What is the fastest possible game in Splendor?
EDIT: fixed violation of limit on taking 2 of same gems (Forbidden when &lt;4 gems remaining).

First of all, @Arcanist Lupus has provided good answer with simple yet efficient approach and also provided link to cards table in the comments, so I want to thank them. But looking at the table I noticed that 4 pts. cards have better conversion rates than 5 pts. ones, and a lot of gems are lost when going straight for 5 pts. cards.

So, assuming all required cards are available, no nobles and no interference from other players, here is my solution:

Cards I'm going for: White 4 for 7 blacks; Blue 4 for 7 whites; Green 4 for 7 blues; Green 3 for 6 greens.

Steps:




+2 black
+2 black
+1 black, 1 green, 1 {any}
+1 black, 2 {any}
+1 black, 1 white, 1 green. Return 3 {any}
Claim White 4 card for 7 blacks. (1 white and 2 green remain in the stash)
+2 white
+2 white
+1 white, 1 blue, 1 green
Claim Blue 4 card for 6 whites + card. (1 blue and 3 green remain in the stash)
+2 blue
+2 blue
+1 blue, 1 green, 1 {any}. Return 1 {any}
Claim Green 4 card for 6 blues + card. (4 green remain in the stash)
+1 green, 2 {any}
Claim Green 3 card for 5 greens + card


Done. 15 points in 16 turns.


steps 3 and 4 are just about getting 2 blacks, since it's forbidden to get 2 at once at that point. Alternatively you can take golden tokens and secure couple of cards for yourself, in that case in step 15 just take 2 greens (you will have 1 less, so it would be legal move).