What is the ruling on the game of "sheesh" that is currently widespread?

As long as the game uses dice, it is not permissible. Scholars have unanimously agreed that playing with dice and chess is forbidden if it involves a wager, as it falls under prohibited gambling (qimar and maysir). Dice are forbidden according to the four imams, whether or not they involve a wager. Any game that includes dice is therefore forbidden to play.