I have been dreaming of an initiative system for a while, I'll explain below and feel free to use and abuse it. If I was designing a big boy system right now, I'd totally employ this.
So, instead of an initiative score, initiative is a resource.
There are no turns, but combat happens by each character and monster on the board "bidding" their initiative resource to take an action. Something like this --
>Assume, for purposes of example, everyone has 10 initiative
>Player 1 sorta wants to go right now, but isn't super worried about it.
>Monster 1 also wants to go
>Player 1 bids 2 initiative
>Monster 1 responds by raising, bidding 3 initiative
>Player 1 doesn't want to raise to 4
>No one else bids, so Monster 1 gets to take its turn
>Monster 1 moves and attacks Player 1*
>Player 1 tries to defends, fails, takes damage**
>Action has been resolved, so another bid takes place
>Monster 1 has 7 initiative left, Player 1 has 8 left
>Now that Monster 1 has attacked, it is vulnerable, so Player 1 really wants to go
>Player 1 bids 4, Monster 1 doesn't raise because it doesn't want to spend more than half current initiative
>Player 1 wins bid, attacks Monster 1, deals damage***
>Monster 1 has 7 initiative, Player 1 has 3 initiative
This goes on until no one has enough initiative to take an action, or no one wants to. Then, the "round" flips and everyone's initiative fills up back to max. Repeat until there's no more combat to do.
* You can build little mechanics in. For example, you can say that you have to bid minimum of 1 initiative in order to "move," and something like 1 more (for a total of 2) to additionally "attack."
** Here, Player 1 has a chance to defend the attack because he bid (even though he lost), so there's benefits for trying to win the bid and having to lose some of your initiative points
*** Here, Monster 1 didn't bid, so it doesn't get a chance to defend, it just takes the damage
>To be continued... character limit