Tuesday 27 February 2018

Tetris versus Puyo on the attack

  

So far, this blog has focused on the general theory of Tetris versus Tetris (TvT), with a small nod here and there to how things may apply to games against Puyo. Playing Tetris versus Puyo (TvP) is a different beast altogether, with different damage, different systems, and different optimal play. Let's start with the mechanics and use it to figure out strategy and tactics.

How Tetris damages Puyo

In Tetris versus Puyo, next to the Tetris board, there is a green bar which fills up. Every clear done within a combo (a series of line clears without a non-clear move) adds to this bar if not used for defense. When one does a non-clear move, ending the combo, the bar is transformed to damage and, if not used for defense, sent to the opponent's board. Various different clears fill the bar a different amount:
  • 1 unit: 2 line clear
  • 2 units: 3 line clear
  • 4 units: 4 line clear (Tetris)
  • 5 units: 4 line clear (Tetris) with back-to-back bonus
  • 1 unit: mini-T-spin single with back-to-back bonus
  • 2 units: T-spin single
  • 3 units: T-spin single with back-to-back bonus
  • 3 units: T-spin double
  • 4 units: T-spin double  with back-to-back bonus
  • 4 units: T-spin triple
  • 5 units: T-spin triple with back-to-back bonus
  • 6 units: all-clear (all-clear is always 6 regardless of whether it's a 1 line clear or a 4 line clear)
  • 1 unit bonus: 2 combo up to 6 combo.
  • 2 unit bonus: 7 combo up to 10 combo.
  • 3 unit bonus: 11 combo up to 14 combo.
  • 4 unit bonus: 15 combo up to...

Note that these figures are for damage units towards the beginning of the round; in very late round, damage units increase. Also note that I tested this and the list below on Switch v1.1; damage may change in future patches.

Observe that T-spins act as just a two-unit bonus on top of a regular clear with that many lines; unlike in TvT, in TvP a T-spin triple is NOT three times as damaging as a T-spin single. Mostly, it's whether we T-spin at all.

How much Tetris damages Puyo

Once our combo ends and our bar is transformed into damage, we send a specific number of damage blocks to the opponent's screen. It turns out this damage is NOT directly proportional to our damage bar units. The first unit gets us 4 damage, the next few don't get us much, and once we've got a lot of units, suddenly our units are paying off big. Here's the list from my testing:
  1. 4 damage
  2. 5 damage
  3. 6 damage (1 line)
  4. 8 damage
  5. 10 damage
  6. 13 damage (2 lines + 1 square)
  7. 16 damage
  8.  20 damage (3 lines + 2 squares)
  9. 24 damage (4 lines)
  10.  28 damage
  11.  33 damage (5 lines + 3 squares)
  12.  38 damage (6 lines + 2 squares)
  13.  43 damage (7 lines + 1 square)
  14.  49 damage (8 lines + 1 square)
  15.  55 damage (9 lines + 1 square)
  16.  61 damage (10 lines + 1 square)
  17.  68 damage (11 lines + 2 squares)
  18.  74+ damage (12 lines + 2+ squares) -- probably 75
  19.  80+ damage (13 lines + 2+ squares) -- probably 83
  20.  92 damage (15 lines + 2 squares)
  21. 102 damage (17 lines)



  22.  132+ damage (22 lines)

  23.  183 damage (30 lines + 3 squares)
  24.  200+ damage (33 lines + ?)
    ...
    34.  318+ damage (53+ lines)
    ...
    37.  398 damage (66 lines + 2 squares)
When I curve fit the first 20 points, I get something like 0.2*n^2 + 0.5*n + 3. Doesn't work for higher numbers, though.

Note that each 6 damage is represented by a big square, and each 30 damage by a red square. Why these particular thresholds? Well, one line of damage for Puyo is 6 squares since the board is 6 wide. The most damage that can drop in a single drop-cycle is 30 squares, or 5 lines, which gives people a very very brief extra bit of time to trigger their counterattacks rather than be instakilled. Beyond that, we get star for 6 reds, and moon for 12. We only see at most 6 damage symbols, so some of the higher damages we only get a lower bound on. They're not particularly relevant--at that amount, either he counterattacks with a huge enough combo to kill us, or he dies.


The damage is represented above his screen, and drops on the Puyo board once he drops his next piece, delaying him with an animation as well as messing up his board. If we send another attack before he drops his next piece, it adds directly to the size of our attack, e.g. 4 + 4 = 8 damage. If he breaks stuff with his drop, his damage is first spent defending against our drop.


A Strategy of Attack

Repeated Small Attacks

If we look at the above charts, we see that it can be much better to attack with two separate small attacks--uncomboed--rather than comboing them together. If you break 2 lines one turn, and break 2 lines the next turn, you'll get 2 units on your bar and drop 5 damage on them next turn, delaying them with one animation. If you break two lines ones turn, break nothing the next turn, then break 2 more lines, you'll instead hit them with 4 damage, causing an animation delay, then hit them with another 4 damage, causing yet another animation delay. We also see that "mini" T-spin singles are pretty good in TvP as long as you have a back-to-back bonus. One of them will do 4 blocks of damage. An unbonused T-spin double only does 6 blocks of damage, which is barely better.

