Question: Which game dates back to at least the Roman Empire: Nine Men's Morris, or Icehouse pieces?

Context paragraphs:
Hairstyle: A hairstyle, hairdo, or haircut refers to the styling of hair, usually on the human scalp.  Sometimes, this could also mean an editing of beard hair.  The fashioning of hair can be considered an aspect of personal grooming, fashion, and cosmetics, although practical, cultural, and popular considerations also influence some hairstyles.  The oldest known depiction of hair braiding dates back about 30,000 years.  In ancient civilizations, women's hair was often elaborately and carefully dressed in special ways.  In Imperial Rome, women wore their hair in complicated styles.  From the time of the Roman Empire until the Middle Ages, most women grew their hair as long as it would naturally grow.  During the Roman Empire as well as in the 16th century in the western world, women began to wear their hair in extremely ornate styles.  In the later half of the 15th century and on into the 16th century a very high hairline on the forehead was considered attractive.  During the 15th and 16th centuries, European men wore their hair cropped no longer than shoulder-length.  In the early 17th century male hairstyles grew longer, with waves or curls being considered desirable.

Military of the Sasanian Empire: The Sasanian army (Middle Persian "Spâh-ī Sāsānīg") was the primary military body of the Sasanian armed forces, serving alongside the Sasanian navy.  The birth of the army dates back to the rise of Ardashir I (r. 224–241), the founder of the Sasanian Empire, to the throne.  Ardashir aimed at the revival of the Persian Empire, and to further this aim, he reformed the military by forming a standing army which was under his personal command and whose officers were separate from satraps, local princes and nobility.  He restored the Achaemenid military organizations, retained the Parthian cavalry model, and employed new types of armour and siege warfare techniques.  This was the beginning for a military system which served him and his successors for over 400 years, during which the Sasanian Empire was, along with the Roman Empire and later the East Roman Empire, one of the two superpowers of Late Antiquity in Western Eurasia.  The Sasanian army protected "Eranshahr" ("the realm of Iran") from the East against the incursions of central Asiatic nomads like the Hephthalites and Turks, while in the west it was engaged in a recurrent struggle against the Roman Empire.

Maka dai dai shogi: Maka dai dai shōgi (摩訶大大将棋 or 摩𩹄大大象戯 'ultra-huge chess') is a large board <a href="Shogi%20variant">variant</a> of <a href="shogi">shogi</a> (Japanese chess).  The game dates back to the 15th century and is based on dai dai shogi and the earlier dai shogi.  The three Edo-era sources are not congruent in their descriptions of the pieces not found in smaller games.  Apart from its size and number of pieces, the major difference from these smaller games is the "promotion by capture" rule.  A more compact modern proposal for the game is called hishigata shogi.

Baths of Antoninus: The Baths of Antoninus or Baths of Carthage, located in Carthage, Tunisia, are the vastest set of Roman Thermae built on the African continent and one of three largest built in the Roman Empire.  The baths are also the only remaining Thermae of Carthage that dates back to the Roman Empire's era.

Morabaraba: Morabaraba is a traditional two-player strategy board game played in South Africa, Botswana and Lesotho.  The game is also known as Mlabalaba, Mmela (in Setswana), Muravava, Umlabalaba.  The game is similar to Twelve Men's Morris, a variation on the Roman board game Nine Men's Morris.

Dai dai shogi: Dai dai shōgi (大大将棋 'huge chess') is a large board variant of shogi (Japanese chess).  The game dates back to the 15th century and is based on the earlier dai shogi.  Apart from its size, the major difference is in the range of the pieces and the “promotion by capture” rule.  It is the smallest board variant to use this rule.

Madiao: Madiao (), also Ma Diao, Ma Tiu or Ma Tiao, is a late imperial Chinese trick-taking gambling card game, also known as the game of "Paper Tiger."  The deck used was recorded by Lu Rong in the 15th century and the rules later by Pan Zhiheng and Feng Menglong during the early 17th century.  Korean poet Jang Hon (1759-1828) wrote that the game dates back to the Yuan dynasty (1271-1368).  It continued to be popular during the Qing dynasty until around the mid-19th century.  The game was also known in Japan from at least 1791.  It is played with 40 cards and four players.

Treehouse (game): Treehouse is a game in which players try to get their configuration of Icehouse pieces to match the central configuration, shared by all players.  The rolling of the special "Treehouse Die" tells the player what kind of move to make to change his own or the central configuration, and then he does so to best move towards the goal.

Icehouse pieces: Icehouse pieces, or Icehouse Pyramids, Treehouse pieces, Treehouse Pyramids and officially Looney Pyramids, are nestable and stackable pyramid-shaped gaming pieces and a game system.  The game system was invented by Andrew Looney and John Cooper in 1987, originally for use in the game of Icehouse.

Nine Men's Morris: Nine Men's Morris is a strategy board game for two players dating at least to the Roman Empire.  The game is also known as Nine Man Morris, Mill, Mills, The Mill Game, Merels, Merrills, Merelles, Marelles, Morelles and Ninepenny Marl in English.  The game has also been called Cowboy Checkers and is sometimes printed on the back of checkerboards. Nine Men's Morris is a solved game in which either player can force the game into a draw.

Supporting paragraphs: Nine Men's Morris Icehouse pieces
Answer: Nine Men's Morris