To forestall any questions: no, this will never come up in a real game of Dominion. It's fun to think about though.
Mandarin is a bad card. Scepter is an okay card, but is limited due to its only letting you replay Actions during your Buy phase. By their powers combined, you can do some funny pileouts.
The core pieces you need in the kingdom are:
- Mandarin
- Scepter
- An Action that will gain a $5 cost Action on-play, while staying in play. Without cost reduction, this basically means Artisan or Altar, although Altar requires having things to trash.
- An Action that draws cards.
The idea is that you play your turn as normally, getting a +Cards and the gainer into play. After drawing N Scepters, you play N-2 of them as Actions, play the N-1th one as the gainer to gain Mandarin (topdecking all your Scepters), then play the Nth one as +Cards to redraw your Scepters. This brings you to the same start state, with 1 fewer Mandarin and 1 Scepter in play. You can repeat this loop until the Mandarin pile runs out, and hopefully your action plays are giving you net +$ or net +buy. At minimum you are piling down the Mandarin pile.
An example with Inventor and Smithy, assuming you start your buy phase with 3 Scepters in hand.
1. Play Inventor and Smithy (now $5 costs are gainable from Inventor)
2. Play Scepter as anything
3. Play Scepter as Inventor, gain Mandarin, topdeck 2 Scepter
4. Play Scepter as Smithy, draw 2 Scepter + Y
5. Play Scepter as Inventor, gain Mandarin, topdeck 2 Scepter
6. Play Scepter as Smithy, draw 2 Scepter + Z
7. Repeat steps 5-6 forever.
In this example, you draw 1 card deeper and get one more cost reduction from Inventor each turn, but you aren't netting Scepter plays. However, once you draw into a 4th Scepter, you get to loop as
(start: 1 Scepter in hand, 3 on top of deck)
1. Scepter as Smithy
2. Scepter as X
3. Scepter gaining Mandarin, topdeck 3 Scepter, back to loop start.
That lets you get in other action plays, until you run out of Mandarins to gain. If you spend X on an action that gains Scepter, you can do increasingly more each loop, assuming you draw into the extra Scepters. Here is an Artisan example, where it's easy thanks to topdecking.
(start: Artisan and Smithy in play, 1 Scepter in play, N Scepters in hand)
1. Scepter as Artisan, gaining and topdecking Scepter.
2. Repeat step 1 until you have 1 Scepter in hand.
3. Scepter as Smithy, draw your topdecked Scepters
4. Go back to 1) and repeat until N = 2
5. When N=2,
5.1 Scepter as Artisan, gain Mandarin, topdeck all Scepters
5.2 Scepter as Smithy, draw Scepeters.
5.3 Repeat Smithy until you redraw all topdecked Scepters, then go to step 1 with a larger N than last time.