On our first game we had an Amoeba which managed to gain its own Super Flare (we are thinking of playing without Flares now) and this enabled him, if I recall correctly, to move as many ships as he wanted to. Even when he was Allying, which then allowed him to send in, say, 10 or 20 ships and receive that many cards if the Defense won compensation. That made most other players feel that there was just no way to fight against the Amoeba anymore.
Technically, this seems to have been played correctly. As others have mentioned, significant combos/advantages like these are the instances in which the *players* need to react appropriately in their own best interest. Super Amoeba isn't nearly as powerful as it might seem, especially since the Super Flare really only gives the advantage while allying. So, eventually players should just stop inviting him to ally. There are other limitations to consider as well. One is that if the Amoeba gets too excited and removes his last ship from a colony, he immediately loses that colony and has to wait to have an appropriate encounter to reclaim it. So really, Amoeba only has a number of ships his disposal equal to "living ships" (not in the Warp) minus the number of colonies he has. And if he pulls away from his home system, remember that less than 3 home colonies immediately nulls your alien power.
Also, his mobility makes Amoeba good on attack but can leave him sapped on defense if not careful. His power lets him move ships either *into* our *out of* the current encounter but he can't otherwise redistribute his ships beyond the normal means.
And like all Flares, if the Super Amoeba is Card Zapped or if Amoeba runs out of Encounter cards, the Flare will leave play, making it a significant-but-short-lived advantage. Also, after the first time it's played, everyone will know he has it…so react accordingly.
Our latest game had a similar situation as we had a Remora that had picked up the Clones Flare and now could recycle Artifacts back to his hand. This enabled him to play a card which let him sacrifice a single ship and then send all Attackers to Warp, win or lose. And since he was the Remora, at the beginning of the next players turn he even got that single ship back from the Warp. We thought that we could have tried to Card Zap that Artifact out of his hand until we realized that one of them was in the hands of the Remora and the other one had just been discarded, which meant that we'd have to play at least an hour until we could get it.
This seems legitimately played as well, though I'm not recalling the exact Artifact that you are referring to at the moment. Again, what keeps this from being too unstoppable is a) when Remora runs out of Encounter cards, he discards his hand (including Wild Clone and the Artifact) and b) after the first time, players and allies should hesitate to throw many defenders against Remora to mitigate potential losses. Even better, play Negotiate against Remora and hopefully steal some of those cards from his hand…then use them against him as payback!
My friends are now calling the game broken as it allows bizarre and uneven combos that totally out-plays all other players. I am not personally totally against this but most of my players seem to be. Are we doing something wrong, are we just lucky/unlucky to have situations like that or is this exactly as it's supposed to be?
The first reaction of one of my friends to Cosmic was a blunt, bold-faced "This game is broken!". He may be right in a certain respect but the game is really more clever than that. Cosmic Encounter is a game where the *unwritten* rules are the most important ones. It's about the player more than the game. By that I mean, it's not the cards and powers themselves that really light up the experience, it's knowing how, when, where and why to use them or not use them that drives the true strategy of play. And that strategy is deep, tense and wonderfully engaging. Knowing when to invite allies and exactly who to invite is a huge part. Keeping careful track of the behaviors of your opponents and what cards have already hit the table. It's true that new players have an overwhelming tendancy to invite too many and too often. After you and your friends pick up on some of these subtler nuances, you'll see the real strategy that evolves from good game of Cosmic.
I'll say that the game does have a "learning curve". Not regarding the rules but rather all the strategy that exists inbetween them. If you can get your players to see this aspect of the game, you'll probably find much greater enjoyment.
Best of luck!