Azul Weekly Puzzle #003

[Effgee]

Welcome back
Hope you enjoyed last week's puzzle, I'm glad that despite appearing very simple (only 5 possible tiles to choose from) the discussion really took off!

Before we head into the new puzzle, we need to settle a notation question, Blue and Black start with the same letter, but using B for either can be an issue for distinguishing player A (you, top) and Bottom (B). Shall we stick with Bl and Bk? Or L (bLue) and K (blacK)?

And now for the new puzzle

puzzle003_censored copy.png (437.72 KiB) Viewed 1292 times

Final round, game end has been triggered and you're losing by 6? What's your next move?

Have fun! And as always, if you have encounter an interesting game configuration, please don't hesitate to screenshot and share with me or post directly

[euklid314]

We might be trailing by 6 points on the scoreboard, but since we have completed 5th row and our opponent has completed 1st row (and one discard) the score is exactly even at the moment. At first glance it looks grim since we will be forced to put lots of stones on our discard pile for negative points.

But since we will not allow player B to get 3 reds or 6 whites, he can score only once with white, either in row 2 for 9 points or in row 4 for 6 points.
Our scoring opportunities are in row 1 for 9 points, row 2 for 9 points and row 4 for 4 points.

If we finish row 1 + row 2 (9+9=+18 points) and (worst-case) fill up our whole bottom row (-1-1-2-2-2-3-3=-14 points) we gain net +4 points and will thus win in 3 cases:
I) if player B does not score positive points at all
II) if player B scores +9 points with whites (his 2nd row) and has to discard 4 more tiles (for -7 points)
III) if player B scores +6 points with whites (his 4th row) and has to discard 2 more tiles (for -3 points)

We can guarantee to finish row 1 AND row 2 (i.e., 18 points) but only if we start with red, optimally with the move 0-R-2. If player B responds with 1-R-3, we can take 4-R-2 and finish row 2. At this moment there is one white left on tabloid 2 and 5 white are left in the middle.

Now Player B is now forced to score with either 0-W-2 or 0-W-4 in order to avoid our win condition I). 0-W-4 is the slightly better of the two moves. Of course player A will always respond with 2-W-1 and finish row 1.

So up to now we have the (more-or-less forced) move sequence 0-R-2, 1-R-3 // 4-R-2, 0-W-4 // 2-W-1 ... where player A scored 18 points and player B scored 6 points. Player A has discarded the start tile for -1 points and player B has discarded 1 white for -1 points. Player A is ahead 12 points and can only lose if he is forced to discard 6 more tiles for -13 points and player B discards not a single tile. But there are only 2 yellow, 2 black and 3 blue left and player A only has to take one of these three sets.

Note that if player A starts with 1-R-2 or 4-R-2, player B does not threaten red directly but takes a white instead with 4-W-2 or 1-W-2, respectively. Then player A is still forced to focus on red and play 0-R-2, discarding 2 tiles (start tile + red tile). I think player A will still win - but I was too lazy to calculate that variant to the end.

Summary: My answer is move 0-R-2.