[betgo]

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If the BB was playing correctly, then the push is correct. There is no way he is calling you with any cards. In the real world, fold, complete, or miniraise.

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Wrong. BB has an incentive to allow you to lose the tournament. He has enough chips to make this happen with reasonable hands.

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Wrong. Unless BB has it in for you, he can fold his way in and it is disadvantageous for him to call, probably even with AA.

However, people don't usually become chip leaders in satellites by playing correctly.