>> Instead, the optimal strategy for the player who trails is to make certain bold plays in an attempt catch up.
The reason that's optimal, if you're losing, is that you assume that your opponent, who isn't losing, is going to use binary search. They're going to use binary search because it's the optimal way to find the secret.
Since you're behind, if you also use binary search, both players will progress toward the goal at the same rate, and you'll lose.
Trying to get lucky means that you intentionally play badly in order to get more victories. You're redistributing guesses taken between games in a negative-sum manner - you take more total guesses (because your search strategy is inferior to binary search), but they are unevenly distributed across your games, and in the relatively few games where you perform well above expectation, you can score a victory.
However, in a two player setting, using the strategies presented in the paper, you will beat an adversary that uses binary search in more than 50% of the games played.
Here's another visual demonstration: https://www.youtube.com/watch?v=zmvn4dnq82U
> in a two player setting, using the strategies presented in the paper, you will beat an adversary that uses binary search in more than 50% of the games played.
This is technically true. But 50 percentage points of your "more than 50%" of games played are games where you exclusively use binary search. For the remainder, you're redistributing luck around between potential games in a way that is negative-sum, exactly like I just said.
Although I think I get your point, saying 'You can't beat binary search in Guess Who' is misleading, considering you would probably describe yourself the optimal strategy as 'play binary search when ahead, when behind, don't'.
> Trying to get lucky means that you intentionally play badly in order to get more victories
That's quite an uncommon definition of good and bad.