You only win the match vs one player.
You wouldn't carry the points to another match.
The trick / insight / value of the doubling cube is not to offer it too early
(just slightly ahead). If you offer it when just one pawn ahead, then any mistake can turn the tables and you've gone sour on two games not one:
Example, one pawn ahead in a first to 5 out of 9 match against one player:
you offer the double. Now you're playing for 2 games.
You lose a knight, now he's ahead and he can double you back. So you either take the cube and play for 4 games, or you now decline and lose two. Shouldn't have doubled so soon.
Case 2: Your ahead a queen, a knight, and three bishops. You finally offer the double. He declines and the game is over. You won one game. You waited too long, but at least the game doesn't drag out to the bitter end, when he accuses you of cheating because you have three bishops.
Case 3: You're playing a slightly stronger player. You get a knight ahead. You double, hoping he will take it and you win. You hold strong and win, now you're 2 games to zero due to his arrogance.
You only can win the one match. Points don't carry over unless it's not a match, you both agree, and you're just playing dozens of simultaneous games, month after month, year after year.
Then you have two scores: Actual wins vs lose against that player.
And "doubling cube" points.
If you care about both scores, you would need to continue playing to the natural end, but then we're not talking about a player who is irritating to you, rather, someone you enjoy always playing with.
For the stranger, if you agree to use the cube, then let's say the weaker player gets ahead.
He might by chance get ahead, offer the cube, and win "two game points"
So now you have a great incentive for the weaker player to accept a rematch, maybe he'll stay ahead, or maybe the stronger player will come roaring back. Either way, the weaker player has an advantage which he may desire to see through. Let's say he wins game #2, now he's got 3 points.
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Bottom line, the great joy of the cube is learning when, exactly to offer the cube, and when to decline. Being a game down - or ahead - in a best of 7 game match changes the risk.
It requires you to know yourself, your abilities, how likely you are to blunder, how likely you are to martial your position to a victory, etc.
It could be especially rewarding to someone who understands board position values. Let's say you have a pawn on the 6th or 7th rank, and the guy offers you the cube because you're down six pawns. You take the double, and pass the pawn, getting a queen, thus being 3 pawns ahead, now you might double back.
I got to double back, my friend.
The only way to find, what I left behind
I got to double back again, double back again.
- ZZ Top, Recycler
It makes sense in chess for a head-to-head match where you are going to play multiple games against the same opponent and it's the first to a particular score. You could offer the cube and if accepted it's double the stakes.
Not sure how it would work
1. If the game finished drawn
2. Round-robin tournaments - would be unfair on the other players if our game is worth a lot more than normal.
3. Team matches. Might be ok but not sure. Could limit the game to 4 (one double each).
Players would just pass the cube back and forth a quintazillion times to have a 8000+ rating after 1 game.