FGO Probability

Summoning Rates

FGOProbability

Total of 100%

5% for 5 stars(20:80)

15% for 4 stars(20:80)

80% for 3 stars(50:50)

Servant

5star(0.043%)

  • 23 -> 1% and 1/23%

4star(0.060%)

  • 50 -> 3% and 1/50%

3star(1.081%)

  • 37 -> 40% and 1/37%

Craft

5star(0.235%)

  • 17 -> 4% and 1/17%

4star(0.480%)

  • 25 -> 12% and 1/25%

3star(1.818%)

  • 22 -> 40% and 1/22%

Condition

  1. One roll is ten tries
  2. At least one card is above **(Servant or craft)
  3. Other nine tries are equal probabilities
  4. Sample space is 174

How do we calculate?

  1. We have two conditions
    • Guaranteed card
    • Equal probabilities
  2. Calculate each conditions

Exercise

  1. What is the probability of getting two ***** servants in a roll(10).
    • P(Guaranteed card as 5star servant) * (1-P(No 5star servant)^9)
      • Sample Space for Guaranteed card : 15
      • 1:3:4:12
      • 5:15:20:60
      • P(guaranteed card as 5star servant) : 5%
    • 1-P(No ***** servant)
      • No ***** servant is 99%
      • we’ve got 9 chances
      • 0.99^9
      • 0.91
      • 1-0.91 : 0.09 : 9%
    • multiply it together : 0.45%
  2. What is the probability of not getting ***** servants or crafts at all in a roll(10).
    • P(Guaranteed card as No 5star card) * (P(No 5star card)^9)
      • We want to inversely caculate it like 1-P = A
      • P(Guaranteed card as 5star card) * (P(At least one 5star card)^9)
      • In other words, 1-P(No 5star card)^9
      • 25% * (1-((.95)^9))
      • 25% * 37%
      • 100% - (9.3%) : 90.7%