Failstacks is a hot subject for discussion with the release of +16 to +20 enhancements. Many consider it essential to build as many failstacks as possible and that doing so would guarantee (or significantly improve the odds) of successful enhancement.
Before we continue with the discussion about failstacks, all of the numbers in this post assumes the KR enhancement table is correct, i.e.
For example, reading the 16 row we can see that an enhancement from +15 to +16 would go from 15% success chance up to 52.5% at 25 failstacks. This may seem like a significant boost of over three times, but how much does that translate into real value?
We know that on average it will take you (1/0.525) = 1.9 tries to enhance a piece of +15 gear to +16 starting from 25 failstacks. However, if you subsequently assume that it takes you (1/0.15) = 6.67 tries to enhance a piece of gear starting at zero failstacks, you would be wrong. The reason is because with each fail, you will build failstacks, and for weapon and armor, +15 to +16 builds 2 failstacks.
The expected number of tries can easily be mapped out with an equation, but instead of confusing everyone I will instead rely on an analogy to explain.
Say 1000 people are flipping a coin, and once you flip heads (success) you don’t have to flip anymore. When every single person is finished flipping, how many flips did each person do on average?
After the first flip, 500 people would have flipped heads on a fair coin. On the second flip, half of the remainder will have flipped a heads. On the third flip, half of the remainder would have flipped heads. On a practical level, we know each of the 1000 will finish flipping, but on a mathematical level, we know that there is a small chance that someone might spend the rest of their lives flipping coins.
The answer to the above question is very simple, 1000 people will flip once, 500 will flip a second time, 250 flip a third….. infinite. Therefore the answer is simply 1000+500+250+125+62.5…… divided by 1000 people. On average, each person will flip the coin twice.
Some of you might have figured out that this question could have been more easily solved by simply dividing 1 by 50% chance of heads, which is true, however that only works if the probability of tossing a heads does not change. It doesn’t change for a fair coin, but BDO enhancing is not a fair coin. Each time you fail, the probability of success goes up because of failstacks.
This method however can be applied when calculating failstacks. We simply need to add the probability of succeeding, the probability of fail->success, the probability of fail->fail->success….. infinite and we will get the expected number of tries on an enhancement.
To save everyone the headache of filtering through a huge list of equations and numbers, I did that for you all on Excel. Yes, I did account for fails giving 4 stacks instead of 1 stack. Here is the average amount of attempts required to successfully enhance a piece of gear from +17 to +18:
Note the above does not take into account the number of tries leveling a +16 piece of gear back to +17 thanks to deleveling. It strictly only measures the amount of times you will put a +17 piece of gear and a concentrated blackstone into the menu and have the Black Spirit laugh at you.
As you can see, if you start from zero failstacks, it will take you 7.4 tries to succeed on average. Doing it at capped 44 stacks drops this to 3.7 tries but 44 failstacks is semi-impossible to build on purpose. Doing it on a modest stack like 25 drops the attempts to 4.5 tries.
It’s always kind of funny watching people on the forums complain about failing +18 three times. The average player is expected to fail 3.7 times even if they start at max stacks.
The above really goes and illustrates a few very important concepts:
- Failstacks does not guarantee success. You need to try many times regardless of how many failstacks you build.
- Valk Blessing that many people are begging to have implemented into our version actually does almost nothing. Going from 34 stacks to 44 stacks drops the amount of tries on average by 0.3 tries. This is negligible.
- It is not always the optimal strategy to build maximum failstacks. Building 40 failstacks costs an astronomical value compared to say 20 failstacks, but only drops your expected tries by a bit over 1 try.
Optimal stacking breakpoints is another monster in itself and maybe we’ll talk about that another day. Hopefully this post is able to provide some insight into BDO failstack system and dispel the myth that there is a huge effect on success at modest values.
If you have any suggestions about this post or on topics to cover, feel free to contact me or leave a message below.