"Aces in all cases. In Double Double Bonus, if the player gets a full house on the deal, he should always toss the other pair and go for the fourth ace and maybe a kicker."  --guru

The complete Double, Double Bonus Poker Solutions includes the following content:

• A set of strategies for the 9-5 and 7-5 payout tables.
  
  
• Tips for Double Double Bonus on triple play, multi-hand, and coinless machines.
  
  

• A sensible discussion for dealing with 75% of the hands where the casino has an edge.

• A pocketsize version to easily remember the strategies
  
  

• An introduction to the random number generator and the card selection process

...but what should the player do with this hand?

The answer is in the payout tables and the mathematical expectations, which explain the net gain for a full house versus the chance for the four deuces.
     On a 9-5 payout, the full house pays 45 coins. The net gain is 45-5 coins wagered or 40 coins (8:1). The three deuces have a mathematical expected value of 6.536, which is less than the full house. In this case the best choice is to keep the full house.
      On a 7-5 payout, the full house pays only 35 coins. The net gain is 35 -5 coins wagered or 30 coins (6:1). The three deuces also has a lower mathematical expectation of 6.413. The comparison of 6.0 or 6.413 is close enough to give up the full house and go for the fourth deuce with maybe a kicker. Even if the fourth deuce does not appear, the player will still get 15 coins for the three of a kind. So the loss from keeping the full house is 20 coins.
      On Triple Play or multiple hand machines, it would be best to go for the deuces because you have additional opportunities to hit the jackpot.

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