Applications of an undo button?

Let's say I have an undo button. It works as follows:

• I enter a number $N$
• The device splits the universe into $N+1$ possibilities
• In one universe, the device outputs "Fail"
• In all the others, it outputs a different number from $0$ to $N-1$
• If it outputted a number, after some time, I can press either "keep" or "undo".
• If the neither "keep" nor "undo" is pressed forever, then it defaults to "keep".
• If it outputted "Fail", it defaults to "keep".
• All the universes that resulted in "undo" are destroyed, and a random "keep" universe is kept.
• In particular, if in every number universe, "undo" was pressed, the "Fail" universe is kept.

The device is basically free to use.

Somethings to note:

• If I get "Fail" due to random chance, I can keep retrying until I get a number.
• Of course, I will never get a number if every number causes an "undo".
• There is only one of this device.
• You can not run another experiment while it's running.
• The different universes have literally no interaction.

What could this undo button be used for? The two ideas had so far is search and rescue (go to a location based on the number, "undo" if the person isn't there, keep if they do (if you get "Fail" repeatedly, they are completely missing)) and the stock market (choose a stock based on the number, if it goes up "keep", if it goes down "undo"). If think there are much broader applications though.

Essentially it outputs a number from $0$ to $N-1$, and if you don't like the number, you can undo it.

Another interpretation of the device is to say it picks a random number from $0$ to $N-1$ (or "fail"), and when you hit "undo", it reverses time and picks another number (or "fail").

• Comments are not for extended discussion; this conversation has been moved to chat. Please edit any clarifications from the comment thread into the question. Commented Jan 20, 2016 at 3:19

You'd probably want to set it up as an experiment each time you use it, even if only mentally, and where the Fail message is the control group.

Say I want to go sky diving, but don't want to die. So I set it for N=1.
One me is going to get the 1, and one me is going to get the fail.
Me=1 goes sky diving. If I=1 dies, you have a friend push the undo button.
Me=Fail does not go sky diving.

Every experiment I would decide what each number will do, and what Fail means.

Gambling stops being a gamble.
Each N is a number on a roulette wheel. Or a horse. Or whatever.
Fail doesn't place a bet.

10 me's duck out of work early to see a movie. 4 are caught for various reasons , are fired, and Undo. 1 me Failed and never left.

One interesting thing about this device is that there is going to be a version of me that only gets Fail, every single time.
Odds of winning the powerball are one in 175 million. So I make N = 175 million. One me is winning, and 174,999,999 me's are not, but Fail never places the bet.

How long would you go on pushing the button, when it always shows fail?
Say you eventually give up?
Doesn't matter, because there's another you that got a Keep 1 time, and it's Failed every time after that.

UPDATE: I've just properly figured out what this means. I'll try and update this with usage examples.

How non-trivial do you want to keep this? Seriously, this could be used for literally everything.

• What way should I drive home from work? (Time to destination)
• Should I ask that girl out or will I be rejected? (Yes/No)
• Is this food going to make me sick if I eat it? (Yes/No)

You could use it to find out whether any venture would be successful before you try it. On a more serious level, Governments could use it for:

• Finding out whether a policy would have a positive or negative affect.
• Gauging public response to a policy
• Whether to go to war
• Whether to dig for oil/any mineral of your choice

Again, literally endless. The only problem would be deciding how many of your life's decisions you were going to use it on, and how to psychologically deal with leaving some things to chance, given that presumably it would suck the enjoyment out of life to be constantly using it all the time.

• As for the food example, if it outputs "No", what do I do? Do I press "undo" or "keep" (how do I know if it was right?) (I assume you are using $N=2$, with $Yes=0$ and $No=1$. Correct me if I'm wrong.) Commented Jan 19, 2016 at 16:27
• Hmm. I think I've just understood something about what you're saying. Basically, if I say N=2, where Fail = It makes me sick, 0 = I don't eat it and thus don't get sick and 1 = I eat it and it doesn't make me sick, If I get 0 first up I have no guarantee that I will not be stuck with "fail" if I don't hit "Keep"? In which case I'd hit Keep, probably, and be conservative. Commented Jan 19, 2016 at 16:34
• The problem is it could output $0$ even though the food is fine. This is still better than nothing, but not perfect. (I think there is a better way to do it though, maybe with multiple tests). Commented Jan 19, 2016 at 16:37
• (Also, keep in mind you can't undo "Fail" (this prevents someone from undoing every possible universe).) Commented Jan 19, 2016 at 16:38
• Yeah that's what I realised. As I said, I'd probably go for the conservative option. It would depend on the risk/reward ratio. There is a better way you could do it, by flooding the system with "acceptable" possibilities (I eat it and only feel a bit queasy after, for instance), that would increase the probability of getting a random result which involves you getting to eat it. It's going to depend on how long it takes to set it all up though, and how important it is. For a trivial decision, you're not going to want to spend hours getting the best possible solution. Commented Jan 19, 2016 at 16:41

Let's see if I can make what you're saying make more sense.

Entering a number effectively tells you how many "retries" you get. When you enter a number on the device, you choose what event you will be affecting - numbered locations, stock market fluctuations, randomly assigned IP addresses, whatever. For example, if you're looking for the best route home, you could enter 3: 0 for the Highway, 1 for Rocky Road, 2 for Smith Lane, and 3 for whatever fail would be - presumably, not making it home in any situation. You decide that when you reach home in under 15 minutes, you'll push "keep." You push the button, and the universes are created. In universe #1, you arrive in 14 minutes, 8 seconds, and push keep; in universe #2, you arrive in 12 minutes, 57 seconds, and push keep; in universe #3, you arrive in 22 minutes, and push undo. The device randomly decides between #1 and #2, resulting in you choosing to take #2, Rocky Road. This results in an acceptable time home.

What this means is that anyone who holds the device will always make the best decisions. Rather than an "undo" button, this is a probability reducer; given the probability of any timed or yes/no event, it will automatically present the best decision, regardless of the probability of that outcome. For instance, the odds of rolling a 6 on a standard die is 1 in 6; however, by entering a suitably large number - say, 100 - and deciding to press "keep" if you roll a 6, and undo otherwise, you are guaranteed to end up with a 6.

Probability simply goes away. All events that are possible become equally probable, for a large enough number of retries. Which is pretty terrifying. If the device were hooked up to a machine able to calculate the probability of any event quickly, it could effectively control time. Any event where there is a non-zero chance of something happening, the computer and device could make that happen. As long as the machine could reduce an event to a distinct number of outcomes (even if that number were huge), it could create that version of events.

• You don't tell the device what event it is affecting. You could write it down if it helps you remember. The device works no matter how use the numbers. Assigning it events is just the most convenient use case. Also, it isn't the first keep, but a random keep. (So you could do "get home in under 15 minutes".) Commented Jan 19, 2016 at 17:39
• Ah, ok. That makes sense. I'll edit my answer to reflect that. Commented Jan 19, 2016 at 17:45