The Ivorians have the better chance of going through, having taken three points from Japan in their opening match. Victory over the Greeks will put them into the last 16 and even a draw might be enough.
Greece have no such luxury. Having taken just a point from their first two matches they have to win, and even then they might lose out to the Japanese on goal difference.
The former European champions have an abysmal record at the World Cup. In their eight matches to date they have conceded 18 goals and scored just twice. Their only victory was a 2-1 win over Nigeria in South Africa four years ago.
Here in Brazil, their usually solid defence let them down in a 3-0 defeat by Colombia in their opener, and they were slightly lucky to scrape a goalless draw against Japan.
Their captain and influential midfielder Kostas Katsouranis was sent off in that match and will miss Tuesday's clash at Fortaleza's Castelao arena.
Coach Fernando Santos has to decide whether to replace him with 37-year-old Giorgos Karagounis, the only other surviving member of Greece's triumphant Euro 2004 squad, or opt for a younger alternative like Andreas Samaris.