5 problems

Let $(p_1,\dots,p_s)$ be the probability vector of an $s$-sided die, with patterns formed from the die's faces. A reversal compares the expected waiting times of two patterns with…

Reversal symmetry conjecture. If $S'$ is the reversal of an ending string $S$, then

Powers-of-two conjecture. The expected value $E(S)$ equals $2^s$ possibly plus some lower positive powers of $2$; asymptotically, $E(S)$ is about $2^s$.

Let a four- or six-round $obreakmathrm{BCCF}$-protocol have four cheating probabilities, one for each party and each coin outcome. Four- and six-round BCCF bias conjecture. Ha…

Let a strong coin-flipping protocol based on bit-commitment be any protocol in the family formally defined in Section, and let its bias be the maximum excess of either party's chea…