Introducing Pack Probabilities [MEGA]

"DuneSeaFarmer;c-1645948" wrote:


So there is a .10% chance of 145 shards OR 330? Huh?

Not really, there is a .2% chance of getting either 145 OR 330 from any single purchase.

Think of it this way. When you buy a pack, you roll a single 1d10,000, then:

your roll <= 1924, you get 10 shards
1924 < your roll <= 5772, you get 12 shards
5772 < your roll <= 8658, you get 15 shards
8658 < your roll <= 9620, you get 20 shards
9620 < your roll <= 9861, you get 25 shards

In other words, in 98.61% of the cases, you get 25 shards or less (and most likely less: in 57% of the cases you get 10 or 12 shards). The remaining 1.4% chance is distributed as follows:

9841 < your roll <= 9957, you get 50 shards
9957 < your roll <= 9976, you get 80 shards
9976 < your roll <= 9986, you get 145 shards
9986 < your roll <= 9991, you get 230 shards
9991 < your roll <= 10,001, you get 330 shards

Clearly there's a rounding error somewhere in those probabilities they posted (probably their code looks like this, but because their randon number generator starts at 0, whereas (ficticious) 10,000 sided dice start at 1, the mistake isn't as immediately obvious that they are dividing by 10,001 rather than by 10,000, but the difference is small enough that it doesn't matter for our purposes.

Now, if you want to know what the chance is of getting either 145 OR 330 shards, you can see this happens if you roll between 9976 and 9986 OR between 9991 and 10,001, in other words, 10/10,001 outcomes give you 145 shards and 10/10,001 outcomes give you 330 shards, so (10 + 10)/10,001 = 0.2% chance of getting 145 or 330 shards.