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Let $\Cant_n$ be the $n$-th generation in the construction of the middle-halfCantor set. The Cartesian square $\K_n$ of $\Cant_n$ consists of $4^n$ squaresof side-length $4^{-n}$. The chance that a long needle thrown at random in theunit square will meet $\K_n$ is essentially the average length of theprojections of $\K_n$, also known as the Favard length of $\K_n$. A result dueto Bateman and Volberg \cite{BV} shows that a lower estimate for this Favardlength is $c \frac{\log n}{n}$.  We may bend the needle at each stage, giving us what we will call a noodle,and ask whether the uniform lower estimate $c \frac{\log n}{n}$ still holds forthese so-called Buffon noodle probabilities. If so, we call the sequence ofnoodles undercooked. We will define a few classes of noodles and prove thatthey are undercooked. In particular, we are interested in the case when thenoodles are circular arcs of radius $r_n$. We will show that if $r_n \geq4^{\frac{n}{5}}$, then the circular arcs are undercooked noodles.

Estimates from below of the Buffon noodle probability for undercooked noodles