The three most important criteria for a good icebreaker are:
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Short / Random / Immediate
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Lengthy / Less interactive / Random
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Short / Appropriate / Participative
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All of the above
Good icebreakers must be SHORT (don't eat into presentation time), APPROPRIATE (relevant to topic/audience, not offensive), and PARTICIPATIVE (involve audience interaction). Random icebreakers lack focus; lengthy ones defeat the purpose; less interactive ones fail to engage.
A good icebreaker needs to be quick so it doesn't eat into the meeting or class time, appropriate for the audience and setting so nobody is offended or excluded, and participative so everyone actually engages rather than passively watching. Random or lengthy activities waste time and can miss the group's context entirely, which is why those options fall short.