Calculation Question

[Soren37]

Okay, a character has a 24% chance of activating a skill. How do I determine the chance that the skill will NOT activate in two attacks?

[Integrity]

Figure out the percent chance for the skill to go off in at least one of the attacks, then the remainder is how likely it is to go off in neither.

I don't feel like maths right now, but that's how to get it.

EDIT: in other words, for one attack it has a 24% chance of going off; ergo it has a 76% chance of not going off.

Edited August 3, 2010 by Integrity

[geozeldadude]

Figure out the percent chance for the skill to go off in at least one of the attacks, then the remainder is how likely it is to go off in neither.

I don't feel like maths right now, but that's how to get it.

EDIT: in other words, for one attack it has a 24% chance of going off; ergo it has a 76% chance of not going off.

but the OP was asking the chance it will not activate in two turns. this is 76% * 76% which equals 58%. this is assuming the RNG is completely fair, which in FE is not quite the case (i.e. you can get a lot of low numbers in a row).

[Tables]

which in FE is not quite the case (i.e. you can get a lot of low numbers in a row).

...Hence it being random. But it's not entirely fair, since IIRC it goes through a sequence of numbers only 65,536 numbers long (it might be 1.84467441 × 10¹⁹), so if you memorise the sequence you always know what's coming next.

And if you can't tell from the sarcasm, I'm basically saying it is random enough for all practical purposes.

As for the calculation, Integrity is correct. The chance of something happening at least once is equal to the chance of it not happening exactly zero times, and the chance of something not happening zero times is (1 - the chance of it happening zero times). In this case, the chance of a skill not activating is 76%, so the chance of the skill not activating, after the skill already didn't activate once - so 76% * 76%. And the chance of it happening at least once therefore must be 1 - (76% * 76%), which is a 42.24% chance of at least one skill activating.

[Integrity]

but the OP was asking the chance it will not activate in two turns. this is 76% * 76% which equals 58%. this is assuming the RNG is completely fair, which in FE is not quite the case (i.e. you can get a lot of low numbers in a row).

yes. I gave him the springboard answer and decided to let him figure it out from there because I didn't feel like maths. Fortunately IET always feels like maths.

[geozeldadude]

...Hence it being random.

the reason i said it doesn't seem truly random even aside from the fact it's a fixed sequence is that i've suspected (although i haven't proven it and i don't know if anyone else feels the same way) that the FE RNG (i.e. random-number generator) purposely puts in long sequences of "high" numbers and long sequences of "low" numbers to make battles more interesting. in a true RNG such sequences would be extremely uncommon. this semi-RNG as opposed to true RNG is compounded by the fact that FE's RNG actually uses the average of two numbers to generate the numbers used for battles, etc. so in that case long sequences of very high or very low numbers would be even less likely, but it seems to happen fairly regularly. maybe it's just me. :P

[Tables]

The fact is, if you divide numbers into 'high' and 'low', in a string N numbers long, you should expect the longest string of 'high' or 'low' numbers to be around N^0.5 long. So if you have 10,000 RNs over a game (probably about reasonable, considering levelups along take 7), you should expect the longest sequence of H/L numbers to be about 100! And that's with a perfectly fair RNG.

As for the sequence, it uses a linear feedback shift register to generate the numbers. I think it's a 16 bit one, but I've heard it's 64 bits as well. Both generate sequences long enough to not be memorable, of course.

[geozeldadude]

The fact is, if you divide numbers into 'high' and 'low', in a string N numbers long, you should expect the longest string of 'high' or 'low' numbers to be around N^0.5 long. So if you have 10,000 RNs over a game (probably about reasonable, considering levelups along take 7), you should expect the longest sequence of H/L numbers to be about 100! And that's with a perfectly fair RNG.

As for the sequence, it uses a linear feedback shift register to generate the numbers. I think it's a 16 bit one, but I've heard it's 64 bits as well. Both generate sequences long enough to not be memorable, of course.

to clarify, i'm not defining "high" as being anything about 50 and "low" as anything below 50. i'm talking about numbers more like lower than 10 or higher than 90. in which case your chance of getting 5 in a row for either of those cases is 0.1^5 = 0.001%.

[Tables]

I've never gotten long strings in those sorts of ranges, personally, and I'd like to know how you know you have, since I can't think of a simple way of checking, unless you have a character with lots of 10% growths, or something.