python3.6 code.py -f boards/board-1-1.txt
....................
....................
.........######.....
........OOOO..#..O..
........O######..O..
........OOOOOOOOOO..
....................
score: 16 closed: 41 open: 29
python3.6 code.py -f boards/board-1-2.txt
....OOO#............
...OO#O#............
..OO#OO#............
OOO#.O#....OOOOOOOOO
....#OO#..OO#.......
.....#OO#OO#........
......#OOO#.........
score: 33 closed: 62 open: 18
python3.6 code.py -f boards/board-1-3.txt
.........OOOOOOOOOOO
.........O#........O
.......##OO#.......O
......#OO#O#.......O
......#O#OO#.......O
......#OOO#........O
.......###.........O
score: 28 closed: 73 open: 4
python3.6 code.py -f boards/board-1-4.txt
OO#.......#......#..
#O#.#####.#.####.#..
OO#OOOOO#.#....#....
O##O###O######.#####
OO#OO#OO#....#...#..
#O####O##.##.#.#.##.
.OOOOOO....#...#....
score: 26 closed: 35 open: 2
python3.6 code.py -f boards/board-2-1.txt
mmmmmffffrrrrrrrrOrrrrrrrrrrrrrrfffmmmmm
mmmffffffffrrrrrrOOOOOOOOOOOOOrfffffmmmm
mmfffffffffffffffffffffffffffOffffffmmmm
mmfffffffffffffwwwwwfffffffffOfffffffmmm
mfffffffffffffwwwwwwwffffffffOffffffmmmm
mmffffffffffffwwwwwwwffOOOOOOOrrrrrrmmmm
mmmffffffffffffwwwwwfffOffffffffrffffmmm
mmfffffffffffffffffffffOffffffffrfffffmm
mmffffffffgggggggggggggOggggggggggffffmm
mmmffffggggggggggOOOOOOOggggggggggggffmm
score: 79 closed: 243 open: 40
python3.6 code.py -f boards/board-2-2.txt
ffffffffffgggrgggggggrggggfffffffrrfffff
ffOffffffgggrrggggggrrggffffffffrrffffff
ffOfffgggggrrggggggrrgggffffrrrrrfffffff
ggOOOOgggggrggggrrrrgggffffrrfffffffffff
gggggOOOOOOOrrrrrgggggffffrrffffffffffff
ggggrrgggggOggggggggffffffrfffffffffffff
gggrrggggggOOggggggffffOOOOOOfffffffffff
ggrrgggffgggOOOOggffOOOOfrffOrrrrfffffff
ggrggffffffffffOOOOOOffffrffOfffrrffffff
ggrgfffffffffffffffffffffrffOffffrrfffff
score: 72 closed: 213 open: 62
python3.6 code.py -f boards/board-2-3.txt
gggggggggwwwgggggmmmmmmmmmmOOOOOOOOmmmmm
gggggggggwwwwggggmmmmmmmmmmmmmmmmmOmgggg
ggggggggggwwwwggggmmmmmmmmmmmmmmggOggggg
ffgggggggggwwwwggggmmmOOOOmmOOOOOOOrgggg
ffggggggggggwwwwwwwwwwOwwOOOOggggggrrrrr
ffffggggggggggwwwwwwwwOwwwwggggggggggggg
ffffffOOOOOOOOOOOOOOOOOwwwwwwggggggmmmmm
fOOOOOOffffgggggggggmmmmmmwwwwmmmmmmmmmm
fffffffffffffffmmmmmmmmmmmmmwwwmmmmmmmmm
ffffffffffmmmmmmmmmmmmmmmmmmwwwmmmmmmmmm
score: 596 closed: 304 open: 32
python3.6 code.py -f boards/board-2-4.txt
wwwwwggggggggggggggggggggggOOOOOOOgrrrrr
wwwwwwwggggggggggggggOOOOOOOwwwwwOOrgggg
wwwwwwwwwwwgggOOOOOOOOwwwwwwwwwwwwOwgggg
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOwwwww
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOwwwww
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOOwwwww
wwwwwwwwgggggOgggggwwwwwwwwwwwwwwOwwwwww
wwwwggggggfffOffgggggggggwwwwwwwwOwwwwww
wwggggfffffffOffffffggggggggggggOOgwwwww
wgggfffrrrrrrOOOOOOOOOOOOOOOOOOOOggggggg
score: 161 closed: 173 open: 72
python3.6 code.py -f boards/board-1-4.txt -v -a "A*"
OO#.......#......#..
#O#*#####.#.####.#..
OO#OOOOO#.#....#....
O##O###O######.#####
OO#OO#OO#xx*.#...#..
#O####O##x##.#.#.##.
xOOOOOOxxxx#...#....
score: 26 closed: 35 open: 2
python3.6 code.py -f boards/board-1-4.txt -v -a Djikstra
OO#x*.....#......#..
