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A set of dice is intransitive (or nontransitive) if it contains X>2 dice, X1, X2, and X3... with the property that X1 rolls higher than X2 more than half the time, and X2 rolls higher than X3 etc... more than half the time, but where it is not true that X1 rolls higher than Xn more than half the time.
The terms "transitive game" or "intransitive game" are not used in game theory. A prototypical example of an intransitive game is the game rock, paper, scissors. In probabilistic games like Penney's game, the violation of transitivity results in a more subtle way, and is often presented as a probability paradox.
In particular, by virtue of being antitransitive the relation is not transitive. The game of rock, paper, scissors is an example. The relation over rock, paper, and scissors is "defeats", and the standard rules of the game are such that rock defeats scissors, scissors defeats paper, and paper defeats rock.
English is rather flexible as regards verb valency, and so it has a high number of ambitransitive verbs; other languages are more rigid and require explicit valency changing operations (voice, causative morphology, etc.) to transform a verb from intransitive to transitive or vice versa.
Many languages, including English, have ditransitive verbs that denote two objects, and some verbs may be ambitransitive in a manner that is either transitive (e.g., "I read the book" or "We won the game") or intransitive (e.g., "I read until bedtime" or "We won") depending on the given context.
Matching two numbers won't win anything in Mega Millions unless one of the numbers is the Mega Ball. A ticket matching one of the five numbers and the Mega Ball is worth $4.
An ambitransitive verb is a verb that is both intransitive and transitive. [1]: 4 This verb may or may not require a direct object.English has many ambitransitive verbs. . Examples include read, break, and understand (e.g., "I read the book", saying what was read, or just "I read all afternoo
In contrast, the verb iru can be used as an auxiliary with non-volitional intransitive verbs to simply indicate a state of being, without the element of volition. Iru also has a basic meaning of 'be' or 'stay', but is used with animate subjects. In this use as an auxiliary verb, iru appears in the form -te-iru.