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Let's say you start an SOS with Munchlax. Munchlax calls for help and a Happiny appears. Instead of defeating Happiny, you defeat Munchlax. Will the SOS chain break if Munchlax is defeated and the other Pokemon(Happiny) is still alive?

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It depends on what exactly you leave standing. Each species has a call rate, and if it's 0, that means a chain where you switch to that species as the only survivor is done, as the survivor will never call for help again.

Example 1: Oranguru cannot call for more of itself; instead its calls will attract Trumbeak 100% of the time. Oranguru has a call rate of 15, while Trumbeak has 9. This means that if you ever switch sides, what you have from then on is a Trumbeak chain, where calls are less likely but still frequent. The surviving Trumbeak will continue to call more Trumbeak and nothing else.

Example 2: Bisharp cannot call for more of itself; instead its calls will attract its pre-evolution, Pawniard, 100% of the time. Typically call rate decreases the further up an evolution line you go, but in this unusual case, Bisharp has a call rate of 15, while Pawniard has 0. This means you have no choice but to preserve the original Bisharp as long as you can; if you ever switch sides and leave a Pawniard up, it can never call for help again and the chain is done.

Example 3: Pichu's calls for help are structured so that, if successful, they will draw in another Pichu 77% of the time, a Pikachu 13% of the time, or a Happiny 10% of the time. Pichu has a call rate of 15, Pikachu has 6, and Happiny has 0. This means that if you switch sides in this chain and it's to another Pichu, the chain remains undisturbed. If you switch sides to a Pikachu, calls for help will become less frequent, but still functional; it will continue to call in the same species with the same odds when calls are successful. If you switch sides when there's a Happiny up, the chain is done--you won't get any more calls from the 0 call rate Happiny.

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