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Tyrion had the conversation with Oberyn when he first came to the city. He knows that Oberyn wouldn't be able to deny an opportunity to kill the Mountain, especially in a setting that was "sanctioned" with no consequences should he win. We also know that Tyrion thinks out of the box in this situation (Bronn was a risky but brilliant choice back in the Eyrie).
Even in a worst case scenario (Tyrion dies), Tyrion will ruin his father's plans. He is one of only 2 males to carry on the name, and with his death, Jamie most certainly hardens his stance to remain in the King's Guard and not serve his father's desire to marry and have children.
So Tyrion is taking an awful situation and creates two alternatives with which he can "win". He either lives and goes free, or dies and ruins his father's plans for the House's future.
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