# Newcomb's Paradox

**URL:** <https://www.thephilosophyforum.com/t/newcombs-paradox/298>\
**Category:** Logic & Philosophy of Mathematics\
**Created:** [March 11, 2026, 3:09am UTC](https://www.thephilosophyforum.com/t/newcombs-paradox/298 "2026-03-11T03:09:32Z")\
**Posts on this page:** 1\
**Showing post:** 367

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**Author:** ![Michael](https://avatars.discourse-cdn.com/v4/letter/m/4bbf92/32.png) [@Michael](https://www.thephilosophyforum.com/u/Michael)\
**Post date:** [March 13, 2026, 7:08pm UTC](https://www.thephilosophyforum.com/t/newcombs-paradox/298/367 "2026-03-13T19:08:22Z")

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The four games in their simplest form are:

**Game 1**

1. There is an empty red box and an empty blue box
2. $1,000 is placed in the blue box
3. If you are predicted to choose only the red box then $1,000,000 is placed in the red box
4. You are asked to choose between either a) the red box or b) the red and the blue box
5. You win the contents of the box(es) you chose

**Game 1.5**

1. There is an empty red box and an empty blue box
2. You are asked to choose between either a) the red box or b) the red and the blue box
3. $1,000 is placed in the blue box
4. If you were predicted to choose (a) then $1,000,000 is placed in the red box
5. You win the contents of the box(es) you chose

**Game 2**

1. There is an empty red box and an empty blue box
2. You are asked to choose between either a) the red box or b) the red and the blue box
3. If you chose (a) and were predicted to choose (a) then you win $1,000,000
4. If you chose (b) and were predicted to choose (b) then you win $1,000
5. If you chose (a) and were predicted to choose (b) then you win $0
6. If you chose (b) and were predicted to choose (a) then you win $1,001,000

**Game 3**

1. There is an empty red box and an empty blue box
2. You are asked to choose between either a) the red box or b) the blue box
3. If you chose (a) and were predicted to choose (a) then you win $1,000,000
4. If you chose (b) and were predicted to choose (b) then you win $1,000
5. If you chose (a) and were predicted to choose (b) then you win $0
6. If you chose (b) and were predicted to choose (a) then you win $1,001,000

These games are equivalent. Whichever is the most rational choice in Game 3 is the most rational choice in Game 1.

I introduced the clone (which thinks itself to be the participant) as an example of how a near-perfect but fallible prediction could be achieved, and to show that the game ought be assessed in terms of game theory. We can state Game 3 as:

**Game 3**

1. There is an empty red box and an empty blue box
2. An exact copy of the participant is created (who does not know that he is a copy)
3. The participant is asked to choose between either a) the red box or b) the blue box
4. The copy is asked to choose between either a) the red box or b) the blue box
5. If the participant chose (a) and the copy chose (a) then $1,000,000 is won for charity
6. If the participant chose (b) and the copy chose (b) then $1,000 is won for charity
7. If the participant chose (a) and the copy chose (b) then $0 is won for charity
8. If the participant chose (b) and the copy chose (a) then $1,001,000 is won for charity

The participant (and the copy) is aware of the above. It is almost certain that the participant and the copy will reason the same way and make the same choice. If we accept that they make the same choice at least 99% of the time then:

1. At least 99% of (a)s will win $1,000,000 for charity
2. At least 99% of (b)s will win $1,000 for charity
3. At most 1% of (a)s will win $0 for charity
4. At most 1% of (b)s will win $1,001,000 for charity

The expected return for choosing (a) is at least $990,000 and the expected return for choosing (b) is at most $11,000.

This is true for all four games.

As such, all rational participants across all four games ought choose (a).

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