Minutiae: More Izzy20 variants

        

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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.