Winning Secrets in Coin Toss

Imagine a scenario where 100 students are participating in a coin-tossing challenge. Each student is provided with a coin to flip. A student wins if their coin lands on heads. However, if the coin shows tails, they must flip it again. On the second flip, if the coin lands on heads, students will falsely claim victory despite not winning. If it lands on tails again, they will truthfully admit defeat. Given that 30 students claim to have won by the end, how many students can we reasonably expect to have truly won the game?