Hey everyone, i’m trying to understand probability.
If we say a character has a 1% pull chance. After 200 pulls is there any increased chance of getting said character.
If i work it out in terms of “chance of not having said character after 200 pulls” its a smaller chance the more pulls i work it out after. But the base chance per pull is still 1%
So how does probability actually work in this context.
Am i any more likely to recieve said character after x amount of pulls?
In: 3
>So how does probability actually work in this context.
However it was programmed to work.
Depending on where you live, companies may be legally required to publicise the per-pull odds, in which case the chance is still 1%, but if you’re anywhere else the 1% may be an average across the entire userbase and individual users see increased or decreased odds depending on their spending patterns.
Assuming a completely unbiased/ ideal gacha, increasing the number of pulls merely to approach the expected rate. At 1%, you’d expect 1 per 100, after 1000 pulls you’d expect 10, but it’s no guarantee. In the case of 1000 pulls you could very well end up with more or less than the expected 10.
Probability works the same way in about every context (as long as there’s nothing dishonest about posted odds): If an event has a 1% chance of happening, it has a 99% chance of it not happening.
It is possible to take the probability of an event happening at least once over multiple attempts. This can be done because the odds of multiple specific things happening can be found by multiplying the chances together, and getting *at least* one is the same as the opposite of not happening every time, which is a specific result. So the odds of getting at least one 1% result out of 100 is about 63% (as the opposite of 100 failures is at 37%), and it increases if you take it over more attempts like you’ve realized.
But there’s a thing known as “[gambler’s fallacy](https://en.wikipedia.org/wiki/Gambler%27s_fallacy)”. Basically, no matter what happens in the past it won’t change the next chance, even though we emotionally think it should. If you try a 1% chance action 99 times and fail 99 times, the 100th attempt has a 1% chance instead of 63%; the 99 times in the past no longer affect the probability. At this point, the 63% is the odds of getting a success in the *next* 100 attempts, even though the total number of attempts is more than 100.
It’s as you say: the rolls are independent events (disregarding gacha pity), so it makes no difference whether you’ve rolled twice or 200 times for your next roll. You *are* more likely to have what you want after 200 rolls than after two, but that’s only on paper and as an end result. Thinking “I really will get it it now, it’s been 300 rolls so it should drop!” is a classic case of gambler’s fallacy.
Also, gacha companies are scum and will deceive you with small print and shitty practices at every legally allowed opportunity.
Assuming you have 1% chance of getting a character on each pull, independently of previous pulls results.
You have, for example, 40% of getting it at least once in 50 pulls
Before starting these 50 pulls, there’s 40% chance you’ll get it at least once.
Once you started these 50 pulls, and made like, 20 of them so far, and got him already : there’s not 40% chance anymore, but 100% chance you’ll get it at least once in these 50 pulls (given that you just got it once)
Different scenario, say you started these 50 pulls, made 20 of them so far, still have 30 to go and haven’t got the character yet. There’s not 40% chance you’ll get it in the remaining 30 pulls. There’s less (26%).
That 40% probability of getting the character at least once in these 50 pulls, is valid before starting the 50 pulls. Once you started them, the probability that you’ll get the character at least once in these 50 pulls, evolves depending on what the results on the first pulls are (it diminishes the more you pull without getting the character yet, and raises and stays at 100% if you do get the character at some point in these 50 pulls)
To put it simply it’s called marginal laws. When you get new info, the probability of something happening, evolves depending on that info. You then have to use a marginal law, that takes into account this info, rather than the general law. For example, take a random person. There’s 40% chance they’ll get cancer at least once in their life. If you then learn that person is a dude, that probability raises to 50%. The relevant probability here, once you learn that the person is a dude, is the marginal probability, that takes into account the info that the person is a dude. Not the general probability.
Think about it as pre-committing to a course of action. If you commit to only 1 pull, your chance of success is 1%. If you commit to 200 pulls, your chance of success is about 87% (the way to calculate this is that you have a .99^200 percent chance of failing every time. This is about 13%, so in the remaining outcomes, you succeed at least once).
