line.
The first player forced to complete a triangle in their own colour loses the game.
The game cannot be a draw because there is no way to colour all the lines without creating at least one triangle.
Example
For example, in the following game Blue plays first and wins after the fifth round because Red cannot play without completing a triangle:
