7 ms·
Almost every person who plays the game will see their money decay towards zero as time goes to infinity.
by civilized 3y ago
Almost every person who plays the game will see their money decay towards zero as time goes to infinity.
- falsandtru 3y agoKnowing the time scale is very important.
- chronolitus 3y agobut, 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.