#O#x#####.#.####.#..
OO#OOOOO#.#....#....
O##O###O######.#####
OO#OO#OO#xxxx#...#..
#O####O##x##x#*#.##.
xOOOOOOxxxx#xxx#....
score: 26 closed: 43 open: 2
python3.6 code.py -f boards/board-1-4.txt -v -a BFS
OO#x*.....#......#..
#O#x#####.#.####.#..
OO#OOOOO#.#....#....
O##O###O######.#####
OO#OO#OO#xxxx#...#..
#O####O##x##x#*#.##.
xOOOOOOxxxx#xxx#....
score: 26 closed: 43 open: 2
python3.6 code.py -f boards/board-2-4.txt -v -a "A*"
wwww*xxxxxxxxxxxxxxxxxxxxxxOOOOOOOxxxxxx
wwwww*xxxxxxxxxxxxxxxOOOOOOO*****OOxxxxx
wwwwww*xxxxxxxOOOOOOOOx*****wwwww*O*xxxx
wwwwwww****xxxxxxxxxxx*wwwwwwwwww*O*****
wwwwwwwwwww***********wwwwwwwwwww*O*wwww
wwwwwwwwwwwwwwww***wwwwwwwwwwwww*OO*wwww
wwwwwwwwgggggO**xxx******wwwwwww*O*wwwww
wwwwggggg****Oxxxxxxxxxxx********O*wwwww
wwggggf**xxxxOxxxxxxxxxxxxxxxxxxOOx*wwww
wgggff*xxxxxxOOOOOOOOOOOOOOOOOOOOxxx*ggg
score: 161 closed: 173 open: 72
python3.6 code.py -f boards/board-2-4.txt -v -a Djikstra
www*xxxxxxxxxxxxxxxxxxxxxxxOOOOOOOOxxxxx
wwww*xxxxxxxxxxxxxxxxOOOOOOO*****xOxxxxx
wwwww**xxxxxxxOOOOOOOOxxxx**wwwww*O*xxxx
wwwwwww****xxxxxxxxxxx****wwwwwww*O*****
wwwwwwwwwww***********wwwwwwwwwww*O*wwww
wwwwwwwwwwwwwwww***wwwwwwwwwwwww*OO*wwww
wwwwwww***gg*O**xxx******wwwwwww*O*wwwww
wwwwgg*xxx**xOxxxxxxxxxxx********O*wwwww
wwgggg*xxxxxxOxxxxxxxxxxxxxxxxxxOOx*****
wgggf*xxxxxxxOOOOOOOOOOOOOOOOOOOOxxxxxxx
score: 161 closed: 189 open: 78
python3.6 code.py -f boards/board-2-4.txt -v -a BFS
wwwwwgggggg*xxxxxx*ggggggggggggggggrrrrr
wwwwwwwggg*xxxxxxxx*ggggggggwwwwwgrrgggg
wwwwwwwww*xxxxOxxxxx*gwwwwwwwwwwwwrwgggg
wwwwwwwwww*xxxOxxxx*wwwwwwwwwwwwwwrwwwww
wwwwwwwwwww*xxOxxx*wwwwwwwwwwwwwwwrwwwww
wwwwwwwwwwww*xOxx*wwwwwwwwwwwwwwwrrwwwww
wwwwwwwwgggggOOx*ggwwwwwwwwwwwwwwrwwwwww
wwwwggggggfff*x*gggggggggwwwwwwwwrwwwwww
wwggggffffffff*fffffggggggggggggrrgwwwww
wgggfffrrrrrrrrrrrrrrrrrrrrrrrrrrggggggg
score: 306 closed: 46 open: 16
The biggest difference is the BFS because it has similar stats to Djikstra in the first, but are a lot worse on the last map. They are based on the same prinsiple but BFS doesn't use the cost of terrain when analyzing the path. This results in fewer nodes opened and closed, but worse score.
A* is superior in all aspects over djiksta and bfs because it has superior prioritizing. A* is the only algorithm using the information about the goals position. Nodes closer to the goal have probably a shorter path to the goal and therefor has higher priority. It will go more straight to the goal than the other algorithms while maintaining a minimum score and will therefor have a lower amount of open and closed nodes. The maintaining of minimum score is only if it assumes best case prediction, if it predicts a cost bigger than it really is it might not return the best possible score.
The advantage/disadvantage over djikstra is based on how good the prediction is (the function h). When it uses that each step has 1 it wins over djikstra by a bit on every attempt. When it uses that each step forward has avg of previous it wins by more on 2-4, but 1-4 is a bit worse (still better than Djikstra). The higher cost it predicts the faster and more risky it gets. If it assumes each field costs 100 it stright crosses the river and get's a score of 306.