HT
Hersha Hospitality Trust Priority Class A Common Shares of Beneficial Interest
stock NYSE

I think it’s second because you can ensure either a 50% chance of winning, or have a slight edge. The key is that the most likely sequences to appear have the third coin as opposite the first, like HTT. Take HTH v HTT, both have same first two coins so equally likely to get to HT, but when HTH fails it’s on a T, so another H is required to restart. When HTT fails on third coin, it’s a H, which immediately restarts. It’s a slight edge, I think requiring a simulation to estimate.
So, if player 1 chooses a sequence where first and third coins are different, you pick a different sequence with that characteristic and it’s 50/50. If they don’t, like THT, you pick the first two coins the same and the last the opposite to have a slight edge, like THH.
Sorry if this is duplicative, I didn’t read all posts

I think it’s second because you can ensure either a 50% chance of winning, or have a slight edge. The key is that the most likely sequences to appear have the third coin as opposite the first, like HTT. Take HTH v HTT, both have same first two coins so equally likely to get to HT, but when HTH fails it’s on a T, so another H is required to restart. When HTT fails on third coin, it’s a H, which immediately restarts. It’s a slight edge, I think requiring a simulation to estimate.
So, if player 1 chooses a sequence where first and third coins are different, you pick a different sequence with that characteristic and it’s 50/50. If they don’t, like THT, you pick the first two coins the same and the last the opposite to have a slight edge, like THH.
Sorry if this is duplicative, I didn’t read all posts