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- Age 30
- Seen Aug 22, 2017
Everybody knows that Pokemon is a game of chance to some degree, but I'm getting the impression that not everybody knows what this means. Therefore, this is a somewhat basic explanation of some of the odds that go into the goings on of the games, or more simply - no, you are not due a shiny.
The main context I hear complaints about the chances in is shiny hunting - I know that we don't have confirmed odds for shinies in the current generation but the theory still stands, so I will assume that the chances of finding a shiny are 1 in 512.
What does that actually mean though? Well, it's simple enough. Imagine having a 512 sided die, and trying to roll a 1. That's pretty much it... not very likely is it? Now imagine having two tries, or twenty, or five hundred. Eventually, you will roll a 1 and get your shiny, but this chance doesn't change as you go along. It doesn't work like that - your 512th encounter is not guaranteed to be a shiny, and has just the same chance as your first one.
However, what does improve as you move along the chain is your chance of having encountered a shiny by THAT POINT in the chain. That is just a statistical confirmation of the idea that you have to roll a one eventually, even if it takes you all year. The maths of this is explained here, but you can skip over it if you want:
Imagine your first two encounters. So your chance of encountering a shiny first go is 1/512, or just a shade under 0.2%. Your chance of encountering a shiny second goes is the exact same, but your chance of encountering a shiny EITHER first OR second go is slightly improved. There are a few possible outcomes from these encounters -
1. The first encounter is shiny (1/512) so we stop hunting.
2. The first encounter isn't shiny (511/512) but the second encounter is (1/512).
3. The first encounter isn't shiny (511/512) and nor is the second (511/512).
The total likelihood of each outcome is obtained by multiplying their individual odds together. Obviously scenario 1 has a 1/512 chance of happining, expressed as a percentage as 0.1953...%
Scenario 2 has a (511/512 x 1/512) chance, meaning an overall percentage of 0.19419...%
Scenario 3 has a (511/512 x 511/512) chance, expressed as 99.61%
Because we would stop hunting after the shiny if we were to get it 1st try, that means there is an ever so slight chance that we don't reach the second encounter, which is why the chance of finding the shiny on your second encounter is slightly lower than your first. In fact, when shiny hunting, the most likely encounter for you to find that shiny is your next one, regardless of when it is.
Most interestingly out of these calculations, though, is what is the overall chance of having a shiny is at the end of the encounters. It is 0.3902%, and this number goes up by a small amount with each next encounter. For example, after 50 encounters you have a 9.313% chance of having encountered a shiny by this point. This doesn't mean that your 50th encounter has a 10% chance of being shiny - it is still 1/512.
The chances of having encountered a shiny increase progressively, nearing but never reaching 100%. Your chances improve at roughly the following intervals -
10% - 54
20% - 115
30% - 183
40% - 262
50% - 355
60% - 469
70% - 616
80% - 824
90% - 1178
99% - 2356
See how this shows that even after 2356 encounters, there is still a 1% chance that you will not have encountered a shiny by this point? In theory, out of every 100 hunts you do, one of them will be over this length. But on the plus side, half of your hunts should be over by the 355th encounter.
This method of calculation applies to other aspects in the game - Razor Leaf is 95% to hit, but the more you use it the higher the chances that you will miss at least one of them; your chances of hitting each individual one is still 95%.
Hopefully this was remotely interesting and useful to read - let me know your thoughts and if anything needs changing.
The main context I hear complaints about the chances in is shiny hunting - I know that we don't have confirmed odds for shinies in the current generation but the theory still stands, so I will assume that the chances of finding a shiny are 1 in 512.
What does that actually mean though? Well, it's simple enough. Imagine having a 512 sided die, and trying to roll a 1. That's pretty much it... not very likely is it? Now imagine having two tries, or twenty, or five hundred. Eventually, you will roll a 1 and get your shiny, but this chance doesn't change as you go along. It doesn't work like that - your 512th encounter is not guaranteed to be a shiny, and has just the same chance as your first one.
However, what does improve as you move along the chain is your chance of having encountered a shiny by THAT POINT in the chain. That is just a statistical confirmation of the idea that you have to roll a one eventually, even if it takes you all year. The maths of this is explained here, but you can skip over it if you want:
Imagine your first two encounters. So your chance of encountering a shiny first go is 1/512, or just a shade under 0.2%. Your chance of encountering a shiny second goes is the exact same, but your chance of encountering a shiny EITHER first OR second go is slightly improved. There are a few possible outcomes from these encounters -
1. The first encounter is shiny (1/512) so we stop hunting.
2. The first encounter isn't shiny (511/512) but the second encounter is (1/512).
3. The first encounter isn't shiny (511/512) and nor is the second (511/512).
The total likelihood of each outcome is obtained by multiplying their individual odds together. Obviously scenario 1 has a 1/512 chance of happining, expressed as a percentage as 0.1953...%
Scenario 2 has a (511/512 x 1/512) chance, meaning an overall percentage of 0.19419...%
Scenario 3 has a (511/512 x 511/512) chance, expressed as 99.61%
Because we would stop hunting after the shiny if we were to get it 1st try, that means there is an ever so slight chance that we don't reach the second encounter, which is why the chance of finding the shiny on your second encounter is slightly lower than your first. In fact, when shiny hunting, the most likely encounter for you to find that shiny is your next one, regardless of when it is.
Most interestingly out of these calculations, though, is what is the overall chance of having a shiny is at the end of the encounters. It is 0.3902%, and this number goes up by a small amount with each next encounter. For example, after 50 encounters you have a 9.313% chance of having encountered a shiny by this point. This doesn't mean that your 50th encounter has a 10% chance of being shiny - it is still 1/512.
The chances of having encountered a shiny increase progressively, nearing but never reaching 100%. Your chances improve at roughly the following intervals -
10% - 54
20% - 115
30% - 183
40% - 262
50% - 355
60% - 469
70% - 616
80% - 824
90% - 1178
99% - 2356
See how this shows that even after 2356 encounters, there is still a 1% chance that you will not have encountered a shiny by this point? In theory, out of every 100 hunts you do, one of them will be over this length. But on the plus side, half of your hunts should be over by the 355th encounter.
This method of calculation applies to other aspects in the game - Razor Leaf is 95% to hit, but the more you use it the higher the chances that you will miss at least one of them; your chances of hitting each individual one is still 95%.
Hopefully this was remotely interesting and useful to read - let me know your thoughts and if anything needs changing.