In a simple game, your history of success or failure at the time you make this commitment does not change these probabilities. If you just pulled 200 times and did not get the character, well then you’ve gotten unlucky, but probability is a cruel mistress, and there’s no mechanism to “balance out” your luck going forward.
In more complex games, there may be hidden routines that *do* actually change the probability of drops based on your inputs. It’s pretty common for games to automatically drop a rare thing if a player has a particularly long unlucky streak, though you typically can’t guarantee that it’s the specific rare thing you wanted. Just remember that all of this is being programmed *by people who want your money*, so any deviations from standard probability are meant to induce you to give them more money, often by manipulating you psychologically. Be careful.
Its like shuffling a deck of 100 cards with 1 Joker and hoping you find the Joker with 1 pull, except if you pick a non-joker card it doesn’t leave the deck but is reinserted in a random position. Pulling cards won’t increase your chances since the deck doesn’t become thinner as you pull, thats a Gambler’s Fallacy. However, pulling for the joker more will technically make it seem like it increases the likelihood of a 1 in 100 chance event to happen, which is why people get addicted to gambling.
Since you mentioned it, lets use a gacha game as an example which conveniently has a 1% chance of getting a 5* (highest rarity) character, Fate Grand Order.
Lets say you want to get a 5* character, it doesn’t matter who:
* If you make 1 pull, theres a 1% chance this character will show up.
* If you make 200 pulls, that doesn’t give you a 200% chance of getting the character, but 200 individual 1% chances.
* 10-pulls don’t increase the chances either, it just speeds up the process.
However, in the context of gacha games, lets make it more difficult. Lets say you want to get a specific 5* character from FGO (lets say Altria Pendragon) from the gacha. Although the rates for a 5* character is 1 out of a 100 (1%), from what i can see in the game right now Altria Pendragon has a 0.029% chance of being pulled. Idk how to express that in math but you should get the idea.
That being said, back to gacha games, there are varying gacha systems. For example in Genshin Impact you are guaranteed a 5* character after around 90 pulls and the rates increase after around 75 pulls. In Fate Grand Order, the gacha system is ruthless as there is no pity or way for the rates to come into your favor. So to answer the question of whether or not pulling enough times will make it more likely to get the character you want, it depends on the game.
Yes you are more likely If the character has a consistent 1% pull chance and you do 200 pulls you would have a 86.6% chance of getting at least 1 successful pull, whereas with a single pull you only have a 1% chance of getting 1 successful pull
The math to calculate that is somewhat complicated but this situation is called a Binomial Distribution. When you have ~n~ trials (200 in your case) with probability ~p~ of success (0.01 in your case)
Of course if you do 200 pulls and don’t happen to get the character (which will happen 13.4% of the time you do 200 pulls) then you have gained nothing probability wise and your next 200 pulls will still have the same 86.6% chance of getting at least 1 character. What I mean is that even if you miss 1,000,000,000 pulls the next pulls aren’t more likely than normal to be successful
>If we say a character has a 1% pull chance.
Then after a single pull, there is a 1% chance to get them. This is true for any single pull. Your first pull has a 1% chance, your 100th pull has a 1% chance, and your 472nd pull has a 1% chance.
>After 200 pulls is there any increased chance of getting said character.
There is an 86% chance that you will get at least one of those 1% characters within 200 pulls.
* Your 199th pull had a 1% chance, your 200th pull has a 1% chance, and your 201st pull will have a 1% chance. Same as above. Nothing changed.
* But what are the odds of *not* getting a single character **after all 200 pulls**? They’re .99^(200), or 0.1339, or 13.39%.
* So if there’s a 13.39% chance of “didn’t get a single one”, then every other possible outcome combined are the remaining 86.61%. And in every one of those, you got at least 1 **from all 200 pulls combined**.
It depends. If it’s true random then no, each pull is independent of any other pull.
However some (many?) gacha games offer at least some level of so-called bad luck protection which will boost your odds of certain pulls over time if you continue to not get good stuff. Check the details of each game to know which ones do it and which ones don’t.
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