crowded anti backgammon - I do not know if that would be a very good game since anti-backgammon is not very popular, I personaly don't think crowded anti backgammon would get too much play either.
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Some of my new "gammon" game ideas:

1. Dark Backgammon Race (or Regular/Nack/Crowded?)
- Basicly just like regular backgammon. You don't see ANY place that you don't have your own piece, so you will never be "blocked" and allowed to move to any place.

Now when you move to a place that is open, your piece stays there. If you move to a place that only has 1 opponent piece, you take it like normal gammon. If you move to a place that has 2 or more oppenent pieces, your piece will be placed back to the bar like it was taken out.

So this game would involve a lot more strategy - making you want to set up many places of 2 or more pieces to take away your opponents pieces when they land on you.

I believe this would be better as Dark Backgammon Race. Also I'm debating if it would be good to hide the opponents dice or not.

2. Backgammon Attack.
- Basicly it is the same as Backgammon, but with the rule that you can also win once you land and move your oppenets piece to the bar for the 10th time. I also think this would be good as Backgammon Race Attack - since then you could try to keep many of your own pieces in your own bar to come out and "attack" unprotected pieces that have been places in your area.

3. Domino Gammon - Basicly instead of dice, each player will have 3 domino's, and can choose which domino to use for their next move, in which the domino that is used is replaced with a new domino. The other player can see your domino, so you can plan ahead since you know the 3 possible "rolls" the other player will have. (With other minor rules like if a player is stuck on the bar, they can change all three domino's)