Deducing casino figures through symmetry
How do I make caída more interesting? Here is an answer based on a scientific treatment of casino: from observation, to model, to hypothesis, to pratical knowledge.
As I have explored in previous articles, all casino figures transition between three positions. One of those, caída, is rather starved compared to the other two (and certainly abierta, from which most figures start); the choice is basically between doing an exhibela or a DQN. There are two ways to alleviate this: by substituting caída with a figure, and by substituting the last bar of DQN. There is a very nice relationship between both, and in fact, by assuming symmetry between them, you can logically deduce the existence of new figures.
- Follower moving clockwise: caída substitutes
- Follower moving counterclockwise: DQN variations
- Conclusion
It’s not obvious that you could deduce anything about dance; in fact, the “it’s all feeling” crowd will tell you it shouldn’t even be attempted, and they would have a point if casino was like interpretative, free-form dance. But it’s not. Fundamentally, the reason why you can think about casino systematically is that the entire structure of the dance comes down to how a leader can get a follower from his left to his right, and from right to left, with either him turning clockwise or counterclockwise, or the follower walking around him either clockwise or counterclockwise. As long as only one arm is held, the arm work does not constrain this process and is hence not important to understand here.
Follower moving clockwise: caída substitutes
What I mean by “substituting” caída is not avoiding figures that end in caída. So then, how will we circumvent caída, if followers can’t anticipate that we don’t want to end up in it? The solution is that there are figures which start from the assumption that the follower is walking into caída, whereas the leader alters his movement so the dance doesn’t halt (or more precisely, reverses direction) in caída.
Enchufate
We have already seen one form of caída substitute: the three types of enchufate that create sencillas (arriba, atras, abajo), of which most famously the right-handed enchufate arriba in the middle of setenta.
You can do these enchufates any time you are about to end in caída. You can also do them with either hand.
Note that an enchufate is not a full figure, but a subfigure. It takes one bar, and then goes into abierta immediately. This video shows an example of an enchufate arriba that transitions into a full vacilala.
The three enchufates have a handful of properties that hold even when they are generalised:
- Arriba and abajo rotate the leader the same way. Atras doesn’t.
- Arriba and abajo rotate against the momentum of the follower. (For example: since walking into caída happens clockwise, enchufate arriba is counterclockwise.)
- Arriba and abajo both rotate the leader 180⁰ to switch place with the follower. Atras, meanwhile, rotates 360⁰ and does not switch place with the follower.
- Abajo always employs a hand behind the back.
Rodeo
When she walks into caída while you’re holding her with left, step forward so she misses you behind your back. The next bar, she walks behind you from your right to your left, and finally she walks in front of you towards caída in the second bar. Effectively, she traces a clockwise circle around you which moves from caída to abierta to caída, in 1 bar each.
The link between enchufate and rodeo is that enchufate (arriba) is a 0-count version of rodeo’s first bar. The arm moves the same and the body similarly rotates counterclockwise relative to the follower – or, equivalently, rotates against the follower’s rodeo path, which is clockwise. This will be important later.
Because rodeo has more than 0 counts, you could put a subfigure inside it. Yet, there are no really natural turns to do on a rodeo’s second bar. Theoretically, you could do a vuelta, but it’s unnatural; if you do that vuelta in place, you prematurely break the rodeo and end in abierta. If she walks it, it’s a single-360⁰ vacilala. If she really pivots hard, she can do two vueltas (a 720⁰ turn) in only 4 counts, which is what happens in a balsero and likely needs a two-hand grip to stabilise her speed.
Another thing you can do on a rodeo is to keep her arm low and have her trace your body, as happens in the second phrase of a rodeo doble. Being hands-free allows you to do a vuelta doble on the second bar.
Cásate
In rueda, there is a figure called enchufla y cásate (from casar, meaning “get yourself married”) where you do a right-on-right enchufla, and – as the setup to substitute caída without the follower’s awareness – use the connection to hook her held arm behind your left arm. Arm-in-arm, you then walk around the circle. En pareja, there is no circle, so you walk around your connection (she walks forwards, you walk backwards). This is cásate.
There exists a subtly different form of cásate where you also walk backwards facing the same way as her, but keeping the right-on-right hold behind your back rather than using it to hook.
Finally, there is a third figure where you “spin out” like you do in the previous video, except you do so by diving under her held arm.
For the sake of naming, because there are three, you could call the classic one “arriba”, the one behind the back “atras” and the one where you go under “abajo”. In fact, this matches the invariants of the enchufates: atras is the only one that rotates the other way (counterclockwise) versus arriba and abajo (clockwise),
Por debajo del brazo
Por debajo del brazo (PDD) goes as follows: do a right-handed vacilala and lead her towards your back like a rodeo, except on 7, do a behind-the-back switch to your left hand, and in the next bar, pull her forwards on your left side with your hand veering left, essentially doing an enchufla without looking. The rest is like enchufla.
It sounds new, but actually, from the follower’s perspective, this is identical to a vacilala and an enchufate abajo followed by an enchufla, just without the leader rotating to face the follower.
By symmetry, this implies two things: firstly, that there are two other variants of PDD, with enchufate arriba and enchufate atras respectively, which in this case just correspond to how you move your elbow over your head. Secondly, that you can do non-rotating enchufates in other situations, like after an enchufla rather than a vacilala. For example, one could wonder if the leader needs to turn to the follower after his enchufate in setenta.
Balsero
This article is not about using two hands, but it’s worth mentioning that some figures are based on rodeo steps, like balsero.
