In many instances in chess. a weaker piece proves to have more force than a piece with greater numerical value.
'cases' would work as a replacement for 'instances', but not 'example'. 'example' is usually used when an actual example is given. This sentence is more of a general statement.
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soheil1What about 'particular instances'?I don't understand your question. Do you mean "In many particular instances" instead of "In many instances"? That's OK.