By now, the Maker-Breaker connectivity game on a complete graph $K_n$ or on a random graph $Gsim G_{n,p}$ is well studied. Recently, London and Pluhar suggested a variant in which Maker always needs to choose her edges in such a way that her graph stays connected. By their results it follows that for this connected version of the game, the threshold bias on $K_n$ and the threshold probability on $Gsim G_{n,p}$ for winning the game drastically differ from the corresponding values for the usual Maker-Breaker version, assuming Makers bias to be $1$. However, they observed that the threshold biases of bo
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