[Other] Let's use the FSRS Simulator to figure out how to implement Load Balancer

[Expertium]

@L-M-Sherlock @jakeprobst @user1823 @brishtibheja Right now, there are two "competing" ideas regarding Load Balancing. Everyone agrees that making the probability of scheduling a card on a specific day inversely proportional to how many due cards that day has is a good idea. However, me and Jake disagree on the details, and it's not clear who's idea is better. Jake proposes N = days in range, where N is the number of cards with the lowest due count. In other words, his idea is to allow Load Balancer to schedule a card on any day within the fuzz range, just with different non-zero probabilities. My idea: N = max(floor(days in range / 2), 2). This ensures that cards can only be scheduled on days with a relatively low due count and cannot be scheduled on a day with the highest (or one of the highest) due count. It may not be immediately clear what's the difference, so here's a visualiztion:

Suppose the fuzz range for a card includes the following days: [23, 24, 25, 26, 27], days in range = 5. Jake's range and fuzz range are the same, the difference is that in Jake's version the probability of a card falling on a particular day isn't the same for every day. My range is narrower, it only includes (in this example) two days with the lowest due count. The probabilities for the other 3 days are 0. This avoids clustering while staying true to the spirit of this feature, which is "do not schedule a card on a day that already has a lot of cards".

In order to test which idea is better, we could ask Jake to run both on his collection, but that would take months. Instead, Jarrett, I would like you to collaborate with Jake to incorporate Load Balancer into your Simulator, so we can test these ideas on a simulation.