Implement Expected Value Calculations

[t1an-xyz]

Summary

Adds expected value calculations to help users decide when to sell turnips. Fixes issue #329.

Changes

• Calculate expected prices for each time slot based on pattern probabilities
• Display "Should you sell now?" recommendation with expected maximum
• Add "Expected Price" line to the chart
• New translation keys in locales/en.json

Translation keys needing community translation

• output.chart.expected
• output.sell-now-title, output.sell-now, output.sell-later, output.sell-advice
• output.should-buy-title, output.should-buy, output.should-not-buy, output.buy-advice

How it works

The expected value for time slot $i$ can be calculated using the formula

$$ \mathbb E[X_i] = \sum_{z\in\mathcal Z} P(Z=z) \mathbb E[X_i|Z=z] $$

where $z$ is the pattern and $\mathbb E[X_i|Z=z]$ is the expected price at time slot $i$ given the current pattern is $z$. Since $X_i$ follows a uniform distribution, $X_i = \frac{a+b}{2}$ is simply the average of the min and max at time slot $i$ given pattern $z$.

The tool recommends selling now if the current price is greater than or equal to the expected maximum price of holding the item and selling later.