I always play on the web version. I refresh the page and then click the game button.
Could you go into more detail about how match making works?
If I run the game a good 40 times right now, does that mean each of those teams is in the pool? How does it decide if I'll encounter them?
Is there any sort of special exceptions for teams that have lots of draws? That's actually probably a factor in this. I play with risky strategies and often double KO the last foe, so I end up playing more games than average.
Does that have anything to do with this?
The primary matchmaking system is that the game queries our server looking for a team that: has the same number of rounds/hearts/wins, is in the same room, and is not the team you just played in the last round. Both versions work the same way in this respect.
If this lookup fails, then the exe version actually has an extra step. When you launch the game, it creates a cache of a few hundred recent teams, and looks for a match among these as well. This is mostly to allow offline play, which is why the web version doesn't bother, as it's kind of an expensive operation, but if there's not a lot of teams uploaded yet then this can happen frequently.
There's also a third condition if it's not able to find a team this way (which should only really happen on the web), where it falls back to a cache of teams that is included in the game build (one purpose of this is to ensure that if the game servers are ever shut down, or you're playing an offline version that has never connected to the internet at all, the game is still playable).
Finally there's a fallback where it creates a fake team, which will have a name starting with "The Fake ..." and you won't see their stats displayed. This is mostly for development purposes so that an opponent can be created when I increase a version number for the first time, but a player could technically encounter it if they're the first to make it to very late rounds in the game where there's no other teams to match.
The primary matchmaker system shouldn't ever give you the same team twice, so it's likely that you're falling into the third condition if you're playing on the web. Since there's not a lot of data there, it makes sense you'd see the same teams repeatedly. Once there's more data from people playing the game, this problem should fix itself. If you happen to see the issue again, take note whether or not the wins & hearts of your opponent exactly match yours. If they don't, then you've fallen into one of the backup conditions.
Regarding having a lot of draws, there's no specific handling of this, but the later your round number gets, the less data there is to match you against, so it's also far more likely to fall into the backup conditions where the matchmaking is less good.