Okay first of all it's a great concept it's literally an AI fighting simulator awesome idea.
The alpha looks great as well, even though the videos aren't generating right now the example video shows promise and that's what I'm counting on. The strategy option is a great addition as well though it doesn't seem like it actually changes anything as of now because of the limited cards available at the start.
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Now for suggestions, I just have one big suggestion and it's somewhat different than what the team is currently going for but either way.
I'd like to see the matches run live somehow, for example in a temporary website. And why I want that is so that we could give prompts to our character mid fight. It wouldn't be possible with the current 20 HPs of course it would be ridiculous, but think of it like this: Two characters with maybe 50,000 HP and they fight normally BUT the users have a small text box where you can give them commands about the way they fight and change it mid game depending on how the match is going. It would give us more control over our character as compared to the current strategy option.
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Even if this suggestion isn't actually implemented, the game seems great as of now too I'll happily play this version as well.