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notes/ANS Theory.md
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@ -32,5 +32,9 @@ To store two coin flips, you might have the first subdivision represent the outc
| $0.50 - 0.75$ | Heads, Tails | | $0.50 - 0.75$ | Heads, Tails |
| $0.75 - 1.00$ | Heads, Heads | | $0.75 - 1.00$ | Heads, Heads |
Imagine a situation where we want to store the coin flip *Heads, Heads, Tails*. Imagine a situation where we want to store the coin flip *Heads, Heads, Tails*.
1. First we subdivide the range by the probability of each event happening. The probability of each is 50%, so that's simple. Encoding this would happen as follows:
2. We know that the r 1. First we subdivide the range by the probability of each event happening. The probability of each is 50%, so that's simple. Referring above, we know that heads is represented by the top half of the range, and tails is represented by the bottom half of the range.
> Because the *first* coin flip resulted in *Heads*, the output value must be between $0.50$ and $1.00$.
2. Subdividing the range $0.50$ and $1.00$ again to store the results of the second flip, we end up with values between $0.50$ and $0.75$ representing the sequence *Heads, Tails*, and values between $0.75$ and $1.00$ representing the sequence *Heads, Heads*.
> Because the *second* coin flip resulted in *Heads*, we know that the output value must be between $0.75$ and $1.00$
3. Subdividing the range $0.75$ and $1.00$ yet again, $0.