Imagine you’re comparing two trading strategies. One has made a handful of successful trades over the past month, while the other shows a different success pattern over a slightly shorter period. Both show promise, but which one truly performs better? And more importantly, how confident can we be in that judgment, given such limited data?

To explore this, let’s turn to a simpler but mathematically equivalent situation: comparing two coins. The first coin is flipped 10 times and lands heads 3 times. The second coin is flipped 9 times and lands heads 5 times. We want to know: what is the probability that the second coin has a higher chance of landing heads than the first?

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