Talk:Salomon Chapter Release/@comment-24469728-20181205210112/@comment-24469728-20181210142625

Mordred.best.waifu: Wrong. The bonus of the 30SQ rolls is  "you are guaranteed to summon at least one 3-5★ Servant and one 4-5★ Servant or Craft Essence(note: this does NOT change the 5★ rate)". If it does not change de 5★ rate then the rate is still 0,7% even with the guaranteed bonus. Unless the information given in that page is incorrect, of course.

KniteFlux: The "law" of averages has nothing to do with this, because this formula is for independent events. This is simple probabilistic. 0,7% of pulling the solo rate-up SSR (this statistic is given by the game) means 0,7/100 or 0,007. If this is the chance of pulling the specific servant which is the rate-up SSR, by subtracting this desired result from all possible results ( 1 - 0,007 ) you obtain 0,993 which is the chance of not picking the rate-up SSR. This holds true for each individual pull, but can be used as basis for a multi-pull of independent events.

For example, let's say you toss a coin 2 times. What is the probability of getting at least one heads? The coin's result on the first toss has no influence on the second toss result (independent events, the same we're dealing with regarding the gacha). The only way of not getting at least one heads is getting all tails, therefore, you need to subtract the chance of getting tails on both tosses from the total of all possibilities. The chance of getting tails in any given toss is 1/2, which means (1/2)^2 is the chance of getting tails in all the two tosses (1/2 * 1/2), because the tosses are independent. So, the chances of getting all tails is 1/4 (25%), which means the chances of getting at least one heads is 1-1/4 = 3/4 = 75%. The same logic goes for the gacha, but in a larger proportion.

PloxFGM: That's the spirit! The "at least one" chance calculated in my original comment is considering independent events. People talking about the gambler's fallacy are thinking that when coming up with the formula I considered the events as codependant, but if I did that the formula would be completely different.

FGOHikaru: True. However my formula does not contradict this. Even if you consider someone who has 1000 rolls, and as such a 99,91% chance of rolling at least one Merlin, this person can still fail because 99,91% is not 100%, and there's still a 0,09% chance this person will roll no Merlin whatsoever after 1000 rolls. The only way of having 100% chance is having infinite rolls, which is just in accord with your speculative scenarios. Same goes for someone who will do just one roll. They have a (1 - 0,993^1)*100% = 0,007*100% = 0,7% chance of pulling at least one Merlin in one roll, but 0,7% is not 0%, so they can still be lucky enough to get one with this 0,7% chance.