The Angel Problem [Game Theory] -

The Angel Problem [Game Theory]

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Like: 162566
A fascinating Game Theory problem proposed by John Conway.

Original Paper:
2-Angel Proof:

Bass Loop – Wooseong


  1. why the hell was this in my recommended

  2. What if the devil manages to go far enough to give him the time to make a giant square around the angel, making the space where the angel can go NOT infinite and allowing himself to slowly take away all the spaces?

  3. The angel only wins if the devil is stupid. You start an arbitrarily large distance away, do as to be able to construct an impassable trench. You encircle the angel thusly, and are free to narrow the area by creating more trenches bisecting the remaining are the angel can move in, into equal parts for efficiency as the angel can move between the soon to be bisected areas until completion.

  4. eh eventually the angel'll screw up and get trapped, even if it does take a century.

  5. since there is infinite space, the devil can build a wall very very far out and easily win in that way well maybe not easily but not that hard either

  6. I have no idea what this is. I've never seen this channel before. It's 12:57 am and I'm exhausted but the algorithm has spoken and I shall watch every second of this.

  7. so i guess the angel can just move faster always to escape the "death box" no matter how far out the devil starts it?

  8. The angel easily wins due to the fact that it's infinite, and you could just always go 10 in one direction forever

  9. But remember it’s just a theory, a game theory!

  10. This seems like a problem only if you overthink it. The point it becomes a problem is when you assume "it's as if those squares have already been blocked". They haven't though. As he describes it, it makes it seem like the devil gets 2 turns for each of the angel's turns, which is false. Just eyeballing it, at no point should the angel have more than a couple of blocked squares in its movement grid to stay ahead indefinitely (but I didn't need a math degree and several years to figure it out). There are legitimate math problems that require complex solutions. This is something I expect a preteen would be asked to solve in school. Am I crazy?
    Edit: after reading most of the comments here, I see that I'm not alone 😀 . You wouldn't know it by the amount of likes the video has.

  11. Ummmm am I the only one who doesn't get anything

  12. Ok but what if the angel just stays still?

  13. There's an old flash game of with this idea on a super small scale. It's called Block the Pig, you play as the devil, the pig is the angel.

  14. This isn't a game theory problem It's something you would never find yourself in a position to have to solve.

  15. So, in other words, if I ubderstood this right, if the devil can win depends on if the angel is stupid enough to not move back to previously used space

  16. The devil can always win over a period of time there is no way the angle can win if the devil starts out far enough and boxes the angle in going all around in a giant square then goes 5 past

  17. I know a game that works like this, instead of an angel there is a cat and the goal of the game is to capture the cat. The map is small and instead of squares there are circles and the cat can move one circle in each turn, but the idea is similar

  18. -States the angel can win
    -Refuses to elaborate

  19. Ok, but y doesn't the devil make a huge box around the angel, too far away to cross through before it’s finished. Cus then the devil can just fill in every space inside the box, winning every time.

  20. If the devil starts blocking from an infinite number down to the angel ?

  21. It is literally 4:30 in the morning and I haven’t slept. Why am I here?

  22. ok but what if the angel just doesn’t move at all

  23. There is an obvious and possible way for the devil to always win if the grid Is infinite just build a shape around the angel that can be built before it gets to the edge that blocks it from leaving and fill in every space within it. I just submitted the answer before seeing the video before the concept.

  24. I think the devil and angel just make up and kiss

  25. But the real question is, can the devil land on the angel?

  26. All the devil has to do to win is a square strategy just go far enough away and make a unjumpable square then you win over time

  27. If the Angel can’t move I guess that’s a win for the Devil, but there’s no solid win condition for the Angel. I feel like there’s an allegory there about not being able to overcome sin, but that’s not the point. If there’s not a way for each side to win, the thought experiment isn’t complete enough to run. Not to mention that if we’re on an infinite grid, of course the Angel can avoid capture forever, that’s kind of the nature of infinity.

  28. The devil should be able to build a wall infinity away from the angel then simply feel everything inside. It would take literally infinity but he should be able to do it

  29. Well actually I was gon comment about how stupid this was
    But suddenly I started thinking about how the devil could defeat the angel
    Now I have a huge math problem I can't solve cause I dropped out and only know 2+2 is 3

  30. But couldn't the devil just make a wall at an astronomically far distance so the angel would be trapped in a container the devil built

  31. Why couldn't the devil just start building a 10×10 wall incredibly far away from the angel, so that the angel couldn't physically get over to the wall until it was complete. After that the devil would just slowly shrink the area, eventually winning no matter what.

  32. Or hear me out go to the corner block every single time

  33. The angel be like
    Okay, there is a way to escape if i go this way however I could have reached that place earlier so if I go there now I will have wasted steps which can't be so I guess I'm stuck now.

  34. How to trap the angel: move 1000000 spaces away and build a big wall, circling a big erea (make sure that its big enough so the angel can't break through it) now just slowly start filling the square until she can't move. Time consuming, but effective.

  35. Why do people use the pronoun "she" for angels in english? I thought they had no gender?

  36. The devil can always win if it’s over infinite turns and infinite space. All the devil has to do is make a wall k thick at a place that the angel cannot reach in time, and then fill in the rest of the wall.

  37. The Devil could easily go far far away and start building a square wall and keep building it towards the center, creating a perimeter and expanding it. At the time the angel arrives the wall will be big enough to keep him locked inside the square closed area, then the devil will keep blocking cells until no more moves can be made inside the square.

  38. couldnt the devil just build 4 walls, k wide, far enough away that even if the angel went directly there they couldnt reach the wall in time to make it through, and then the devil just fills in from there, eventually ending up blocking off the angel fully?

  39. Infinite time and space, correct? Devil goes like 3 billion blocks out, completely walls off the square the angel is in with no way out, then just shrinks it over however many years. Eventually, the Devil wins

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