How to simulate 1/3 probability with coins, and arbitrary probability?

Suddenly I remembered something very interesting.How to simulate a 1/3 probability with a coin, or even an arbitrary probability?
I happened to talk with a friend about how to simulate any probability with a coin. At that time, I thought it was impossible, because the coin has two sides, and the base of the simulation result must be 2^n.
Today, I reviewed a classic conditional probability problem, and suddenly thought that it is feasible to simulate any probability with a coin.
Simply put: tossing n different coins, throwing the re-throwing event A3 and re-throwing, throwing the failure event A2 to judge the failure, and throwing the successful event A1 to judge the success.
In addition, when simulating the probability of base x, you must toss n different coins at a time, and 2^n is greater than or equal to x.
In fact, this is very clear.
Take the probability of 1/3 as an example, toss 2 different coins each time, when all are tails, it is a re-toss, otherwise, when all are heads, it is judged to be successful, otherSituation determination failed.
The proof process is as follows

Then, simulate any probabilityWhat about the situation?