I’m being a little presumptuous with the “official”, but I think I’ve developed a fun game with the trappings of AB that’s at least moderately engaging for the adult mind and could be played with members of the community.
I call it Abagammon. (Littles are allowed to freely degrade the name to Aba-Gabba at their discretion. Bigs are free to correct them and discipline them for impertinence.)
You sit opposite a ten-row abacus (commonly a “school” abacus… Mellisa and Doug makes a nice one) arranged with five beads pushed to each side on every row. You roll two six sided dice and “give” (move left to right) your opponent as many beads as the dice say, separately or added. You have to give exactly the number on one die or both added, and you forfeit dice for that turn if there is less than that value on open rows. Once you give all the beads on a row, it’s cleared and can’t be given away, unless the roll is a double, in which case the doubled value can be given from a cleared row, reopening an otherwise safe row.
Examples: If you just started the game, rolling a five and a six would let you give one row of five to your opponent and clear that line for you, but you can’t use the six because there is no open row with at least six. Play passes to the opponent who rolls double threes. They use it to break the row you cleared by moving three beads off it, instead of moving three-plus-three beads on open rows.
The game ends when all rows are cleared to one side or the other. The player with the most cleared rows wins. Ties are explicitly deemed “everybody wins”.
The game is expressly designed to be played as a game of generosity and sharing, and playing it in a manner where you steal beads from your opponent is considered offensive and contrary to the spirit of the game.
It could evolve into a game that’s played at community gatherings or an activity for DD’s to teach their LG’s. Substitute a large bead rollercoaster table for added fun and littleness.