By quickly and repeatedly hitting him with small attacks, we delay his building and mess up his board with each one. Also, when he's high up, we can kill him outright, blocking him from moving pieces around his columns, choking him to death, and adding the just-one-more-piece on his third column needed to finish him entirely.

Big Combo Attacks

On the other hand, we see big damage can result by combining large attacks--multiple T-spins, T-spin plus Tetris, multiple Tetrises, or T-spin plus all-clear done within a combo, for example. So another strategy that's implied here is to hit big, combine our attacks, and even use long combos. When our board is high with damage blocks, a big combo is often both the fastest way to clear our way to safety, and able to be long enough to get the big damage. Of course, we don't actually hit them until we end our combo, which can be a problem with comboing too long.

With our big attacks, we fill their board with garbage and can totally block off what they've already built. Rather than disrupting them, we make it hard to build at all. If we hit big enough, we can entirely fill their board up and finish them off even with very little built on their screen.

Putting it together

While blitzing with fast small attacks can win on its own, and a big attack can win on its own, each do different things and have different strengths. A combined approach suggests itself:
  • Use our repeated small attacks to slow our opponent down and limit his attacks, giving us room to build our big attacks.
  • Use our big attacks to fill up his board and kill him.
  • Once he's high up, again use our repeated small attacks to finish him off and prevent him from clearing down, or make time for another big attack to finish him.
This isn't to say you can't sometimes open with a two T-spin combo or a T-spin + Tetris combo--these are worthwhile plays. But your opponent should never be confident that he'll get time to build his chains without being disrupted with a fast attack. Mix it up.


A sample game

I picked this game because it was won not by perfect execution of powerful and uncertain tactics (like doing a fast T-spin + all-clear combo) but instead upon gaining advantages via our strategy of attack despite mistakes. It was played against a 15K+ rated player from Japan, ranked about 300 in the world at the time.

In the first round, I opened with a high-damage 2 T-spin 5-combo opening, running straight into my opponent's 6 chain for no damage and losing to his followup chain. In the subsequent rounds, I opened much faster and smaller.

Round 2 starts with me screwing up my opening and just doing a 2 line clear as my first attack:

    

Against Tetris, this would be worthless. But we see above that in TvP, a 2-line clear by itself does almost as much as a T-spin double. We drop 4 blocks instead of 6, and waste an equal amount of their time with the block dropping animation. And it's faster than a T-spin, since we can hard-drop it.

    

    

The next two attacks follow rapidly on its heels: two T-spin singles. In TvT, these would be far worse than T-spin doubles, doing 2 and 3 lines of damage respectively versus 4 and 5. We see that in TvP, however, these are almost as good: the first does 5 damage and the second 6. Doubles here would only do 6 and 8 respectively, so in both cases we cause equal animation delay and about a line of damage per attack. But the singles leave us more material for our next move, the big attack:

    

This a two T-spin triple combo. Our opponent counter-chains, but our disruptive earlier attacks means it is hard to break too much of his screen. After his counter, we still do almost 4 lines of damage and put him near the top.

We then finish him off with a series of rapid small attacks. He dies before the last one:

    

Note that I intentionally dropped the S before the L on the next attack, to separate the prior T-spin from the 2-line L break. This does two attacks of 8 and 4 damage respectively, which is much better than 1 attack of just 10 which we would've gotten from the T-spin + 2 line combo if we hadn't interposed a non-break drop.

    




For round three I again screw up my opening and end up with just a T-spin single:

    

This runs into his 3-chain. We take a bit of damage, but at least his material is depleted.

We now do our big attack: a two Tetris combo:

    

As we might expect given our lesser disruption this round, our opponent's counterchain is bigger than last time. We end up with just a bit more than a line of damage sent.

We follow up with a series of smaller attacks preventing him from getting back on his feet:

    

    

Note that the next two attacks, a Tetris and a two-line clear, are separated by dropping the J. However, due to his slow drop and one-group clear on this move, these still end up adding up to one single attack (10 + 4 = 14 damage). This is all good; whether he slows down and takes one attack animation, or does a fast drop and takes two attack animations, he's still slowed down. And doing the Tetris plus the two-line clear together in a combo would've only done 13 damage, so we did more damage by separating the attacks.

      

We then finish him off with a T-spin + Tetris combo. Our opponent's small counterchain is insufficient to save him (Sequence: ITSI for 3-combo):

      

These rounds demonstrate the basic principles: we gain time for our big attack with our rapid repeated small attacks, put him closer to the top with our big attack, and use more small attacks to either finish him off or gain time for another big attack.

We do many things which would be very strange in TvT, such as intentionally taking T-spin singles instead of doubles just to get more material, and intentionally separating our small attacks so as to NOT combo them and cause more attack animations, more disruption, and for small attacks, more damage. We also see the intentional execution of either multiple T-spins, multiple Tetrises, or T-spin plus Tetris together in a small combo, which for TvP allows a combined large attack, but which (given a 1-combo) would do no more damage than doing them separately in TvT.


Conclusion

We now have a general theory of offensive play in TvP and how it differs from TvT. Of course, there's always more to it than that. We certainly do want to get the occasional free round from offensive tactics like piece 15 T-spin+all-clear, and we certainly want to hone our speed and tactical execution, and we certainly want to figure out defensive play, handling screen-clearing and attrition, and we certainly want to have deeper theoretical ideas about when to attack and when to defend. Perhaps we'll discuss these things in future posts.

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