The chicken road game is a multiplicative process with an absorbing state
Chicken Road 2.0 by InOut Games is built on one of the most efficient structures in gambling design. A chicken stands at the edge of a road. Each lane it crosses raises your multiplier. At any point you can stop and collect. Cross one lane too many and the round ends with nothing. That is the whole game, and it is worth naming what it is in mathematical terms rather than poultry terms.
It is a multiplicative process with an absorbing state. Multiplicative, because your position grows by a factor each time you advance rather than by a fixed amount. Absorbing, because there exists a state — the loss — from which no recovery within the round is possible. Once you are absorbed, the accumulated multiplier does not degrade gracefully or partially refund. It is zeroed.
That combination of properties is not exotic. It describes leveraged investing, epidemic spread, and a fair number of natural systems. It also has a well-documented and slightly counterintuitive behaviour: multiplicative processes with an absorbing barrier behave very differently from the additive processes our intuition is calibrated on, and the difference is not in your favour. Understanding that gap is the whole of this article.