The percentages need to be on a per player basis, not the player base as a whole, this way an individual player doesn't get shafted.
Basic math says should need at most 20 materia for a single 5% meld.
When you poll the player base as a whole that may be a correct estimation, but we don't experience the whole. What we experience is our own little sliver of numbers in the game.
Assume that 5th meld on all gear except tools, the 5% one. As a singular player it is perfectly reasonable to assume a 5% chance and 10 pieces of gear, it should about 200 materia to meld them all, given it's probability and not an exact number we'll say ± another 25%. meaning 250 materia would meld them all.
Again very basic math here.
Now when you add probability into the mix things get a little more complicated.
We obviously want to know the expected number of attempts to guarantee a success at 5%. That equation will look something this.
100% - (95% ^ X) = y
100% being what we want our chance to be, 95% ^ X is the failure rate of 95% times itself equal to the number of attempts made. Y being the expected success rate after the combined attempts.
For instance 5 attempts would look like this.
100% - (95% ^ 5) = 33.7%
Written out would be this
100% - (95% x .95% x .95% x .95% x .95%) > 100% - 66.3%
100% - 66.3% = 33.7% chance of single success in all attempts combined.
If we plug in 13 attempts, we get a projected 49% chance of success.
At 14 attempts we get a projection of 52% chance of success.
At 50 attempts the projected success rate is 93%.
At 90 attempts the projected failure rate is less than 1%.
So my proposal is this, instead of letting a computer do unchecked RNG, because they are horrible at it. How about a line of code gets added in that once the projected success rate breaks, let's say 75% during a BULK MELD, it becomes an automatic success. This would still leave the RNG in place so it's still "random", but it will put a hard cap on the number of Materia. Keeping the personal experience closer to the stated estimated chance percentage.
It could still be a decent number burned in the end.
The percentages for BiS melds are generally 17%, 10%, 7%, and 5%. This would put the hard caps for these specific numbers at...
%-chance-|Materia-Cap-|-actual-%-if-you-hit-the-cap-every-time
17%- | 11 | 9.09%
10%- | 14 | 7.14%
7%- | 19 | 5.26%
5%- | 28 | 3.57%
While it would still feel bad to always hit that cap, it would make for a very nice safety net.
This would be a great way to ease the burden of over-melds, help to keep the programs RNG in check, as well as show better respect for a player's time.
Continue reading...
Basic math says should need at most 20 materia for a single 5% meld.
When you poll the player base as a whole that may be a correct estimation, but we don't experience the whole. What we experience is our own little sliver of numbers in the game.
Assume that 5th meld on all gear except tools, the 5% one. As a singular player it is perfectly reasonable to assume a 5% chance and 10 pieces of gear, it should about 200 materia to meld them all, given it's probability and not an exact number we'll say ± another 25%. meaning 250 materia would meld them all.
Again very basic math here.
Now when you add probability into the mix things get a little more complicated.
We obviously want to know the expected number of attempts to guarantee a success at 5%. That equation will look something this.
100% - (95% ^ X) = y
100% being what we want our chance to be, 95% ^ X is the failure rate of 95% times itself equal to the number of attempts made. Y being the expected success rate after the combined attempts.
For instance 5 attempts would look like this.
100% - (95% ^ 5) = 33.7%
Written out would be this
100% - (95% x .95% x .95% x .95% x .95%) > 100% - 66.3%
100% - 66.3% = 33.7% chance of single success in all attempts combined.
If we plug in 13 attempts, we get a projected 49% chance of success.
At 14 attempts we get a projection of 52% chance of success.
At 50 attempts the projected success rate is 93%.
At 90 attempts the projected failure rate is less than 1%.
So my proposal is this, instead of letting a computer do unchecked RNG, because they are horrible at it. How about a line of code gets added in that once the projected success rate breaks, let's say 75% during a BULK MELD, it becomes an automatic success. This would still leave the RNG in place so it's still "random", but it will put a hard cap on the number of Materia. Keeping the personal experience closer to the stated estimated chance percentage.
It could still be a decent number burned in the end.
The percentages for BiS melds are generally 17%, 10%, 7%, and 5%. This would put the hard caps for these specific numbers at...
%-chance-|Materia-Cap-|-actual-%-if-you-hit-the-cap-every-time
17%- | 11 | 9.09%
10%- | 14 | 7.14%
7%- | 19 | 5.26%
5%- | 28 | 3.57%
While it would still feel bad to always hit that cap, it would make for a very nice safety net.
This would be a great way to ease the burden of over-melds, help to keep the programs RNG in check, as well as show better respect for a player's time.
Continue reading...