- Episode Title: Calculate Alex
- Episode Number: 09
- Series: Last Exile
- Original Air Date: 6/02/2003
- English Air Date: 3/12/2004
The episode begins with Duke Henry Knowles receives his son's broken sword.
Claus and Lavie are trying to repair their damaged vanship when the Silvana heads to Horizon Cave, where The Cave Horizon Eight race is being held. Claus and Lavie enter the race as a team, as do Tatiana and Alister. They are surprised when Dio and Lucciola also join the race.
Claus and Lavie start the race in last place due to difficulties getting their vanship started. Tatiana and Alister are supposed to be carrying out a mission rather than winning the race, but Tatiana begins behaving recklessly after having her ego pricked by Dio.
While the vanships are racing, Alex Row attends a black market auction being held by Giancarlo. Duke Knowles sits next to Alex at the auction. Alex doesn't bid until Giancarlo introduces the final item, which he claims to be a key to unlocking Exile.
Silvana crew members
- Alex Row
- Sophia Forrester
- Tatiana Wisla
- Alister Agrew
- Anthony Kostabi
- Ethan Pelerin
- Gale Frank
- Godwin Austin
- In chess, to caculate is to carefully plan a series of moves while considering possible responses.
- A map of Horizon Cave is shown; visible place names on it are δευπη ωαλλεψ (death valley), σηιωα τεμπλε (shiva temple), ιταλια (italia), τοωερ οφ σετ (tower of set), οωερτακε ποιντ (overtake point), μοηαωε ποιντ(mohave point), and ρεδ ωαλλεψ (red valley). There is also one spot marked οφφλιμιταρεα (off limit area), and several names that are cut off by the edges of the screen.