Sure! Here's a simple game that meets your requirements:
Make sure to replace `'emozi_bear.png'` and `'emozi_all/player.png'` with the actual file paths to your cave and player pictograms. The game uses arrow keys for movement. The player can move around the cave, and after every 10 units in distance, there is a 20% chance of encountering bats that decrease the player's health by 20%. The health bar and distance counter are displayed on the screen. The game ends if the player's health reaches zero.