Sunday 14 October 2018

Minutiae: More Izzy20 variants

        

---

For various reasons, I've been using the Izzy20 a lot more recently.

      

When I first discussed the Izzy20, I gave 6 different variants:

    No-Z 1 and 2.

      No-S 1, 2, and 3.

  No-L.


However, there are a couple more I've also used a bit of lately, via minor transforms of this:

  No-L --->      No-J

This one can be really handy with an early O, when the regular No-L does not apply. We can't play the Z until we've cleared the third line, so we'll have to have played the O, L, and S, but it turns out this constraint fits almost perfectly into the hole in our existing option coverage.

  No-S3 --->    No-Z3

Kind of an edge-coverage of an edge-coverage, but this ends up covering a lot of cases of early T,I that No-S3 and the other variants don't hit. The No-S3 requires Z < J, thus working well with a later J, and the No-Z3 requires J < S, thus working well with a earlier J. They end up being quite complimentary.

Traditionally, I analyze the full ordering constraints of each variant. Here goes!

No-J: O|L|S < Z, either T < S|I or T last.

No-Z3: T < I < J|O, S last (requires S or Z as the last piece of the third deck before piece swapping comes into play.)

Constrained as these look, with these plus the other 6 variations given above, we have fills for most deck orders.


One more minor variation for the road. When I first posted about the Izzy20, I gave this alternate setup with fewer second-deck constraints:



This leads to a No-J as follows, congruent to the above No-L:
  <--->  
  <--->  
  <--->  

It turns out we can just invert our second-deck L, and we can build a congruent No-L to this No-J:

  <--->  
  <--->  
  <--->  
Constraints: either T < I|S or S|I|O|Z < T, either J < I|Z or S|I|O|Z < J, either O < I or S|I|Z < O, I must be after at least one of Z, O, or S.
Rule of thumb: once we've played J and T, it pretty much always works. But it also works with T or J or both at the end!

Placing the L towards the latter half of the second deck, we can just look at our third deck to decide which one to do, based on whether the J or L comes earlier. We end up getting the all-clear a lot more than if we were just going for a No-L on the regular Izzy20 due to being able to pick the easier one. Constraint wise, we require second-deck-T < third-deck-J  in the No-L which means we can only get a T-spin single, but we're otherwise slightly less constrained: we can play Z < J, or Z < L in the No-J, so long as the J or L comes after Z, S, and O as well.

Monday 24 September 2018

The Izzy15: a broad survey

When I first discussed the Izzy15, I listed some of the more popular variants, but left the general question open for the reader to explore. It's fairly deep--there are all sorts of ways to all-clear at 15, and new ways constantly come up in improvisation. Here's a bunch from my files.


1. A quick review

        

            

    

These all-clears can be done with either an O or an L in the first two pieces of our third deck, given the T we have in hand at this point. With an O, we get a T-spin double. With the L, just a single.


2. The upright J

        

It turns out we can also all-clear with an upright J, getting to the same hole. This is nice, both because it works well with an early second-deck I, and because defaulting to the upright J and getting other pieces, we can also set up an Izzy dub-dub into an Izzy20:

            


3. More flexible upright J

    

I got this from iljain, Taiwan's top player who constantly plays interesting and surprising all-clears not common in the current metagame. Given a late T or S/Z, we end up with a flexible hole with an S or Z and a T to play. The one on the left is especially nice, as it's only a couple pieces different than the above O/L fill: we can often just switch to it if we end up not having the third-deck O or L. Here are a bunch of all-clears we can do:

T&S: J, L, O, and Z

              

Note that the O and Z fills require playing T last, and thus need O or Z as the first piece of the third deck. L and J work either as the first or second third-deck piece, since you can play the T and hold the first piece.

T&Z: I, J, and S

        

Yeah, the SZT fill is the same as above, and requires S as the first piece of the third deck.

Note that we don't get our second T-spin here. Not so good for bopping a central Long Combo, but just fine for killing a side Long Combo or a Left-O + Long Combo build.


