Sure! Here's a simple game that calculates the value of pi by randomly generating points inside a square and checking if they lie within a circle. This game can be played on a smartphone using pictograms as requested. Note that this is a simplified version and not a complete and optimized implementation. Please copy the code below and save it as an HTML file to play the game.
Points: 0
Approximation of π: 0
To play the game, simply open the saved HTML file in your smartphone's web browser. You will see a square canvas representing the game area. Tap inside the canvas to generate a point. The game will calculate the approximation of pi based on the ratio of points within the circle. The number of points generated and the current approximation of pi will be displayed below the canvas.