I don't know how to format a table, but here is what I want the game to be:

A-action B-action A-winnings B-winnings

• 2-box 2-box $1 $1
• 2-box 1-box $1001 $0
• 1-box 2-box $0 $1001
• 1-box 1-box $1000 $1000

Now compare this with Newcomb's game:

A-action Prediction A-winnings

• 2-box 2-box $1
• 2-box 1-box $1001
• 1-box 2-box $0
• 1-box 1-box $1000

Now, if the "Prediction" in the second table is actually a flawless prediction of a different player's action then we obtain the first three columns of the first table.

Hopefully the rest is clear, and please forgive the triviality of this observation.