7 ms·
but, since it is somewhat like a random walk, isn't it guaranteed that if you go on for infinitely many tosses, at some point you will be very rich? [1] https:
by chronolitus 3y ago
but, since it is somewhat like a random walk, isn't it guaranteed that if you go on for infinitely many tosses, at some point you will be very rich?
[1] https://math.stackexchange.com/a/493446 https://math.stackexchange.com/a/493446
- chronolitus 3y agoif true, an interesting question is - on average - how many tosses are needed for you to reach some arbitrary value (e.g. $1M)?
- civilized 3y agoIt's exactly like a random walk... with downward drift. If you take the log of the wealth, the steps are: log(1.5) = 0.18, log(0.6) = -0.22. So at each step, there's a 50% chance you go up 0.18, and a 50% chance you go down 0.22. Random walks with downward drift don't inevitably go up arbitrarily high like ones without drift.