Hogh-Christensen is guaranteed to pick up a medal, as is Ainslie as long as he finishes, but the pair will go head to head for the gold medal in Sunday's Medal Race in a winner takes all battle.
"Wow," said the overall leader on the finale, "I'm really looking forward to the Medal Race. It will be very exciting. It will be whoever beats who in the final race so it will be an epic battle. That is what we have here and why I love racing."
If Ainslie wins gold he will eclipse Paul Elvstrom to become the most successful Olympic sailor of all time and with a lot on the line he added, "It's going to be a very important race. It's a huge opportunity to race in front of a home crowd. Obviously there's a lot at stake but it is going to be fantastic."
The Dane trailed Ainslie in second place in Race 10 but slipped up which allowed Pieter-Jan Postma (NED) to overtake and finished second, "Pieter is fighting for bronze and he is fighting hard," said Hogh-Christensen. "I made a lot of mistakes and Pieter overtook me. I wanted to keep Pieter at close quarters because I knew if Ben came back to give me bad air I would have to do the same to Pieter."
Although Ainslie comfortably took the race win the Danes mistake meant Ainslie reduced the deficit, Ainslie said, "The overall points were very close so it was important for me that the Dutch sailor overtook the Dane, and finally he got past. I sailed my own race and the Dutch did that."
Postma's excellent day included a Race 9 win and a second behind Ainslie in Race 10. He moves up into bronze medal position on 42 points whilst Jonathan Lobert (FRA) and Ivan Kljakovic Gaspic (CRO) trail him on 47 points. Also in contention for the final podium spot is Vasilij Zbogar (SLO).
The Finn Medal Race takes place on the Nothe Course at 14:00 on Sunday 5 August.
1. Jonas Hogh-Christensen (DEN) - 26pts
2. Ben Ainslie (GBR) - 28pts
3. Pieter-Jan Postma (NED) - 42pts
4. Jonathan Lobert (FRA) - 47pts
5. Ivan Kljakovic Gaspic (CRO) - 47pts
Follow all the action on the ISAF Olympic Live Blog which will bring competition updates and instant reactions to the action on the race course. Fans can check in and ask our media team questions to get the very latest information. The blog will start one hour before racing each and every day of the competition.