The Time Traveler's Profit Maximization Guide

Ivan Vanchev

Tuesday, May 20, 2014

A couple of weeks ago, I came across an interesting discussion on reddit (as I so often do, several times per day), regarding a scenario in which one is allowed to send a 1GB flash drive 5 years back in time to oneself. The question posed was what would one put on it. Predictably, the majority of the debate revolved around people wanting to provide themselves with easy earning opportunities by sending back lists of lottery-winning numbers and stock market data.

Now, I have gotten quite used to a certain fashion of looking at outcomes of random draws in terms of their underlying probability distributions. So this got me thinking whether in a statistician's eyes having this miracle information from the future would actually have any impact on the outcome of a random draw at all (if we assume a lottery draw is such). Can an event be independent with itself? After all, if we roll a die twice and get a \(6\) both times, these two events are considered independent. Would it matter if the second draw was just a re-occurance of the first one? It seemed to me that statistically having knowledge of a random draw's outcome would really not provide you with any useful information, as the draw would be once again random once you observe it. This was getting a little too confusing for me, so naturally I decided to bring it up with Plamen and try to confuse him too.

Ivan Vanchev: So, I was reading through this reddit post, and it got me thinking...

Ivan Vanchev: Would lottery number drawings actually be the same from the point of view of your future self?

Plamen Ivanov: Hmm...

Plamen Ivanov: We get into a strange place.

Ivan Vanchev: Yes.

Plamen Ivanov:

  1. time travel
  2. stability of events in time travel
i.e the first drawing will likely be correct. The second less so...

Ivan Vanchev: But even the first one...

Plamen Ivanov: ... with some progressively lower chance of the same outcome as you change things.

Ivan Vanchev: These are all random variable outcomes.

Ivan Vanchev: What ensures that we'll get the same outcomes twice?

Plamen Ivanov: Depends on the time travel you subscribe to.

Ivan Vanchev: Indeed.

Plamen Ivanov: But imagine there is a sting of non-predictable things, and you knew what those were by observing them. You still can't predict them really...

Ivan Vanchev: Exactly.

Plamen Ivanov: ... but you could show someone what they "will be". So, my point is that there is no reason for those things to change.

Ivan Vanchev: Maybe not for stock prices...

Plamen Ivanov: ...unless you made some disturbance which changes their initial conditions.

Ivan Vanchev: ... but for random draws?

Plamen Ivanov: Well, it depends on whether a time travel event "resets" the random number generator.

Ivan Vanchev: What ensures that the draw you saw 5 years ago will be the same if you go to observe it again? That was precisely my question. Does it reset? Does anything in physics address this?

Plamen Ivanov: It is not the draw from 5 years ago; it is the same draw. You just had the chance to observe it.

Ivan Vanchev: Well, in a fair draw all draws are the same draw in a way.

Plamen Ivanov: i.e time travel, which generally seems impossible, so if you can resolve it...

Ivan Vanchev: Ignore the time travel problem.

Plamen Ivanov: ... you likely can answer the question of random draws.

Plamen Ivanov: eee

Ivan Vanchev: As in, assume you can send the data back in time.

Plamen Ivanov: Then I can assume the random events (regardless of how random) will be the same as long as you do not change things in their light cone of causality.

Ivan Vanchev: Fair enough I guess. If the conditions are physically the same, you are likely to get the same draw.

Plamen Ivanov: The thing with that is that there may be some unpredictable process which connects the two events (me receiving the data and the random chain of events generating the data). Well, the conditions which directly affect the draw.

Ivan Vanchev: Yes, and you placing a bet on those numbers adds another new event.

Plamen Ivanov: Eh, but one would assume that buying a lottery ticket doesn't affect in any way the actual draw.

Ivan Vanchev: May be, may be. Too many variables to predict, though.

Plamen Ivanov: This is another probabilistic thing.

Ivan Vanchev: Mhm. It's a curious topic.

Plamen Ivanov: I am only saying the likelyhood will be very very small.

Ivan Vanchev: Yes.

Plamen Ivanov: For the first draw, you'd likely have a reasonable probability of identical outcome. And it will decrease as you keep doing things which are not as you would have done them. Your perturbance keeps creating more and more changes.

Ivan Vanchev: Winning the jackpot in week \(x\) instead of week \(x+1\) changes everything afterwards it seems

Plamen Ivanov: Well, winning the jackpot vs not winning it. But mine is another case - \(x\) people win. Now you win too, so \(x+1\) people win the jackpot.

Ivan Vanchev: Yeah.

Plamen Ivanov: This may still not affect the next draw, but it seems that eventually you will affect something.

Ivan Vanchev: That's a better bet probabilistically at least in the short-to-medium term but smaller payout for you potentially vs. choosing to win one big jackpot only and not bother with less probable future lottery drawings. So which scenario would you want to recommend to your past self? We need to check the numbers.

Plamen Ivanov: Then there's the stock market - much lower chance of me making an actual splash. That's what I'd send to myself.

Ivan Vanchev: The stock market is a different problem. You could still set off automated trade algorithm responses to your actions if you're not careful.

Ivan Vanchev: emi you can still set off automated algorithm reactions if you're not careful

Plamen Ivanov: Someone suggested using a lottery win to get initial capital and then playing on the stock market. So, next thing for me would be to get a few books on stock markets and how to minimize my own effect on the market.

Ivan Vanchev: Easy. Play small.

Plamen Ivanov: Well, yes. However, I am sure there are other things which are more complicated than that.

Ivan Vanchev: Sports events may also be nice opportunities, as long as we assume no player involvement in game fixing.

The discussion trailed off at this point as it so often does when discussing interesting problems. What should we put on the 1GB time-travelling flash drive? I think Plamen nailed it in his answer toward the end. I would also probably have included all my writing assignments and problem set answers for the last five years. Just throwing the idea out there...