Is it permissible to play entertainment games that rely on paying a sum to catch dolls with a robotic arm within a specified time, with the possibility of catching nothing?

If the intention of the game is for the player to win a prize (such as dolls or similar items), then it is maysir (gambling) and forbidden qimar (gambling), because its reality is risk and oscillation between gain and loss. Gambling is taking a person's money with the risk of either receiving compensation or not, and it is a form of consuming people's wealth unlawfully. Allah Almighty said: {Do not consume your property among yourselves wrongfully, but let there be trade by mutual consent among you}. And al-batil (wrongfully/unlawfully) is that which contravenes the Sacred Law, or that which is taken without compensation. However, if its intention is merely playing and testing skill, then there is no harm in it.