I always thought a cool chess variant would be quantum chess where you can move a piece to more than one square and assign a probability to each position. Your opponent could do the same. But I never worked out how it could work from there.
If you add probabilistic moves, the optimal way to play would be to give each alternative move the same weight (ie probability) that you think it will win you the game. You would pull this probability out of your mental representation.
Something like, "I think this is the best move, but this one is really good too so I will do it as well".
So I guess it could be fun to be able to try out all the moves you think are good in this way. But then an easier way to achieve this is to just play the game normally and go back to an interesting previous position once you have won.
But maybe a set of rules that will allow you to still win the game 'in retrospect' after all the 'best' moves were played by going through all the alternative superpositions as well.
So basically just play normally, but when you doubt what move is best, you make a superposition (and assign probabilities), which means you will be going back to this position later.
The winner would be the one who won most often, with each win weighed by the probability of that outcome (calculated based on the assigned probabilities along the game).
Sounds like fun.
The game starts with each player having 50 points "in the bank". In addition to moving normally, players may opt to move and split the timeline. If they split, they choose how many points to dedicate to the new timeline, which are put in its bank, distributed evenly between both players. Points must be whole numbers and each timeline must have at least 2 (max 50 timelines). Play continues normally on the original timeline, and they may opt to split again, if they have the points.
When a given timeline is played to checkmate, the winner secures all of their own and their opponent's points from that timeline. In the case of a tie, points are split evenly. First person to secure over 50 points wins.
The game keeps track of the history in each timeline. If one timeline's board enters a state that already occurred in a different board's history, both players are asked whether they'd like to merge timelines, in which case the banks from each timeline are combined and play continues on the board that is farther in the future.
The UI allows players to switch which timeline they are looking at freely So, both players can be playing at once, in different timelines. Initial implementation can show a single board at a time, a number showing which timeline you're viewing, how many points each player has banked in that timeline, and arrows for moving between timelines. Should be pretty easy to add, actually.
Competitive variant is timed. There is a single clock for each player, which counts down by the sum of all timelines in which it is their turn, scaled down by the % of total remaining points in that timeline.
That is, say we're playing 10+10 and there are currently two timelines, one with 20 points and one with 80. It's my turn in the 80 point timeline and yours in the 20 point timeline. While we wait here, my clock ticks down by .8 seconds per second, and yours by .2. Then I play. I gain +8 seconds, and my timer stops while yours starts ticking at full speed.
---
You'll note this isn't quite the original idea; a faithful implementation of that would have a shared pot of points that each player can split arbitrarily (including fractions of a point). But I didn't want to allow infinite splitting because that would make the game unplayably long (or, in timed variants, might lead to optimal strategies of overwhelming your opponent with many splits). And if infinite splitting is not allowed, then I don't want to allow one player to do all the splitting, that's no fun for the opponent.
The one thing I don't like is that this allows the stronger player to reliably win by never splitting and just winning the original board, since it will always have >50 points. This is probably fixable, not going to spend more time thinking about it right now though; this post has taken long enough :)
for extra fun if one board gets to a position that another board already had, the tree could be merged again.
You have to think several turns ahead, in a chess sort of way. But your "best" move may be a low probability move, so you have to weigh that. Same for thinking about what your opponent may do in return.
There exists some optimal play for both white and black, we don't know what it is yet, but someday we might and then chess would be truly solved like tic tac toe.