Let's name the files from A to E and the rows from 1 to 5.
Each player will either go through the board and bring victory, or reveal the position of exactly one squid by their generous sacrifice.
Player 1 can try the path a3-b3-c3-d3-e3.
- If they go through, hurray!
- If they die on e3, they have revealed a safe path until d3: player 2
will try to exploit this by going a3-b3-c3-d3-d2-e2.
- If they die on d3, they have revealed a safe path until c3: player 2
will try to exploit this by going a3-b3-c3-c2-d2-e2.
- If they die on c3, they have revealed a safe path until b3: player 2
will try to exploit this by going a3-b3-b2-c2-d2-e2.
- If they die on b3, they have only revealed one useless safe square a3, from where one can only try to go to a2 or a4, squares already accessible from the starting point. Player 2 should goind through either the row 2 or the row 4.
- If they die on a3, it's just the same.
We can continue the strategy: if a safe path has been opened until the B-file at least, exploit it with the remaining options that avoid known squids. Otherwise, try to open a path on a new row.
Calculating exact probabilities might be boresome, but I think I will revert to computer simulation when I can find some time...