I checked programs of top 5 for two cases:
1 3
...
1 4
....
Those program give out following result:
Case #1: 4
Case #2: 4

But, I did not find four opening moves for those cases.
For Case #1 I found TWO opening moves with which Becca will win:
1. 0 1 H -> Terry do not have an empty cell
2. 0 1 V -> Terry should select: 0 0 or 0 2 -> Becca: other variant ->
Terry do not have an empty cell
other moves are losing for Becca:
1. 0 0 H -> Terry: 0 2 H -> Becca do not have an empty cell
2. 0 2 H -> Terry: 0 0 H -> Becca do not have an empty cell
3. 0 0 V -> Terry: 0 1 H or 0 2 H -> Becca do not have an empty cell
4. 0 2 V -> Terry: 0 0 H or 0 1 H -> Becca do not have an empty cell

For Case #2 I found TWO opening moves with which Becca will win:
1. 0 1 V
2. 0 2 V
other moves are losing for Becca:
1. 0 0 V -> Terry: 0 2 H -> Becca do not have an empty cell
2. 0 3 V -> Terry: 0 1 H -> Becca do not have an empty cell
3. 0 0 H -> Terry: 0 2 H or 0 3 H -> Becca do not have an empty cell
4. 0 1 H -> Terry: 0 3 H -> Becca do not have an empty cell
5. 0 2 H -> Terry: 0 0 H -> Becca do not have an empty cell
6. 0 3 H -> Terry: 0 0 H or 0 1 H -> Becca do not have an empty cell

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