It seems like a possible optimal strategy would be:

• If an entire color scheme can be eliminated with the next flood choice, choose that color

• Else: select the color that increases the surface area between the current $\left( f_n \right )$ and next step $\left( f_{n+1} \right)$

In this case, surface area would be defined in a more practical sense than just the unit length of the total edges of the flood. It would be a count of the total number of blocks touching the flood, which prevents double counting and ignores the edges of the playing board.

This is different from the greedy algorithm in that counting the touching blocks maximizes only the increase in the flood's size this turn, whereas the surface area I defined would increase the flood's ability to grow in subsequent turns, optimizing growth throughout the game.

This method will not always be optimum, also. There are cases where sacrificing turns for a more strategic and rewarding flood in the future would be optimum. If we ran thousands of simulations to compare the a) average time of computation and b) number of turns until success for i) this simple algorithm and ii) a machine learning model or backtracking model, we could compare the tradeoff between the two. I think that if the board's starting points are generated randomly, this quick algorithm would still work pretty well.

It seems like a possible optimal strategy would be:

• If an entire color scheme can be eliminated with the next flood choice, choose that color

• Else: select the color that increases the surface area/border length between the current $\left( f_n \right )$ and next step $\left( f_{n+1} \right)$

In this case, surface area would be defined in a more practical sense than just the unit length of the total edges of the flood. It would be a count of the total number of blocks touching the flood, which prevents double counting and ignores the edges of the playing board.

This is different from the greedy algorithm in that counting the touching blocks maximizes only the increase in the flood's size this turn, whereas the surface area I defined would increase the flood's ability to grow in subsequent turns, optimizing growth throughout the game.

This method will not always be optimum, also. There are cases where sacrificing turns for a more strategic and rewarding flood in the future would be optimum. If we ran thousands of simulations to compare the a) average time of computation and b) number of turns until success for i) this simple algorithm and ii) a machine learning model or backtracking model, we could compare the tradeoff between the two. I think that if the board's starting points are generated randomly, this quick algorithm would still work pretty well.

It seems like a possible optimal strategy would be:

• If an entire color scheme can be eliminated with the next flood choice, choose that color

• Else: select the color that increases the surface area between the current $\left( f_n \right )$ and next step $\left( f_{n+1} \right)$

In this case, surface area would be defined in a more practical sense than just the unit length of the total edges of the flood. It would be a count of the total number of blocks touching the flood, which prevents double counting and ignores the edges of the playing board.

This is different from the greedy algorithm in that counting the touching blocks maximizes only the increase in the flood's size this turn, whereas the surface area I defined would increase the flood's ability to grow in subsequent next turns, optimizing growth throughout the game.

This method will not always be optimum, also. There are cases where sacrificing turns for a more strategic and rewarding flood in the future would be optimum. If we ran thousands of simulations to compare the a) average time of computation and b) number of turns until success for i) this simple algorithm and ii) a machine learning model or backtracking model, we could compare the tradeoff between the two. I think that if the board's starting points are generated randomly, this quick algorithm would still work pretty well.

It seems like a possible optimal strategy would be:

• If an entire color scheme can be eliminated with the next flood choice, choose that color

• Else: select the color that increases the surface area between the current $\left( f_n \right )$ and next step $\left( f_{n+1} \right)$

In this case, surface area would be defined in a more practical sense than just the unit length of the total edges of the flood. It would be a count of the total number of blocks touching the flood, which prevents double counting and ignores the edges of the playing board.

This is different from the greedy algorithm in that counting the touching blocks maximizes only the increase in the flood's size this turn, whereas the surface area I defined would increase the flood's ability to grow in subsequent turns, optimizing growth throughout the game.

This method will not always be optimum, also. There are cases where sacrificing turns for a more strategic and rewarding flood in the future would be optimum. If we ran thousands of simulations to compare the a) average time of computation and b) number of turns until success for i) this simple algorithm and ii) a machine learning model or backtracking model, we could compare the tradeoff between the two. I think that if the board's starting points are generated randomly, this quick algorithm would still work pretty well.