Bit Choosing Algorithm Explanation

The Bit Choosing Algorithm is designed to pick the next concept—or "bit"—for you to study. It balances three key factors: how well you’ve mastered the bit, how important it is, and how it fits into its section. This approach aims to make your learning as efficient and effective as possible.

How the Algorithm Works

For every bit, the algorithm uses Bayesian mathematics to calculate the probability that you know it right now. We call this probability $P_{\text{known}, t}$. Over time, since your last review, this probability decreases—or "decays"—because memory fades without practice.

Here’s the formula that describes how this decay happens:

This formula includes several components:

• $P_{\text{known}}$: The probability you knew the bit when you last reviewed it.
• $f = 8 \times 10^{-7}$: A constant that controls how quickly your memory decays (set to a very small value, meaning decay is gradual).
• $\Delta t$: The time (in seconds) since your last review of the bit.
• $S_{\text{memory}}$: A parameter representing your memory strength, which affects how fast the probability decays.

If you’ve never reviewed a bit before, we start with a default probability: $P_{\text{known}, t} = 0.2$. This assumes you have a basic chance of knowing it even without prior study.

Bits are organized into sections—like chapters in a book. For each section, we calculate a mastery score, $M_{\text{section}}$, and an overall mastery score for the entire collection of bits, $M_{\text{overall}}$. These scores are weighted averages of $P_{\text{known}, t}$ for all bits, adjusted by how important each bit is.

If any section’s mastery is below 60%, the algorithm focuses only on bits from that section until it improves to at least 60%. This ensures you build a solid foundation in weaker areas before moving on.

Once all sections are at 60% or higher, the algorithm considers all bits but gives extra attention to those in sections below a special threshold, $T$. This threshold is calculated as:

Here, $M_{\text{overall}}$ is your overall mastery, and the formula ensures the threshold stays between your current level plus 10% and a maximum of 90%. Bits from sections below this threshold get a 1.5x boost in their priority.

Finally, the algorithm picks the bit with the highest score, calculated as $(1 - P_{\text{known}, t}) \times \text{importance} \times \text{boost}$. It tries to avoid the last two bits you reviewed to keep things varied, balancing what you’re less likely to know, how important it is, and progress within each section.

Why Use This Approach?

This algorithm blends two powerful learning techniques: spaced repetition (reviewing material just before you forget it) and section-based grouping (mastering related concepts together). It adapts to your progress, giving extra focus to weaker sections while ensuring you don’t neglect the bigger picture. This keeps your learning optimized and engaging across all topics.