The games that have the most importance to the Nuggets tonight are:
Sacramento @ Houston
Utah @ LA Lakers
Indiana @ Milwaukee
Nuggets @ Portland
What's at stake?
1) Number of draft picks in the 2016 draft:
If Houston wins, they get the 8th seed in the West and The Nuggets get their pick, which is guaranteed to be pick #15.
If Houston loses, then the result of Utah @ Lakers matters. If the Lakers win, Houston is still in the Playoffs. If Utah wins, then the Nuggets have lost that #15 pick.
2) position of draft picks (excluding lottery)
The Nuggets own Portland's pick, at #19. If the Nuggets win tonight and the Pistons win @ Cleveland, then that pick would go down to #18. This gets a little trickier than that, as several teams can end up with the same 43-39 record. Memphis and Portland have split games this year, but Portland has a better division record than Memphis. That means that even if the Nuggets win tonight and Memphis loses, Memphis would have the highest pick. If Dallas beat the Spurs, and also end up at 43-39, they would leapfrog Portland, by virtue of their head-to-head record, and then have the pick go down to #17. So basically the Portland pick can at best be #17, with everything falling right (a nuggets win, a Dallas win, a Memphis win).
If Portland wins, their record is 44-38 and they could be tied with Indiana, should they lose to the Bucks (more on that later). Portland won both games, so that would make them have the highest pick number, at #20.
I hope I am not forgetting anything, but the take-home message is that the Portland pick can end up between 17 and 20.
3) Chances in the NBA lottery (aka ping pong ball)
The number of combinations of ping-pong balls that are allocated to each team is based on the standings. In the event of a tie, the tie breaker rules don't apply as they do for the playoffs standings. Instead, the combinations are split evenly between teams with the same record, with I think a coin toss for the potential odd combination left.
Denver, Milwaukee and Sacramento are all at 33-48 right now, and could end up with the same record at 33-49 (or 34-48). In that case the probability of the #1 pick would be 1.9%, down from 2.8 if the Nuggets got the 8th 'seed' (if Milwaukee and Sacramento both win). It might not seem like much since we have the right to swap with New-York (set at #7), but the odds of #1 change from 7.1% if Denver is #8 to 6.2% if Denver is tied with Milwaukee and Sacramento, and 5.4% if only Denver wins tonight.
I thinks that's about it! Enjoy tonight's games!
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CORRECTION:
It turns out that the draft seeding of teams outside of the lottery (and just these) is determined by a random drawing. So teams finishing with the same record have equal chances of getting the highest draft picks of those two or three. Unlike playoffs seeding, there are no tiebreakers.