3 Blind Mice Card Game

Has anybody beaten 'Three Blind Mice,' the crescent shaped level where you have to use Reconnaissance cards to see how many armies the AI has? It seems impossible to overcome the substantial bonus deficit, to say the least of the fog situation.

I'm doing it currently, I'll let you know if I find a way.

the best idea is just to play 2-3 games and review yourself what the behaviour of the emeny commanders are, that way you could easily find them and just eliminate them. This is just a tactic you can use for many of the campaign levels so just keep that in mind.

Yes, I just played three games - won on my third try. Here's how to do it:
The AIs very quickly raise their income above yours, so it's impossible to expand against all of them at once. In the south, just get the Lizard Tribes bonus and the two territories beyond it called Manticore Lairs and Drake Hills This stops AI 1 from getting those two large bonuses, and it's fairly easy to defend, so this effectively knocks him out of the game, because the two other AIs have larger income. Take the island in the middle and slowly build there, but don't attack the eastern part just yet, because AI 2 and AI 3 use up a lot of income on each other in that region by fighting. Your main offensive should be in the north. Send your general and build up a a lot of troops there, and just sweep across. Because almost your entire force will go here (other than just a few defenses in the island and in the south), AI 2 cannot defend well enough, and eventually it will just give up. Once you've got to Green Elf Principality, you've won. At this point, you can start expanding from the island and in the south, as your income will be much higher than the AIs'.
Hope this helps :)
EDIT: Make sure your front line is water-tight, don't leave any 0's on your border.
Edited 6/17/2016 14:25:42

Took me about 3 or 4 tried but yeah, north is the way to go. I find the AI won't aggressively attack the island holding nor the south if you hold 2 border regions. Keep your numbers up to about 10 and drive hard on the north.

the best idea is just to play 2-3 games and review yourself what the behaviour of the emeny commanders are, that way you could easily find them and just eliminate them. This is just a tactic you can use for many of the campaign levels so just keep that in mind.

I fully agree with wakanarai, it's the best advice for this level and for many others.
After failing my first attempt(I tried to expand everywhere, it didn't end well), I looked over the history and checked where the enemy commanders hid. Then instead of focusing on expansion, I tracked them down one by one with the cards and this is how I won on my second attempt.
You don't necessarily have to play this level like some others, where you need to take every territory on the map to win. Just find the commanders and kill them. When I reached the last commander, I believe the AI had 10 or 20 times my income. But it didn't matter, since I just needed to kill the commander to end the game.

Not surprisingly, rakleader is correct. Cut through the middle with a hunter pack. Stalemate the north and south and use your stack to root out the commanders.
You'll need this technique for other levels too like the remade Europe (which you've already beat) or Caesar's Challenge

While I agree that in any level where the AIs have a Commander, your easiest win is to track them down and kill them (although I have made the suggestion to Fizzer to add some code for the AIs to actually defend their commanders, and I believe it is now implemented), in this level it's definitely possible to win on good play alone.
Just be aware that the AI will make a lot of 'blind' attacks and play largely defensive at your borders unless you know exactly what's going on. Let them fight each other and expand when and where you can.
I believe that on my play-through I first took the island and then found the Southern Commander. Heading into the middle of the crescent proved challenging, so I eventually spread North as well. By then I outproduced the two remaining AIs so badly that it wasn't a challenge.

Regarding AI defending their commanders, they definitely do defend themselves. The other day I thought I had Caesar's Challenge Parthian AI beaten... had 50 stacks to take out the commander and his two possible escape routes. He dropped 100 on his commander, squashed that attack and my commander bit it the next turn.