Imagine you have a random number generator that outputs 1, 2, or 3 with equal probability. You repeatedly draw numbers from this generator. You decide to stop the experiment as soon as the product of the current draw and the immediately preceding draw is 4 or greater. What is the expected number of draws until you stop the experiment?

你正在进行一个实验。假设你有一个生成器，每次能等概率地生成数字1、2或3。你重复操作生成器，记录下每次生成的数字。你决定在满足以下条件时停止实验：当前生成的数字与紧邻前一个生成的数字的乘积首次达到或超过4。请问，你期望进行多少次操作才能停止实验？