EX-AP is incorrect, and this decision is not particularly close.
First thing you do is you plug in your 7/5 paytable into here:
https://wizardofodds.com/games/video...hand-analyzer/
Which returns a value of:
Hold Three Aces: 12.592969
Keep Full House: 7.00000000
Now, there is the matter of the 3x multipliers on the current hands, so I'm going to do this on a one-hand basis because it's all the same thing:
12.592969 * 3 = 37.778907
7.00000 * 3 = 21.00000000
We also know that the game returns .960969 * 11 = 10.570659 Added Value (per hand) to the next hand.
That brings the final value of keeping the Full House to 31.570659 (half units per hand).
Keeping the three Aces is automatically better. It's already better, even ignoring the following factors:
---Each Three-of-a-Kind final hand receives a 4x multiplier.
---A full house final hand receives a 12x multiplier, which just requires drawing two of the same cards.
---Any Quads get a 2x multiplier.
EX-AP is likely correct if there are no multipliers on the current hand. I think his OP doesn't fully appreciate the effects of the amount won on the current hand being multiplied.