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When you say "I thought she might have had a chance to win it." it seems (at least to me) that she's not won! Indeed you've used the PP to stress the result. However, when you say "I thought she might have a chance", it's possible that you're still in the middle of the action, that is not possible or so idiomatic with the PP. 

When you say "I thought she might have had a chance to win it." it seems (at least to me) that she's not won! Indeed you've used the PP to stress the result. However, when you say "I thought she might have a chance", it's possible that you're still in the middle of the action, that is not possible or so idiomatic with the PP.

When you say "I thought she might have had a chance to win it." it seems (at least to me) that she's not won! Indeed you've used the PP to stress the result. However, when you say "I thought she might have a chance", it's possible that you're still in the middle of the action, that is not possible or so idiomatic with the PP. 

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When you say "I thought she might have had a chance to win it." it seems (at least to me) that she's not won! Indeed you've used the PP to stress the result. However, when you say "I thought she might have a chance", it's possible that you're still in the middle of the action, that is not possible or so idiomatic with the PP.