4. Back to the faceup J

We can try applying what we used in the upright J to the faceup J. If we just rip off the ZSOL left side of the screen used in the O/L fill, we get here with a T and I to come:



It turns out this hole can be used for both an L-fill and an I-fill, giving us a nice alternative to the L/O with just as many outs:

    

Moving back one piece, an O-fill is still possible in addition to the I/L--arguably giving us even more outs:

    


5. More possibilities on the faceup J

It turns out that we can all-clear in the faceup J with more pieces than just I, O, or L at the beginning of our third deck. We can figure out some of these by moving our second-deck O or L to clearing our central hole, rather than a third-deck O or L, and seeing what pieces could fill the remaining hole. An advantage of this method is that the fills are easily adapted from our usual play: we can often play the first few pieces of our second deck as if we were going for the high-probability O/L fill, then switch to one of these if we need a different third-deck piece.

J-fill: move the L to the central hole.

  ->  

  ->    

I-fill: move the J to the central hole.

  ->  

Z-fill: move the O to the central hole.

  ->  

Note that this requires Z as the first piece of the third deck, as we have to hold a J.

T-fill: Same as the Z-fill, just play the J first.

  ->  

This one, however, works with the T either first or second: we can play the J whenever. Similarly, we can play the Z whenever by modifying the rightside JOL:

  ->  

This also works with a T, if we just play the L after the T-spin:

  ->  

To get S-fills: flip the J and L or J and J from the Z-fills:

  ->  

  ->  

  ->  

The first requires playing the S before the L, so S must be the first piece of the third deck. The second and third don't have this issue, and work with S as both the first and second piece.


6. Back to the upright J

We can apply the above technique and some of the fills to the upright J, getting fills for more tetrominos even with a second T-spin. Of course, our second-deck piece order has to cooperate:


Z-fill: rotate the J and L.

  ->    

Much like our first S-fill, this requires holding the L and thus for the Z to be the first piece of the third deck. Also gives up the T-spin, except in the rather unlikely flipped version.

T-fill: rotate the J and J.

  ->  

Yeah, pretty much the exact same T-fill works with both upright and faceup J.

I-fill: Move the O to the central hole.

  ->  

J-fill: Rotate the J, L, and I:

    ->    

The I-fill is especially useful to all-clear a second time after a no-I all-clear, such as the WumbOJ20 no-I, and the J-fill or its mirrored L-fill after a no-J or no-L all-clear, such as the Izzy20 no-L. The useless-looking Z-fill is actually marginally useful to all-clear again after a no-Z all-clear.


7. I-fills

I-fills have a special place in my heart, given my use of them after the WumbOJ20 no-I all-clear. While I've listed a bunch useful for that situation in the linked post, here are some that work well in a vanilla opening Izzy15:

      

  

            

The first row I've already covered. The second row has the standard all-clear used in the facedown-J variant, and a more freeform fill, still getting our second T-spin. The third row is all sorts of freeform and fanciful all-clears that give up a T-spin.

I-fills work with a huge range of second-deck piece orders, given imaginative placement. For example, here's a crazy one I executed with an S-spin, a T-tuck, and a divebomb Z-spin:

        


8. Transposition for the all-clear

We can alter the above tilings by using various transpositions. For example, OZS -> SZO as seen in a couple J-fills above.



  ->  

If we're willing to give up a T-spin, ZTO -> OZT|ZOT can help with ordering constraints in a bunch of the above:



  ->  

We can of course play everything in mirror image given a mirror-image Izzy; I've left out mirror images for brevity:

  ->  

We can also swap the left and right 8/9s in a lot of the faceup-J fills, which can help with I-placement ordering constraints:

  ->  


9. File Miscellany

There's lots of all-clears which don't exactly fit into the above categories, which come up from improvisation or off-track alterations of the above. Here's a few from my files.

  L-fill.

  O-fill.

  T-fill. The I can be played before T and Z. Yeah, you can also get a Z, S, or I fill by spinning the Js around.

  T-fill. Left-right swapped version of the above. Can be used or O-fill and S fill by moving the L slightly.

