1) They win the tournament.
2) Fiji lose to South Africa (if they win, they will take out their second title, the first since 2006).
3) South Africa lose their semi-final (however, if South Africa lose to New Zealand in the final, New Zealand will still win because of what's expected to be a significant points differential).
"Fiji have probably got more depth than any team at present," said New Zealand coach Gordon Tietjens. "That quarter-final will determine our world series chances. One of them will fall by the way."
"It will give us an outcome," said Fiji coach Ben Ryan, whose side broke a late 19-19 deadlock with Argentina in their opening match.
"I'm pleased we've done the whole season unbeaten in the pool stages, that's a big achievement. It's also good to be in control of our own destiny. We are [effectively] in a Cup final tomorrow morning, anything after that is irrelevant."
A Fiji series win would also boost the country's hopes of attaining their first Olympic medal next year. Along with Fiji, South Africa and New Zealand, England (on behalf of the wider Team GB) became the fourth and final automatic Games qualifier. That means the likes of Australia and Samoa will play off for the vacant Oceania berth.
Back at the tournament, New Zealand compounded their injury concerns. Sam Dickson hurt his knee against Japan and sat out the Australia match. The side has recently lost Joe Webber, Tim Mikkelson and Ambrose Curtis to injuries.
Tietjens' biggest concern from a tactical perspective was how his side went 14-12 down to Japan at half-time, giving the match a sense of 'hang on a minute' anticipation.
"We undid the good work of the first game against Wales. We were put under pressure and had to bounce back to redeem ourselves.
"Over the day Gillies Kaka had some outstanding games and Scott Curry was a machine who stood up. Rieko Ioane played every minute and also keeps scoring great tries (he scored four).
Tonight's other quarter-finals see Australia play Scotland and Canada meet the United States.
The New Zealand women's side lost their first tournament of the series. They were beaten 24-5 by Australia in the semi-finals and edged the United States 24-19 to win the third-placed play-off. Australia beat Canada 20-17 in the final.
New Zealand sits on 96 points and wins the overall series regardless of this week's last round in Amsterdam where the winner takes 20 points. Canada and Australia are second-equal on 76 points. Teams earn one point for qualifying.
*ANDREW ALDERSON IS AT THE LONDON SEVENS WITH ASSISTANCE FROM NEW ZEALAND RUGBY.