Follower moving counterclockwise: DQN variations
Now, interestingly, one of the above caída substitutes has a known mirror image: indeed, rodeo is often taught in the same breath as rodeo inverso. Yet, rodeo is just one of the possible caída substitutes: by analogy, it should be possible to mirror all others into an “inverso” version too, which can then take place whenever rodeo inverso is taught to take place, namely at the end of a DQN. Let’s take a look.
Rodeo inverso
At the end of a DQN, rather than opening the position, lead her to your back like rodeo did, with your arm passing over your head. This is rodeo inverso.
Rodeo rotates clockwise from caída to abierta to caída. Rodeo inverso rotates counterclockwise from abierta to caída to abierta. Since DQN is the only figure we know that transitions to abierta, rodeo inverso is done right after a DQN. In a sense, it is an “abierta substitute”.
Rodeo inverso lends itself to a reina in its second bar. When done two-handed (a.k.a. Bayamo), it lends itself to a peinala.
It does not lend itself to hands-free tracing, because the controlled hand of the follower (her right) is on the outside of her counterclockwise path.
Paseala
Exact same as rodeo inverso except you don’t go over your head, but switch hands behind your back. Paseala is, essentially, an alias for “rodeo inverso abajo”.
Symmetry dictates that a rodeo abajo (or “paseala inverso”) should also exist. It would start with a right-on-right hold, have the left arm take over and pull behind the back, and then have the right arm take over to pull from the front.
Coca-Cola
Coca-Cola can be seen as a DQN with peinala followed by a rodeo inverso wherein unlike rodeo inverso and paseala, the leader steps make him turn too, and unlike enchufate, with the follower’s walk.
Enchufate inverso
Here is the most powerful implication due to symmetry. Rodeos happen to substitute caída. Enchufates happen at the same time as rodeos and are 0-count versions of their first bar, which passes through abierta. Meanwhile, rodeos have mirror images that happen to substitute abierta after a DQN. Thus, there should exist enchufates that happen after a DQN and are 0-count versions of the first bar of rodeo inverso, which passes through caída. Introducing: enchufate inverso. Since they are enchufates, we know there should be three to look for.
Let’s start with enchufate inverso arriba. We know that it should rotate against a follower’s rodeo inverso, so it’s clockwise. We know it is a 180⁰ rotation for the leader. We know it happens in the second bar of DQN and that it ends with the follower in caída, i.e. on his right rather than his left. What you get is what Steven Messina incorrectly calls “DQN paseala” in this video.
Enchufate inverso abajo has the same exact properties, except behind the back. One of my teachers, Francesco Pagliuca, does one in this video when he comes out of closed position, ending in caída to start an exhibela.
That leaves enchufate inverso atras. We know the following about it: it also ends in caída, rotates 360⁰ counterclockwise (the opposite of arriba and abajo), has the arm going over the leader’s head, and importantly, unlike the other enchufates, the follower should not change her rotation.
It’s not obvious that this is possible; indeed, there are also only 2 types of rodeo inverso (arriba, i.e. the default one, and abajo, i.e. paseala). However, this argument doesn’t really work since there are three regular enchufates and only one rodeo.
There is indeed one problem: in the second bar of a DQN, followers do a 180⁰ turn while walking. If the leader turns 360⁰, there is no way he can walk to end in caída with her. And, as predicted by enchufate atras, the solution is that the follower should not turn at all, i.e. walk in a straight line leftward while the leader does a 360⁰ turn counterclockwise, and it is up to him to block her usual DQN turn. Since enchufate atras can use a hook turn with the right foot hooking behind the left, enchufate inverso atras can use a hook turn with the right foot hooking in front of the left.
I’ve tested this in practice, and it works. During your turn, push her clockwise with your left arm and push on her back with your right so her DQN is blocked. The turn will feel like an enchufate arriba at first (because it’s counterclockwise), but it’s a 360⁰ right-over-left hook turn, not a 180⁰ enchufate. You can step through this hook turn if you pivot your left foot 90⁰ on 4.
Here is an overview in tabular form that shows how enchufates and rodeos relate.
| Figure | Leader | Follower | Starts in bar | After 0 bars | After 1 bar | After 2 bars |
|---|---|---|---|---|---|---|
| Rodeo | / | walks clockwise | 1 | caída | abierta | caída |
| Rodeo inverso | / | walks counterclockwise | 1 | abierta | caída | abierta |
| Paseala | / | walks counterclockwise | 1 | abierta | caída | abierta |
| Enchufate arriba | walks and turns 180° CCW | turns 180° CW | 2 | moving into caída | abierta | / |
| Enchufate atras | turns 360° CW | / | 2 | moving into caída | abierta | / |
| Enchufate abajo | walks and turns 180° CCW | turns 180° CW | 2 | moving into caída | abierta | / |
| Enchufate inverso arriba | turns 180° CW | walks and turns 180° CCW | 2 | moving into abierta | caída | / |
| Enchufate inverso atras | turns 360° CCW | walks straight | 2 | moving into abierta | caída | / |
| Enchufate inverso abajo | turns 180° CW | walks and turns 180° CCW | 2 | moving into abierta | caída | / |
Bayamo
Again, this article is not about two-handed figures, but it’s worth pointing out that Bayamo is just a rodeo inverso in essence. It is the counterclockwise equivalent of balsero.
Conclusion
From the existence of rodeo, its mirror image rodeo inverso, and the three enchufates, we extrapolated two things: we recognised that these figures are a positional substitute (a caída substitute and an abierta subtitute) and found several existing figures that fit the same idea, and we predicted how to do several novel figures from looking at symmetries, among which the enchufate inverso.
