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Wiktionary
thumb war

n. (context games English) A children's game in which the two opponents interlock each other's right- or left-handed fingers, each attempting to press and subdue the other's thumb.

Wikipedia
Thumb war

A thumb war (pea-knuckle or pea-knuckle war in New Zealand) is a game played by two players in a tournament called a thumb-a-war (or thumb war) using the thumbs to simulate fighting. The object of the game is to pin the opponent's thumb, often to a count of three. The San Francisco Chronicle called the game "the miniature golf of martial sports."

The players face each other and each holds out their left hand or right hand in a " thumbs up", and they link hands such that each player's fingers curl around the other player's fingers. Gameplay has several tactics such as " playing possum", aiming for the knuckle rather than the nail for a pin, going for a quick strike, and waiting for one's opponent to tire. Variations include making the thumbs "bow", "kiss", or both before warring, and to war with both hands at once; or sneak attacks, which involve using your pointer finger to take over the opponent.

The game is typically initiated with both the players uttering the rhyme "One, two, three, four, I declare a thumb war", passing their thumbs over each other in time with this rhyme. The rhyme is sometimes extended with "Five, six, seven, eight, try to keep your thumb straight." or "Five, six, seven, eight. This should be a piece of cake." In Spanish, the starting song is "ésta es la pulseada china", with the same thumb dance as in English.

Competitive matches on thumb wrestling have been held on Long Island and at Lowestoft. The 826 Valencia Foundation holds an annual thumb-wrestling competition, which has been won three times by San Francisco Chronicle book editor Oscar Villalon.