PokéBase - Pokémon Q&A
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Like, at 10 chains, does that mean there’s a 70% chance of my chain breaking by then?

BDSP poke radar

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Pokeradar

So, the pokeradar. Truly an interesting item. Able to assist you in a brilliant way while catching a shiny pokeymans. However, there is a problem. While doing the method, there is a 7 percent chance of the chain just...dying. (Really good explanation). As you cry yourself to sleep, you might thing that this is unfair, at 10, you get to 100, and it's stupid, ILCA should've never made the game. However, here is where probability comes in.
Discord
Ok, so if there was an experiment with 10 marbles, 5 blue and 5 green marbles, the probability of getting a blue marble is 5/10, or 1/2. Then, if you picked a green marble, it would be 5/9, as you only have 9 marbles. This is what you call dependent probability, where the outcome depends on another event.
Discord part 2 wtf
Now, this is INDEPENDENT probability, the outcome of the first event does not matter to the second event. So, this is why that wouldn't work (fortunately, that would be so scuffed if you could only go to ten). So, going off of your example, I like to calculate the probability of you actually getting a mon, it makes it more obvious on what is happening.
Here is a graph to explain further: Fancy graph

So you have the probability here, the y value is the probability of the chance. For 10 encounters, it'd be 48.39%

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That's what I said, and has to do with all of shiny hunting.
Yeah I was answering before I saw your answer
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It means every time you catch a Pokemon, there is a 93% chance that the chain continues, and a 7% chance it doesn't. The chance of doing everything correctly and successfully getting a chain of 40 is 5.49%.

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What about at a chain of 10 though? What are the odds of it breaking by then?
93^10/100^10 = 48.39% chance of getting to a chain of ten.