  S-fill. Another way to left-right swap this, getting the S on either of the two third deck start pieces. Can also be used for an O-fill by rotating the J.

  J-fill.

  L-fill. Can T-spin single.


10. Two-piece fills

There are plenty more all-clears one can do by holding a piece and playing the first and second piece of the third deck. I generally don't write these down, because you rarely see the same ones twice and you might as well just improvise them. Here are a few that you might run into on your way to other variants.

  No-L JI: occurs on the the facedown-J variant.

  No-Z LO: occurs on iljain's flexible upright J.

  No-S IO or IL: occurs after missing on a J-fill.

Unless you have a favored variant for your T-spin followups for which one of these might apply, I wouldn't worry too much about them.


11. An Example



We do a quick Izzy with blah to come. We end up with the J in hand, so we can choose faceup or upright J. Nice!

  To play: J. In hand: J. To come: SILZO

We play our J and S. Given the upcoming SL, we start towards the left-side SLZI formation by placing the S upright on the left.

  To play: I. In hand: J. To come: LZOT,T

Now we can see the first piece of the third deck, since we see five pieces ahead, have a piece in hand, and a piece currently dropping. It's a T! We could do this all clear:



However, playing as fast as we possibly can, we miss this and obliviously play our second J.

  To play: L. In hand: I. To come: ZOT,TI

All is not lost: the second piece of the third deck is an I. We can now do this I-fill:



However, we continue blindly rushing ahead and miss it, playing the inverted L then just doing the O/L hole.



Given that we're playing TvP, this is just fine: the I-fill didn't get a second T-spin, a T-spin with material left on the board isn't really worse than an all-clear, and we just go into a T-spin + Tetris pattern and win the round:



   



We see from the example that we can, if we wish, quickly figure out an all-clear possibility right after we've dropped the first piece of our second deck: the eighth piece we play. We again can figure one out after dropping the second piece of the second deck: the ninth piece. However, it's totally reasonable to blindly play as fast as possible and miss stuff; if there happened to be an O or L towards the beginning of our third deck, as happens the majority of the time, we still would've gotten the all-clear with a second T-spin to boot. Speed is the name of the game, even if you don't always play optimally.


Thoughts

Blindly racing for the L/O or L/I fill, without looking at our third deck until we do our second T-spin, is already pretty good--we'll get an appropriate tetromino in the first two pieces of our third deck the majority of the time.

Iljain's flexible hole can be really nice, despite giving up our second T-spin. The 14+ damage hard-counters vulnerable openings like the side Long Combo, and soft counters T-spin openings that don't hit their second attack till near the end of the second deck, like the WumbOJ and RJ's Joy. But of course by giving up our second T-spin, we end up behind if we get hit by damage before we can all-clear.

It's really nifty that we have fills, second T-spin included, for all 7 tetrominos we might see at the beginning of our third deck. But the value of knowing these turns out to be surprisingly marginal. We've often foreclosed the possibility of using the right one by the time we can peek at our third deck, and of course L/O and L/I fills already work the majority of the time. We see the highest value here with second deck starts like S,L (for left SLZI, right JJ) or Z,S (for left ZSOL or ZSJI), which allow us to play enough pieces to peek and still adapt.

Given just blindly going for the variants above, we can all-clear with fairly high probability. Careful looking ahead at the next 5 pieces can allow us to pick the proper path with even higher probability. I suspect that calculating out the decision tree to maximize all-clears with a computer will give us something in the realm of 75% all-clear given a first-deck Izzy, two-thirds of them including two T-spins, but that's just my off-the-cuff.

If Long Combos and especially side Long Combos get even more popular, it may be worthwhile to do this simulation to bust out as counterplay. While a human couldn't do the full decision tree at maximum speed, we could boil it down to just a human-executable set of rules and still maybe all-clear 67%+ of the time.


Conclusion

All-clears at 15 can be a strong opening and a powerful counter. We can hit them even more often by being willing to give up a T-spin, and the 14+ damage we get still puts us ahead. But the possibilities are very wide, and generalized research into the matter could allow us to use them even more powerfully.