But let's say that you hate it when C-3PO tells you the odds, so you commit to Game 2 because you like the upside potential of $15, and you think the potential loss of $5 is tolerable. After all, Han Solo always beat the odds, right? Well, before you so commit, let me encourage you to look into my crystal ball to show you what the future holds…not just in one future, but many.
Here's what we see. For Game 1, the accrued earnings range from ~$4,500 to ~$5,500 by the 1000th step.
But take a second look. That second-from-the-top band for Game 2 converges on the second-from-the-bottom band in Game 1. These are the upper and lower 5th percentile bands of the outcome, respectively.
So it is in the fantasy of Hollywood that the mere mention of long odds ensures the protagonist's success. Unfortunately, life doesn't always conform to that fantasy. Over a long time and many repeated occasions to play risky games, especially those that afford little opportunity to adjust our position or mitigate our exposure, EV tells us that our potential for regret increases for having chosen the lesser valued of the two games. Depending on the relative size of the EVs between the two choices, that potential for regret can occur rapidly as the inherent outcome signal implied by the EV begins to overwhelm the potential short-term lucky outcomes in the random noise of the game.
So how can you know when you will be lucky? You can't. The odds based on short-term observations of good luck will not long be in your favor. Your fate will likely regress to the mean.
(This post was also simultaneously published at the Lumina Blog.)