Azul Weekly Puzzle #006

[Effgee]

Hi all!
Apologies for skipping last week, will try to do a better job sticking with the weekly cadence!
In this game we're in round 5, we're in good position but losing by no less than 16! Can we win this game in this round?
Keep in mind that we are in complete control of whether we want to wrap things up in this round or go to a 6th round...

puzzle006_censored copy.png (477.75 KiB) Viewed 1275 times

Curious to get your thoughts/comments!
Fabian

[euklid314]

If we take 2 black and put them in 5th row we are guaranteed to still get at least 1 yellow and 1 red for rows 3 and 1.

Thus we end the game in round 5 and we finish 1 full row and 1 full column. We get tons of points (9+4+5+2+7) while our opponent is limited to max. 4+6 points in this round (row 1 and row 4). Since we also threaten to take 2 red for row 2 our opponent is forced to put some of them in his discard row. Hopefully his bottom row will be as full as ours - then we win...

Final remark: Taking 1 of the two yellows is highly important to hinder our opponent getting the +10 bonus for yellow. I will start with 2 blacks, however, in order to kill our opponents 2nd and 3rd row.

[Edit: My suggestion seems to be losing, though. If we take 2 black from pile 3, our opponent will answer by taking 1 blue from pile 4, thus clustering 2 yellow and 4 reds in the middle. If we then take the 2 yellow he takes 1 black from pile 1 and all the 5 reds are connected. Are we really forced to rely on round 6?]

[admitted]

I lean toward not ending this round because having starter token is massive considering both need 2 whites and 3 blacks.
In addition, 3 blacks complete the color along with a row which is massive.

So my move is 2 reds on row 2 with starter token

Opponent pretty much has to take 2 blacks on row 2 because we threaten taking 2 blacks altogether to deny row 2. We just have to make sure to grab 1 yellow, I think likely 2 yellows and floor. We also have a threat of 4 blues but realistically we will end with 3 reds or 3 blues which arent bad either case if we place them on row 4

[euklid314]

I agree with admitted that taking 2 reds and start tile for row 2 is the correct way to go.

After opp takes 2 black (he might take 1 yellow as an intermediate move where I immediately would take the other yellow - but then again opp will surely return to taking 2 blacks), I would take 1 black and complete row 5.

Next, whatever happens, I will take 1 or 2 yellows. When it is again our turn there will be almost a guarantee there is still a red left (most probably a group of 3). Since we have already completed row 2, 3, 5 we can estimate precisely if we NOW want to end the game in round 5 (by putting red in row1. We would get 9+6+7+7+2+7 = 38 points. Our opponent will have probably completed row 1 (in white), 2 (black) and 4(white) for 4+8+6=18 points. At this late stage of round 5 we can exactly determine the end state of the discard rows and if 38 vs 18 is enough for a win.

This, we can decide before our 4th move of round 5 if we need a 6th round (and we already have the starting tile in hand). A perfect position of strenght...

[Effgee]

Thanks Euklid314 and Admitted for your thoughts!
Glad this puzzle was a bit tricky, and no real consensus on whether we could force a win or would need to go to a 6th round...

So taking the 2 blacks from 3 and placing them on fifth row is indeed what I went for. Get that row done and still keep options open for red and yellow.
But then what?

Euklid314 wrote:
[Edit: My suggestion seems to be losing, though. If we take 2 black from pile 3, our opponent will answer by taking 1 blue from pile 4, thus clustering 2 yellow and 4 reds in the middle. If we then take the 2 yellow he takes 1 black from pile 1 and all the 5 reds are connected. Are we really forced to rely on round 6?]
--> if opponent takes 1 blue from 4, we're still good actually! we respond not with yellow but with red 1R1, not much he can do after, and we can place clustered reds on rows 2 or 4.

In the actual game, my opponent had the good idea to go for blue indeed, but took it from center instead of 4. I stuck with the strategy from above with 1 red from 1, and then a couple moves later they conceded! I don't think I've ever had an opponent concede in round 5 when leading by 16!

Very fortunate that I didn't need to go to round 6 which could potentially have gone either way!

[euklid314]

Thanks Euklid314 and Admitted for your thoughts!
Glad this puzzle was a bit tricky, and no real consensus on whether we could force a win or would need to go to a 6th round...

So taking the 2 blacks from 3 and placing them on fifth row is indeed what I went for. [...]

--> if opponent takes 1 blue from 4, we're still good actually! we respond not with yellow but with red 1R1, not much he can do after

Well he can take 2 yellow for 11 points in row 5 (1+10 bonus). In my counting that is enough to secure his victory.

[Effgee]

Thanks Euklid314!
The situation after the moves described should look like this:

Screenshot 2023-09-21 at 4.57.28 PM.png (480.19 KiB) Viewed 1079 times

Taking 1 red feels risky if we can then get the yellows and 10 point bonus, but we can a row and a column! And they will be left with taking final tiles and force lots of blue down their throat!

After that, we are left in the middle with 3 reds, 3 blues, 1 black, and 1 white.
I feel we should take white on row 2, they will take 1 black to avoid red and blue, we will take 3 red on row 2 for more points and leave them with the three blues to their floor. That'll be -1 for our floor, to their -8 (they also picked the 1st player token).

I think the math will work in our favor, we narrowly win what looked pretty desperate at the end of the 4th round!

[euklid314]

Effgee, I did not think my analysis through till the very end (having to discard 3 blues) but coincidentally I was still right. With your analysis you will lose the game by 2 points.

Correcting your typo "we will take 3 red on row 2 for more points" into "we will take 4 reds on row 4 for more points" (since there are 4 reds, and row 2 is already blocked by color white) - both you and your opponent will finish column 1,4,5.

You get 9 + 3 + 7 points plus 2+7 bonus with -1 penalty. This is 27 points.

Your opponent will get 4 + 6 + 1 points plus 10 bonus with -8 penalty. This is 13 points.

Since you only gain a net difference of 14 points, you lose the game. Although my gut feeling also was to start with the 2 blacks for row 5 (with the goal of ending the game in 5 rounds) it looks like this is a losing move.

[Effgee]

Apologies, replying a bit late, but loving the conversation!
After all the steps we discussed, the situation is as follows (sorry for the ugly powerpoint edits, anyone aware of a tool to nicely place tiles in hypothetical settings?)

Screenshot 2023-09-29 at 10.36.33 AM.png (477.96 KiB) Viewed 956 times

If my math is correct:
our score is 20 + 9 + 3 + 7 + 2 + 7 + 7 - 1 = 54
their score is: 36 + 4 + 6 + 1 + 10 - 8 = 49

I think in your math you forgot to add our bonus for second column! Hence we don't lose by 2, but win by a comfortable 5. Starting the round with a 16 point deficit, that's pretty nice!

Puzzle 7 will be out shortly....

[euklid314]

I think in your math you forgot to add our bonus for second column! Hence we don't lose by 2, but win by a comfortable 5. Starting the round with a 16 point deficit, that's pretty nice!

Thanks for your reply, Effgee.

Yes, I did not consider the first completed column since it was already finished at the beginning of the problem. In other words, we did not need to find 16 points in the problem, but only 9. I realize that only now!

In hindsight, this would have felt much easier for me - I only considered moves that might reduce the deficit by 16 points! Thus, I solved a different problem... You tricked me with the wording "We are losing by no less than 16".