Penney's Game: Probability of HTT or TTH in a series of coin tosses

When you flip a coin to make a decision, there's an equal chance of getting heads and tails. What if you flipped one coin several times, so that one option would win as soon as HTT showed up in a row on that coin, and one option would win as soon as TTH? Would each option (HTT and TTH) still have an equal chance?
Make your decision.
Title: "Coin Flip Dilemma: Equal Chances or Not?"
Description:
Welcome to our latest video where we tackle a fascinating problem that students in the MYP 5 IB program at the prestigious IB World School 1531 Raszyńska have been exploring. We all know that when you flip a coin, there's an equal chance of getting heads or tails. But what if we take it a step further?
In this video, we delve into a scenario where one coin is flipped several times, but with a twist. One option wins as soon as the sequence HTT (Heads-Tails-Tails) appears in a row, while the other option wins as soon as the sequence TTH (Tails-Tails-Heads) appears. The question is: would each option still have an equal chance of winning?
Our students have put their critical thinking skills to the test to analyze this intriguing problem. Through mathematical reasoning and logical deduction, they've explored whether the probabilities remain balanced or if one option has an advantage over the other.
Join us as we unravel the mystery and make our decision based on rigorous analysis and thoughtful deliberation. Whether you're a math enthusiast, a curious mind, or simply love a good intellectual challenge, this video is sure to captivate your interest.