These are good info to study. After looking at IV changes for a period of time, you will develop an intuitive sense of how they change with time and underlying movement. I find that developing a deep understanding of the anatomy of a butterfly trade is more beneficial than learning multiple styles of trading butterflies. Because once you have that intuitive feel, you'll naturally come up with sensible approach to trading the position.
The second article you linked is a very good one. The findings are consistent with my own research and live trading experience. Bearish butterfly is very resilient to downward movement, not just because it has negative delta (this one is obvious) but also because its vega isn't as negative as what is shown in the analyzer. Despite the fact that butterfly has negative vega theoretically, as the article has shown, depending on the IV skew movement and the magnitude of the IV increase, the weighted vega of butterfly can be neutral or even positive. Therefore, an increased IV can actually help a bearish butterfly vega-
wise. I know this is completely counter intuitive to what we were taught as a student, just like the weighted vega of a calendar can be negative, but if we look at enough data and spend enough time monitoring, we'll realize that's the reality.
As the article showed, when market drops, IV goes up, but IVs of strikes below money, ie OTM Puts, increase much less than those above money (I say below money strikes because the same strikes are ITM for Calls. Just to avoid confusion.). Sometimes, the IV skew rotates counter clockwise (ie flatten) so much that some of the lower strike IVs actually decrease. As a result, IVs of the 2 butterfly short strikes are usually quite well protected as long as you keep them tugged below market. So we end up seeing bearish butterfly being more resilient than expected in a downward market. One side note though - when there is crisis-level fear, the entire IV curve gets lifted up vertically. All bets are off then. That's when the vertical movement overwhelms the effect of IV skew change and as a result, even bearish butterfly will hurt in a big way.
In a typical situation, the BB resilience starts to wear out when market hits short strike on the way down. By the time RUT is 10 to 20 pts below market, the IV increase will hurt the short strike more than expected and at the same time, delta turns positive. So, a butterfly will be hurt by delta and vega simultaneously plus if it's near expiration, by gamma as well. That's a triple whammy. P&L will meltdown if RUT continues to go down. Therefore, typically, I'd shift the shorts down or the entire butterfly down when RUT is between 10 to 20 pts below the short strikes, regardless of the position delta or the T+0 line. This has been my practice for a while.