Nova's Shuffle: Understanding the Odds

Editorial by The Fallen

In Novas Shuffle there are 24 items that are possible to drop with six items that have a 7% chance, three items have a 6% chance, three items have a 4% chance, four items have a 6% chance,  three items have a 2% chance, and finally six items have a 1% chance of dropping. This may vary depending on the shuffle available at the time.

Read the following for a greater understanding of your chances at getting a 1% item to drop from Nova's Shuffle.

If you hope to get the rare Flame Formed Arm for example, we know that it has a 1% drop chance. That means that every time you spin a single shuffle you have a 1% chance of getting the Flame Formed Arm. 1% on the first attempt, and 1% on the 100th attempt. However, over the course of 100 attempt, you have a much higher probability of getting the Flame Formed Arm. But not 100%. Never 100%.

Join me after the cut where we take a friendly and gentle look at understanding probability.
Thus we can learn that if we attempt the shuffle 100 times, we have a 63.4% chance of getting the Flame Formed Arm drop at least once.Your Chance on Each Attempt is the Same

If your Flame Formed Arm has a 1% chance of dropping, it will always be 1% on every single attempt. The Gambler's Fallacy trap that many fall into is assuming that previous results will change future results -- or put in our terms, "I've run this 50 times, so it must be really likely to drop now!" And it really feels like it should be that way. But it's not any more likely on the 50th spin or the 500th spin, it's still 1%. Every. Single. Time.

As an example, let's say you're flipping a coin. There's a 50% chance that it lands heads. You flip and get tails. Next time the chance is still 50%. Tails again. The next chance is still 50%. The past results don't affect the chance of the next result. That's randomness for you.

Your Chance Over Multiple Attempts Increases

Even though your chance on each single attempt always remains the same, the probability of getting your drop over the course of multiple attempts increases. I know at first this sounds like crazy talk that contradicts what we just discussed, so another example is in order:

We're flipping our coin again. We know that we have a 50% chance of getting heads on any given toss, and it doesn't matter at all what results we got before. But I think we can all agree that if we flip a coin 100 times it's very, very likely that we'll get heads at least one of those times. The chance on the first toss is 50%, and on the 42nd toss it's 50%, and on the 100th toss it's 50%. But over the course of 100 tosses, the probability of getting heads is way more than 50%. (In fact, the chance is 99.999999999999999999999999999921% that we'll get heads at least once.)

So the more often we attempt a shuffle , the more likely we are to see the loot that we want. Instinctively we all know this, that's why we keep going back and keep going back, and eventually our persistence is rewarded. Sometimes you'll get lucky, and sometimes you'll get unlucky, and the more you try the better your odds are overall. But the chance will never be 100%. It's never guaranteed.

How to Calculate It for Yourself

The formula to calculate your drop chance ( x ) over any given number of runs ( y ) is this:

1 - ( ( 1 - x ) ^ y )