In this position, Beta would like to begin to deploy their Doomsday machine to destroy Alpha's blue star in two turns and their yellow star in three. However, the machine is incomplete. What's missing?
What does it take for a three-turn Doomsday phase to succeed?
Suppose that Beta follows the 2-turn blue, 3-turn yellow Doomsday script and that Alpha responds passively (rather than using their large- and yellow-ship advantages to create threats that Beta must respond to).
Beta demolishes Alpha's blue star and moves a y1 and than a y3 to Alpha, Beta has created a catastrophe threat but not a direct assault threat. Beta does not have enough red or green power. Alpha doesn't need to worry about Beta taking over all of their home ships (or building into an overpopulation), so Alpha can freely counterattack:
Beta can't capture Alpha's home ships quickly enough, and Alpha's counterattack will win. Beta might have won if they had given themselves enough firepower to quickly end the game with captures if Alpha tries the counterattack above. For example, Beta could play:
Even with this improved move, Alpha has so much material that I believe they should win by ignoring the ships moving into their home and launching a counterattack.
This position is from a casual game on SDG.