#threes303

The prettiest snake

The key is to notice that in the still frame from yesterday, you have exactly a Traven (96)'s worth of material with the combination of your bottom two rows plus the 12 and 24 in the third column. From there it's a tricky matter of shimmying the right way to get everything all lined up before gridlock sets in.

A little Independence Weekend group discussion

What would you aim to do from here over the next 10-15 moves?

Tough decision: why I went down

With a Terrence (1536) on the board, giant spawns can be up to Threejay (192). Each of the six plus blocks arrive at a ~17% rate. With that in mind, here's our rank-ordering of choices:

1. Down. The player is best off building along the top row in this screenshot, since most of her material is consolidated in that direction. Since Down keeps the first and second columns anchored, it would slot any large plus blocks right in where they want to be and strengthen the anchoring of the top row. Anchoring along an edge is a more stable position than clustering large blocks in a corner.

In addition, at this stage of the game, you need to have constant fear that a giant will spawn. It is not if, but when. Down best allows the player to flexibly accept larger material--more on that later.

2. Right. It's ideal to keep all your largest blocks along one edge. But if you can't - or don't notice that you could - then clustering your big blocks in one corner is the second best thing.

3. Up. Up is very interesting from the previous position (go back and take a look). Only the fourth column is free, so envision going UUU. By then going L, the player has a 67% chance at creating a hole in the top row where the 3s will combine, in which case she can go U again to migrate the potential giant all the way up to the top row. And even if it doesn't work out, the giant is still in the second row, which is generally fine.

What's the right move? Probably not up, but what about the other three directions?

The shift-combine

As discussed in the previous post, the natural tendency is to try to build material up into the top row via the far corner. But don’t be deceived! As tempting as it feels, it’s rarely correct. We present here a fairly advanced technique, in the spirit of alternating between basic strategic building blocks and more advanced ones. (Don’t worry, sometimes we’ll just do pretty pictures too.)

The best way to aggregate material in your top row is via the shift-combine. This is a move wherein you combine multiple blocks up from the second row into the top row with one move. In order to do it, you need to first line up blocks in your second row that match the ones above them in the top row. This is usually accomplished by moving Right and then Up - hence, the shift (Right) and combine (Up).

In this gif, you can see the shift-combine happen at the end. The player is building up her second row like a mirror of the top row, but with the biggest block being equivalent to the second-biggest top row block.* When she has everything in place, she completes the mirroring by moving Right, combining her Treycees (12s) into a Tristine (24) and then combining the resulting second row Up with the top row.

Though the shift-combine is a difficult move to master, the payoff is huge. The alternative (combining material leftwards across your top row) leaves a gaping hole at the right side, which will be quickly occupied by incoming filler blocks (1/2/3). Having such small blocks in your top row can be a big problem, since it can become hard to move large material out of the middle of the board.

Over the next day or two, we’ll post some pretty stills of successful shift-combines to illustrate the point, in (many) fewer words.