Here is another solution. Assume a head multiplies your money by `r = q/p', and a tail divides by `r'. This bet is fair (the expected value of a dollar is a dollar: `p r + q 1/r = q + p = 1').
Start with a dollar, after several tosses you have `r^(head-tail difference)' dollars. The game ends if head-tail difference is `N - i' (with probability `x') or
if head-tail difference is `-i' (probability is `1 - x'). The expected
value is still a dollar:
Interactive fluid simulation running in the web browser. The domain is filled by a mixture of two liquids with different densities and viscosities, effects of gravity and surface tension. Many parameters can be changed dynamically. Various boundary conditions can be set on the edges of the domain or a solid body. The plain text configuration described in the documentation is encoded in the URL for easy sharing.
I am puzzled by the paper of this groups [1]. The only evidence they present for "change points in the COVID spreading rate" is slightly better fit of the number of daily reported cases. In this repository for "Scenario assuming three change points with a weekly modulation of reported cases" they use 16 parameters to fit a smooth line (wavy pattern is because of lower case reports around the weekend). An elephant needs 8 [2]!. I also asked for clarification on stats.stackexchange [3].